River Rapids Conference Proceedings of the Society for Experimental Mechanics Series Special Topics in Structural Dynamics & Experimental Techniques, Volume 5 Matt Allen Sheyda Davaria R. Benjamin Davis Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics 2022 River Publishers
Conference Proceedings of the Society for Experimental Mechanics Series Series Editor Kristin B. Zimmerman Society for Experimental Mechanics, Inc., Bethel, CT, USA
The Conference Proceedings of the Society for Experimental Mechanics Series presents early findings and case studies from a wide range of fundamental and applied work across the broad range of fields that comprise Experimental Mechanics. Series volumes follow the principle tracks or focus topics featured in each of the Society’s two annual conferences: IMAC, A Conference and Exposition on Structural Dynamics, and the Society’s Annual Conference & Exposition and will address critical areas of interest to researchers and design engineers working in all areas of Structural Dynamics, Solid Mechanics and Materials Research.
River Publishers Special Topics in Structural Dynamics & Experimental Techniques, Volume 5 Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics 2022 Matt Allen • Sheyda Davaria • R. Benjamin Davis Editors
Published, sold and distributed by: River Publishers Broagervej 10 9260 Gistrup Denmark www.riverpublishers.com ISBN 978-87-4380-028-6 (eBook) Conference Proceedings of the Society for Experimental Mechanics An imprint of River Publishers © The Society for Experimental Mechanics, Inc. 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, or reproduction in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Preface: SEM 2022 IMAC XL – Volume 5 Special Topics in Structural Dynamics & Experimental Techniques represents one of nine volumes of technical papers presented at the 40th IMAC, a conference and exposition on structural dynamics, organized by the Society for Experimental Mechanics, and held February 7–10, 2022. The full proceedings also include volumes on nonlinear structures and systems; dynamics of civil structures; model validation and uncertainty quantification; dynamic substructures; rotating machinery, optical methods, and scanning LDV methods; sensors and instrumentation, aircraft/aerospace, and dynamic environments testing; topics in modal analysis and parameter identification; and data science in engineering. Each collection presents early findings from experimental and computational investigations on an important area within structural dynamics. Special Topics in Structural Dynamics & Experimental Techniques represents papers highlighting new advances and enabling technologies for experimental techniques, finite element techniques, system identification, and additive manufacturing. The organizers would like to thank the authors, presenters, session organizers, and session chairs for their participation in this track. Provo, UT, US Matthew Allen Blacksburg, VA, USA Sheyda Davaria Athens, GA, USA R. Benjamin Davis v
Contents 1 Multi-Cellular Damping for Composite Material Applications .......................................... 1 Beckett Andersen, Luke Hardy, Matthew Borrowman, and Matthew Snyder 2 Novel Data Acquisition Utilising a Flask Python Digital Twin Operational Platform................. 7 Ruiyang Wang and Matthew S. Bonney 3 Model Validation for Combined Inertial Acceleration and Vibration Environments.................. 15 Moheimin Khan, David M. Siler, Garrett K. Lopp, and Brian C. Owens 4 Modal Testing with Piezoelectric Stack Actuators......................................................... 35 Garrett K. Lopp, David M. Siler, Moheimin Khan, and Brian C. Owens 5 Generative Adversarial Networks for Labelled Vibration Data Generation ........................... 41 Furkan Luleci, F. Necati Catbas, and Onur Avci 6 Validation of an Impulse Response Filter for Impact Force Reconstruction on a Hammer Drill .... 51 Luis M. Zapata, Wim Desmet, and Frank Naets 7 Determination of Nonlinear Joint Forces and Nonlinear Identification of Jointed Connections UsingFRFs ..................................................................................................... 57 Hossein Soleimani, Ender Cigeroglu, and H. Nevzat Özgüven 8 Investigation of Using Log-Spectrum Averaging (Cepstral Averaging) for Blind Reconstruction of an Unknown Impact Input Force ...................................................... 63 Sa’ed Alajlouni, Vijaya V. N. Sriram Malladi, and Murat Ambarkutuk 9 The Application of a Force Identification Method Based on Particle Swarm Optimization to Compression Steel Bars.................................................................................... 69 Stefan Dudenhausen, Markus Waltering, and Wolfgang Kurz 10 Degree of Freedom Selection Approaches for MIMO Vibration Test Design........................... 81 Christopher Beale, Ryan Schultz, Chandler Smith, and Timothy Walsh 11 Vibration Mitigation of Bladed Structures Using Piezoelectric Digital Vibration Absorbers ........ 91 J. Dietrich, G. Raze, A. Paknejad, A. Deraemaeker, C. Collette, and G. Kerschen 12 An Open-Source Automatic Modal Hammer Suitable for Studying Nonlinear Dynamical Systems ......................................................................................................... 95 Aryan Singh and Keegan J. Moore 13 Crack Diagnosis and Prognosis of Miter Gates Based on a Global-Local Model and Image Observations ................................................................................................... 99 Zihan Wu, Travis B. Fillmore, Manuel A. Vega, Zhen Hu, and Michael D. Todd 14 A Hierarchical Filtering Approach for Online Damage Detection Using Parametric Reduced-Order Models ....................................................................................... 103 Konstantinos E. Tatsis, Konstantinos Agathos, Vasilis K. Dertimanis, and Eleni N. Chatzi vii
viii Contents 15 A Tutorial on an Open-Source Python Package for Frequency-Based Substructuring and Transfer Path Analysis........................................................................................ 107 Ahmed El Mahmoudi, Miha Kodricˇ, Domen Ocepek, Francesco Trainotti, Miha Pogacˇar, Tomaž Bregar, Gregor Cˇ epon, Miha Boltežar, and Daniel J. Rixen 16 Miniature Underwater Robot – An Experimental Case Study........................................... 119 Sheyda Davaria, Manu Krishnan, Vijaya V. N. Sriram Malladi, and Pablo A. Tarazaga 17 Benefits of Using a Portable Coordinate Measurement Machine to Measure a Modal Test Geometry ....................................................................................................... 123 Steven Carter
Chapter 1 Multi-Cellular Damping for Composite Material Applications Beckett Andersen, Luke Hardy, Matthew Borrowman, and Matthew Snyder Abstract Future lightweight aircraft will increasingly rely on advances in lightweight, strong, highly damped, multifunctional composites. Increased damping capacity of these materials will grow in demand to ensure safe operations across adverse dynamic conditions. Traditional composite materials cannot provide this capability primarily due to a mismatch in the strength and stiffness between the fibers and hosting matrix. The purpose of this project is to design, fabricate, and test a damping material conceived as a cellular system, incorporating a periodic arrangement of tunable, non-linear, spider web-like absorbers. This novel approach proposes to produce a cellular material system incorporating an array of vibration absorbers to damp out structural-scale vibrations at the micro-scale level. The benefits include enhanced damping capacity with no weight penalty and tunability to maximize the kinetic energy transfer as required for the structure of interest. For this project, the USAFA team partnered with a team of researchers in Rome, Italy to create a macro-scale variant of a proposed carbon nanotube absorber system as a proof of concept. The team modeled, tuned, printed, and tested a structural-scale printed model of the repeating cellular system and showed an increase in damping ratio based on the tuned properties of the resonating structure. Keywords Multifunctional · Honeycomb · Damping · Additive manufacturing · Modal testing 1.1 Introduction Reinforced fiber composite materials offer several advantages to traditional isotropic materials particularly for applications requiring high, or tailored, strength properties and low weight. However, mechanical resonance can shorten the life of a composite as these vibrations may exacerbate existing damage in the matrix leading to failure. Multifunctional composites represent a class of composite materials that may provide structural composited with enhanced properties [1]. One particular area of focus has been metamaterials with higher damping ratios [2]. In addition, carbon nanotube (CNT) composites have shown promise in providing a way to increase the strength of the composite while allowing energy to dissipate [3]. A proposed way of increasing the life of composite, is to produce a cellular material system incorporating an array of vibration absorbers which damp out structural-scale vibrations at the micro-scale level. Figure 1.1 [4] shows the proposed structure. In this case, electro-spun CNT wires connect the walls of a repeated cellular structure to a central absorber mass. The mass, wires and cellular structure are all tuned to produce a resonant response on par, but out-of-phase, with the global modes of the plate-like structure. This results in a decreased structural response. The following paper describes the design and evaluation of a macro-scale variant, produced as a proof of concept. In this case, the team additively manufactured a tuned, repeated honeycomb cellular structure with small cantilever beams protruding from one wall of each cell. The dimensions of the cellular structure, cantilever beam, and tip mass applied to the beam were optimized to move the cantilever beam fundamental frequency close to the first global mode of the plate-like structure. By the time of presentation, the response Distribution Statement A: Approved for public release: distribution unlimited. Disclaimer: The views expressed in this article are those of the author and do not necessarily reflect the official policy or position of the United States Air Force Academy, the Air Force, the Department of Defense, or the U.S. Government. PA#: USAFA-DF-2021-337. B. Andersen · L. Hardy · M. Borrowman · M. Snyder ( ) Department of Mechanical Engineering, United States Air Force Academy, Air Force Academy, CO, USA e-mail: matthew.snyder@usafa.edu © The Society for Experimental Mechanics, Inc. 2023 M. Allen et al. (eds.), Special Topics in Structural Dynamics & Experimental Techniques, Volume 5, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-031-05405-1_1 1
2 B. Andersen et al. Fig. 1.1 Cellular metamaterial with spider web-like absorbers Mode 1 82.637 Mode 2 113.71 In collaboration with Dr. Matt Snyder, Department of Mechanical Engineering, USAFA Mode 3 163.91 Mode 4 187.88 Mode 5 200.28 Mode 6 204.71 Mode 7 First frequency (215Hz) Cantilever with tip mass 209.89 Mode 8 214.52 Mode 9 214.58 Fig. 1.2 Macro-scale honeycomb structure with cantilevered beam resonators of the beams to excitation will be captured using both a laser vibrometer and small accelerometers and the damping ratio calculated. These results will be discussed in the presentation. 1.2 Background To prove the spider web-like damping concept, the authors created a macro-scale variant of the structure, Fig. 1.2. The addition of a matrix embedded cellular honeycomb structure with resonating beams may provide a method to maintain the strength of the composite while providing enhanced damping capability [5]. The unit cell design includes a repeating hexagonal cellular structure, honeycomb, with a cantilever beam protruding from a cell wall to the center of the unit. A tailorable point mass is fixed to the end of the beam to tune the dynamic response of the structure. 1.3 Analysis This particular study involved design, analysis and testing of the hexagonal cellular structure where each cell was sized at 1 inch. Initial analysis included modeling of the resonator to determine ideal geometric and material properties modeling a single unit cell. The first test results were different from the predicted values. The team reasoned that the results were different because the bulk material properties were different from the post printed material properties. To find the corrected material properties, dog bone testing was completed along a wide range of infill percentages. The team decided that the
1 Multi-Cellular Damping for Composite Material Applications 3 Fig. 1.3 Honeycomb structure with cantilever resonator Table 1.1 Initial testing model response data Test number 1 2 3 4 Average Std dev Peak 1 (Hz) 121 121 121 121 121 0 Peak 2 (Hz) 234 235 234 234 234 0.34 0.001 0.0009 0.0008 0.0007 0.0006 0.0005 Magnitude (m/s) 0.0004 0.0003 0.0002 0.0001 0 0 100 200 Frequency (Hz) Magnitude vs. Frequency 300 400 500 Fig. 1.4 Frequency response graph of the 6-inch cantilever beam material properties changed the least when the plastic was printed with an infill of 100%. The 3D printer that as used to print the models used ASA as the printing material. Based off of the bulk material properties, the predicted value for the first cantilever mode was 150 Hz. This single cell is shown in Fig. 1.3. After performing this computational investigation, the team additively manufactured the proposed concepts to test them using accelerometers and a laser vibrometer to characterize the response. The team clamped one edge of the unit cell and measured the response of an enlarged cantilever beam, measuring 1 ×.5 ×6 inches, due to excitation by an impact hammer. The first two frequencies are shown in Table 1.1 and Fig. 1.4 and show a typical response. The first natural frequency occurred at 121 Hz for all four tests. The second peak that coincides with the second natural frequency of the beam was determined to be 234 Hz. The fundamental frequency of the beam is given by Eq. (1.1). Using the bulk material properties, the team calculated the fundamental frequency to be 123 Hz. The difference between the two is accounted for in the variation of bulk to as-printed material properties and the team tuned the printed modulus of elasticity from 2.05 GPa to 2.0 GPa to match the experimental results. ω=3.51602 EI ρAl4 (1.1) With the corrected property values for the materials, testing was once again resumed on creating and predicting the response of an m × n unit cell matrix. The model was then extended to 8 × 10-unit cells matrix, each measuring 30 millimeters wide. For this analysis, the team used the FEA capabilities organic to Fusion 360. When the model without
4 B. Andersen et al. Fig. 1.5 Honeycomb structure with protruding cantilever beam cantilever beams was run in Fusion 360, the first modal frequency was predicted to be at 112 Hz with the second frequency predicted to be at 118 Hz. When the cantilever beams were added, the frequency changed to 132 Hz and 212 Hz, for the first and second modes, respectively. The authors then tuned the cantilevers to match the matrix frequencies. This then changed the first and second frequencies to be 185 Hz and 223 Hz. Figure 1.5 shows the honeycomb structure with protruding cantilever beams. The overall dimensions of the structure are 180 ×163 millimeters, the dimensions of the cantilever are .5 ×2 ×20 millimeters. Each cantilever beam has a tip mass with the dimensions of 1.5×2×2 millimeters. The team is in the process of manufacturing and testing the specimens (Fig. 1.6). The team is planning on testing both a specimen that has no cantilevers, which can be seen in Fig. 1.7, and a specimen with the cantilevers. This will show the difference in between a non-damped specimen and one with damping added to the system. The team will capture the response of both the “no cantilever” and “with cantilever” specimens to compare the experimental to predicted response. 1.4 Conclusion Multifunctional composites show much promise to give structural composites enhanced, tuned properties dependent on application. This study showed that the addition of a hexagonal walled matrix with cantilever beams protruding from the hexagonal walls in a composite matrix led to increasing the damping ratio of the composite which will lengthen the life of a composite. Results of the experimental validation of the computational model will be complete and presented at the conference. Acknowledgements The team would like to acknowledge the support of Prof. Walter Lacrabonara and Prof. Giulia Lanzara in assisting with modeling the honeycomb structure. In addition, Mr. Jeff Logsdon and Mr. Lonn Rodine, Applied Mechanics Laboratory, USAFA, were instrumental in assisting with the printing and testing of the structure.
1 Multi-Cellular Damping for Composite Material Applications 5 Fig. 1.6 Experimental test set up Fig. 1.7 8×10 honeycomb no cantilever matrix test article
6 B. Andersen et al. References 1. Zhanhu Guo, J., Song, K., Liu, C.: Polymer-Based Multifunctional Nanocomposites and Their Applications. Elsevier (2018) 2. Hussein, M., Frazier, M.: Metadamping: an emergent phenomenon in dissipative metamaterials. J. Sound Vib. 332, 4767–4774 (2012) 3. Lacarbonara, W., Lanzara, G.: Bridging high strength and dissipation in carbon nanotube composites. EOARD-AFOSR Grant No. FA9550-141-0082, 2014–2017 4. Lacarbonara, W., Lanzara, G., Snyder, M.: A high damping cellular material with integrated arrays of nanocomposite web-like vibration absorbers. American Society of Composites 36th Annual Technical Conference, 19–23 September 2021 5. Talo, M., Carboni, B., Formica, G., Lanzara, G., Snyder, M., Lacarbonara, W.: Nonlinear dynamic response and identification of nanocomposite cantilever beams. Nonlinear Dynamics Conference, Rome, Italy (2019)
Chapter 2 Novel Data Acquisition Utilising a Flask Python Digital Twin Operational Platform Ruiyang Wang and Matthew S. Bonney Abstract Remote live sensor supervisory control and scenario prediction are vital aspects for asset management of deployed industrial systems. Additionally, this information can be used to schedule regular repairs and give advance warning to potentially harmful operational conditions to allow for risk mitigation procedures to be activated. This project presents some novel work in human–computer interaction via the remote sensing of a deployed structure. To demonstrate this work, modifications to DTOP-Cristallo is performed to remotely sense the acceleration of a three-storey structure. The implementation of the platform includes coding of Python, Html and Flask. With web page-based interface, the users can modify data acquisition parameters and investigate the current state of the structure. This remote sensing was performed using DTOP-Cristallo and the benchtop model of the three-storey structure deployed at the University of Sheffield. Keywords Digital twin · Twin connectivity · Data acquisition · Python 2.1 Introduction Digital twin (DT) technology is a currently popular topic of research for bridging the industrial needs with academic interest [1–4]. These DTs are used for a wide variety of twins (systems, processes and networks) such as aircraft [5–7], manufacturing processes [8–10], additive manufactured systems [11, 12] and a wide variety of other systems. The ability to utilise DTs for a wide range of systems makes it an appealing topic for industrial collaboration. There are two main connectivity areas when discussing DTs, these are the connectivity between the physical twin (PT) and DT and between the DT and the user. However, the recent work in Digital Twin Operational Platform (DTOP) development has developed a third main area of connectivity, the connection between the PT and the user through the DTOP [3]. This studies the interaction between the user and data generated from the PT as well as direct interaction between the user and PT. To further the work performed in [3], which gives an example use for the connectivity between the user and data generated from experimental testing of the PT, this work is the initial study on connecting the PT and user through the developed DTOP. There are several types of connectivity between the user and PT via the DTOP. This work focuses on the collection of data given from sensors for further use in simulations, such as model updating. The other types of connectivity, control scheme updating for example, is currently planned for future work. 2.2 Digital Twin Operational Platform A DT is a virtual representation of a physical object. This kind of representation can be used for digital simulation and problem solving. In this project, DT is deployed for a three-story structure, aiming to accurately represent the dynamic characteristics of the structure. The DTOP introduces a methodology to connect the user to DT, PT and the data generated from both twins. This methodology is expressed as connecting three layers that are shown in Fig. 2.1. This work focuses on the interaction between the interface layer and the Internet-of-Things (IoT) layer. Sensors are attached on the physical twin and data are streamed through the network to the user and the data storage (within the cloud computing layer). The interface layer addresses how R.Wang ( ) · M. S. Bonney Dynamics Research Group, Department of Mechanical Engineering, University of Sheffield, Sheffield, UK © The Society for Experimental Mechanics, Inc. 2023 M. Allen et al. (eds.), Special Topics in Structural Dynamics & Experimental Techniques, Volume 5, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-031-05405-1_2 7
8 R. Wang and M. S. Bonney Digital twin operational platform Cloud computing layer Interface layer Internet-of-things layer data acquisition control NETWORK Server(s) User devices sensors actuator(s) Physical twin(s) cloud services datastorage HPC Fig. 2.1 Layers of connectivity for the digital twin operational platform the user interacts with the twins. This includes how the users investigate the data, provide parameters for simulations and on what devices they can access this information. This work established the connection between the PT and the user through the DTOP. Previous work [3] discusses the connection between the interface and cloud computing layers. 2.2.1 DTOP-Cristallo The DTOP provides users a browser-based interface for interacting with the DT, PT and scheduling numerical simulations. For monitoring the PT, the users are able to activate the data acquisition system for the collection of sensor data. Upon the collection of data, the DTOP displays the raw sensor data visually to the user. In addition to displaying the data, it is also able to be saved to a local Microsoft Excel spreadsheet for post-processing and storage. This capability for reading in the sensor data was rigorously verified against the manufacturer’s provided software and produces identical results. This is further discussed in Section 2.3.2. This platform makes it possible for engineers to monitoring the vibration of structure remotely.
2 Novel Data Acquisition Utilising a Flask Python Digital Twin Operational Platform 9 2.3 Experimental System 2.3.1 Setup Three accelerometers (353B18) are attached on each floor of the structure. In addition to the three accelerometers, an impact hammer (SNLW35743) is also used to excite the structure and record the impact force. All these four sensors are connected to a signal conditioner in series with the PicoScope DAQ system for signal enhancement. The PicoScope is connected to the computer by USB port for data transfer. This connection and the equipment used in this work are shown in Fig. 2.2. 2.3.2 Code The DTOP uses Python wrappers to control and read data from the DAQ system. To establish the connection between DTOP and the PicoScope, the SDK from the manufacturer’s website is deployed. Python wrappers ‘picosdk-python-wrappersmaster’ is a manufacturer-provided example Python wrappers for the C interface that was used as the template for this implementation. The PicoScope accepts some key command relating to Buffer Size, Number of Buffers and total samples. For the sake of convenience, Samplerate, Buffertime and Number of Buffers are set to be the user input given via the DTOP. These parameters are then transformed into the key commands mentioned previously through simple calculations. Samplerate is the rate of sample in Hz, and the SampleInterval is the inverse of the Samplerate, which determines the time between each data point. Buffer size is calculated as BS =Buffertime×Samplerate,whereBs is the size of the buffer, and it determines the total number of samples in each buffer. And the total number of samples is calculated as T otalSamples =Bs ×Nb, where Nb is the total number of buffers. The DAQ hardware has a native unit system of picoseconds, so all these intake parameter are converted from unit of s to ps. In order to verify that this novel connection between DTOP and PT sensors is accurate, this part of code is examined by comparing its output plots with the plots from PicoScope official software show in Figs. 2.3 and 2.4. On these graphs, the Fig. 2.2 Experimental setup
10 R. Wang and M. S. Bonney Fig. 2.3 Plots on PicoScope official software Fig. 2.4 Plots generated by DTOP scale of each axis is related when changing measuring parameters, and therefore, the customised user-inputted parameters are correctly transferred to the DAQ hardware. There are four channels active in this Python code. Channel A the hammer and Channel BCD for the accelerometers on each floor. By running this tool, the DTOP will gather data from the PicoScope, plot them by using ‘plotly’ command and record these dataset to a local Excel spreadsheet.
2 Novel Data Acquisition Utilising a Flask Python Digital Twin Operational Platform 11 Fig. 2.5 Web interface of the platform 2.4 Results This work resulted in a browser-based platform for collecting data from the PT. On this platform, the users can set customized parameters and get real-time data from the connected sensors. Figure 2.5 shows the interface of the web page. The variable adjustment is available in the section ‘Capturing Variable’. Capture Sample rate, Buffer Time and Number of Buffers can be customized in this section. After clicking the start button, the PicoScope will start to collecting data from sensors based on these parameters. After the data collection, this web page will be refreshed automatically and give back the Actual Sample Rate conducted on the PicoScope. At the same time, the acceleration data will be plotted in graphs in the section plots. There will also be a download button on the bottom of the web page for raw data downloading. This raw data is stored in a Microsoft Excel (.xlxs) file. Figure 2.6 shows the formatting of this Excel file. It lists all the acceleration data captured on each channel with reference to time. Capture parameters are also recorded for metadata purposes. This operational platform works well on the three-storey structure in the laboratory at the University of Sheffield. One advantage of this platform is the ability to access it in a remote sense. Python flask is able to be deployed in standalone, local network and general Internet instances. This allows the ability to gather sensor data remotely. The remote collection test was also conducted on the local area network. With the host of the DTOP being connected to the DAQ hardware, another computer successfully accessed the operational platform via the Internal network IP address. This means that this platform is capable of remote collection of data, should physical access to the PT be difficult. During testing, there appeared to be an error when downloading the data using the Google Chrome browser. The data file cannot be downloaded correctly. This may be caused by the Chrome cache profile, because this issue does not arise when using the Firefox browser. The current work is being performed to fully identify and fix this issue. 2.5 Conclusions Digital twin is the fundamental of this work. With accelerometers placed on the physical structure, the collections on the physical system are gathered accurately within the digital twin. Therefore, the connection between PT and DT is established in the fundamental work of this project. In this work, one complete digital twin system is developed, which has the capability of monitoring vibration state on the structure. With this digital twin system, further works are done on the connectivity between the user and PT. This work demonstrates a successful example of connecting the PT and user through the developed DTOP. In this platform, the users are allowed to set customized capturing parameters for connected sensors and get data directly from the browserbased interface. It successfully provided an implementation example for the third main area of connectivity, the connection between the PT and the user through the DTOP. In this platform, data captured in real-time are presented in figures via the HTML interface and available for local download for future use in simulations, such as model updating. Meanwhile, it is
12 R. Wang and M. S. Bonney Fig. 2.6 The downloaded Excel spreadsheet ready to be deployed on servers for remote assessment. This platform was tested and well-functioning on the three-storey structure deployed in the University of Sheffield. And other feature such as control scheme updating is planned for future work. References 1. Wagg, D.J., Worden, K., Barthorpe, R.J., Gardner, P.: Digital twins: state-of-the-art and future directions for modeling and simulation in engineering dynamics applications. ASCE-ASME J. Risk Uncert Eng. Syst. B Mech. Eng. 6(3), 030901 (2020) 2. Worden, K., Cross, E.J., Barthorpe, R.J., Wagg, D.J., Gardner, P.: On digital twins, mirrors, and virtualizations: frameworks for model verification and validation. ASCE-ASME J. Risk Uncertain Eng. Syst. B Mech. Eng. 6(3), 030902 (2020) 3. Bonney, M.S., Gardner, P., Wagg, D., Mills, R.: Case study of connectivity of digital twins and experimental systems. In: Proceedings of the 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Streamed from Athens, Greece, pp. 1416–1425 (2021) 4. Karve, P.M., Guo, Y., Kapusuzoglu, B., Mahadevan, S., Haile, M.A.: Digital twin approach for damage-tolerant mission planning under uncertainty. Eng. Fract. Mech. 225, 106766 (2020) 5. Li, C., Mahadevan, S., Ling, Y., Choze, S., Wang, L.: Dynamic Bayesian network for aircraft wing health monitoring digital twin. AIAA J. 55(3), 930–941 (2017) 6. Seshadri, B.R., Krishnamurthy, T.: Structural health management of damaged aircraft structures using digital twin concept. In: 25th AIAA/AHS Adaptive Structures Conference, pp. 1675 (2017)
2 Novel Data Acquisition Utilising a Flask Python Digital Twin Operational Platform 13 7. Tuegel, E.J., Ingraffea, A.R., Eason, T.G., Spottswood, S.M.: Reengineering aircraft structural life prediction using a digital twin. Int. J. Aerospace Eng. 2011, 154798 (2011) 8. Rosen, R., von Wichert, G., Lo, G., Bettenhausen, K.D.: About the importance of autonomy and digital twins for the future of manufacturing. IFAC-Papers OnLine 48(3), 567–572 (2015). 15th IFAC Symposium onInformation Control Problems in Manufacturing 9. Schleich, B., Anwer, N., Mathieu, L., Wartzack, S.: Shaping the digital twin for design and production engineering. CIRP Ann. 66(1), 141–144 (2017) 10. Tao, F., Cheng, J., Qi, Q., Zhang, M., Zhang, H., Sui, F.: Digital twin-driven product design, manufacturing and service with big data. Int. J. Adv. Manuf. Technol. 94(9–12), 3563–3576 (2018) 11. DebRoy, T., Zhang, W., Turner, J., Babu, S.S.: Building digital twins of 3d printing machines. Scripta Mater. 135, 119–124 (2017) 12. Knapp, G.L., Mukherjee, T., Zuback, J.S., Wei, H.L., Palmer, T.A., De, A., DebRoy, T.: Building blocks for a digital twin of additive manufacturing. Acta Mater. 135, 390–399 (2017)
Chapter 3 Model Validation for Combined Inertial Acceleration and Vibration Environments Moheimin Khan, David M. Siler, Garrett K. Lopp, and Brian C. Owens Abstract Aerospace structures are often subjected to combined inertial acceleration and vibration environments during operation. Traditional qualification approaches independently assess a system under inertial and vibration environments but are incapable of addressing couplings in system response under combined environments. Considering combined environments throughout the design and qualification of a system requires development of both analytical and experimental capabilities. Recent ground testing efforts have improved the ability to replicate flight conditions and aid qualification by incorporating combined centrifuge acceleration and vibration environments in a “vibrafuge” test. Modeling these loading conditions involves the coupling of multiple physical phenomena to accurately capture dynamic behavior. In this work, finite element analysis and model validation of a simple research structure was conducted using Sandia’s SIERRA analysis suite. Geometric preloading effects due to an applied inertial load were modeled using SIERRA coupled analysis capability, and structural dynamics analysis was performed to evaluate the updated structural response compared to responses under vibration environments alone. Results were validated with vibrafuge testing, using a test setup of amplified piezoelectric actuators on a centrifuge arm. Keywords Combined environments · Model validation · Coupled finite element analysis · Modal analysis · Piezoelectric actuators 3.1 Introduction Aerospace structures are often subjected to combined inertial acceleration and vibration environments during operation. To accurately evaluate the resulting effects on system and component dynamics, both the acceleration and vibration loadings must be considered simultaneously. This coupling of environments can result in two main impacts to structures: (1) altered contact state at an interface due to preload caused by inertial acceleration, and (2) material stiffening effects as a result of the preloaded stress state. This work focuses on the first case, with geometric changes due to the influence of preload on the contact state. A linear vibration analysis about the deformed preloaded state results in altered structural characteristics compared to the unloaded part, such as the natural frequencies, mode shapes, and dynamic response. It is important to be able to predict these effects using modeling and simulation to properly assess structures of interest. A typical aerospace structure can be subject to significant operational loads, which can include axial or lateral acceleration, random vibration, sine vibration, and shock [1]. Structural dynamic quantities of interest (QOI) include mode shapes & natural frequencies, displacements, accelerations, and stress, which are used to assess performance. Traditional qualification approaches independently evaluate these environments for each individual axis due to ease of testing and repeatability [2]. However, this approach neglects any combined effects, which can result in substantially different dynamic response. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. M. Khan ( ) · D. M. Siler · G. K. Lopp · B. C. Owens Sandia National Laboratories, Albuquerque, NM, USA e-mail: mkhan@sandia.gov © The Society for Experimental Mechanics, Inc. 2023 M. Allen et al. (eds.), Special Topics in Structural Dynamics & Experimental Techniques, Volume 5, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-031-05405-1_3 15
16 M. Khan et al. Assessing the QOI under concurrent acceleration and vibration environments is vital to accurately characterize the dynamics of the structure. To address the complexities of combined environments testing, Sandia National Laboratories has developed advanced capabilities such as the “vibrafuge,” which merges centrifuge inertial acceleration with mechanical vibration testing [1]. The vibrafuge approach uses amplified piezoelectric actuators (APAs) to apply controlled mechanical vibration while simultaneously applying centrifuge-induced inertial acceleration. Additional research has also been conducted to incorporate spin, creating an advanced “superfuge” testing capability. As these test methodologies mature, modeling and simulation has been developing in order to validate test results and improve predictive capability. In this work, model validation was performed for a research structure subjected to combined inertial acceleration and vibration environments. SIERRA coupled analysis was conducted by utilizing the handoff capability between SIERRA Solid Mechanics (SM) and SIERRA Structural Dynamics (SD) codes. SIERRA/SM is a finite element code that provides capabilities to solve nonlinear solid mechanics problems with large deformations and contact [3], while SIERRA/SD focuses on solving linear structural dynamics problems [4]. Coupling the two SIERRA codes involves preloading the cantilever beam structure using SIERRA/SM, updating and handing off the contact state, and evaluating the preloaded structural response using SIERRA/SD. Finite element (FE) model results were validated with vibrafuge testing using piezoelectric actuators on a centrifuge. Comparisons to test data showed that the SM to SD handoff model was able to account for the updated dynamic response due to the inertial acceleration preload. Trends were consistent with test data, although boundary conditions for the vibrafuge setup were only approximately represented, leading to discrepancies in some frequency bands. Validation metrics were also computed to quantify comparisons between the model and test data. This work demonstrates the development of an improved approach for combined mechanical environments analysis and model validation using SIERRA. 3.2 Unit Description 3.2.1 Design The research structure studied in this work consists of an inverted cantilever beam, which functions as a simple acceleration switch. The goal was to study the dynamics of the cantilever beam in a vibrafuge scenario since the tip contact state changes under applied inertial acceleration and vibration. Cedrat Technologies APA230L [5] amplified piezoelectric actuators (APA) were chosen to apply the vibration environments. This selection was made due to their optimal balance of high force output and large stroke – a requirement for adequate load restraint and effective excitation of the relevant frequencies. Figure 3.1 details the parts contained in the cantilever beam assembly. Each component in the assembly was designed and selected to meet project requirements and function within the capabilities of the APAs and centrifuge: Fig. 3.1 Cantilever beam assembly details with beam (1), tip mass (2), support block (3), base block (4), and actuators (5)
3 Model Validation for Combined Inertial Acceleration and Vibration Environments 17 Fig. 3.2 Centrifuge setup 1. Aluminum beam- sized large enough to fit accelerometers; contains notches for larger total deflection 2. Tungsten mass- chosen for its high density and to tune the first bending mode natural frequency; contacts support block under centrifuge acceleration 3. Aluminum support block- beam bolts directly into the side; 0.02-inch initial contact gap from mass, which is designed to close completely within 100 G of centrifuge-induced acceleration 4. Aluminum base block- supports the rest of the assembly and is readily available fixturing; one attachment point at each actuator 5. Piezoelectric actuator- Cedrat APA230L stainless steel frame with central piezoelectric stack; static deflection and dynamic properties are appropriate for size of cantilever beam assembly 3.2.2 Centrifuge Setup In the laboratory, combined inertial and vibration environments can be simulated using a “vibrafuge” setup, in which vibration is applied simultaneously with inertial loading generated by a centrifuge. To complete the vibrafuge configuration, the cantilever beam and APA assembly discussed in the previous section were placed on a centrifuge and additional fixturing (large aluminum reaction mass and angle bracket) was used to secure it to the centrifuge arm, as depicted in Fig. 3.2. Not included in the figure are a polyurethane rubber sheet (0.5-inch-thick, 30OO durometer) and rounds (5/16 thick, 40A durometer) used to isolate the centrifuge from the applied vibration stimulus. Here, the centrifugal acceleration causes the tip mass on the cantilever beam in the subassembly to close the initial gap and contact the support block structure. At the same time, the piezoelectric actuators apply dynamic loading to the base of the test article, allowing for testing with combined inertial and vibration environments. Once the vibrafuge setup was complete, initial experimental characterization was done in the form of linear modal and random vibration testing. A number of triaxial accelerometers were bonded to the reaction mass, piezoelectric actuator frames, and test subassembly hardware with instant adhesive. The transducer’s cabling was routed through the centrifuge’s slip rings to an external, combined vibration controller and data acquisition system. 3.3 Experimental Characterization Experimental characterization was conducted to evaluate the dynamics of the cantilever beam assembly and provide validation data for subsequent modeling and simulation activities. Linear modal testing was performed both on and off the centrifuge to ascertain the effects of the centrifuge fixturing on the subassembly dynamics. Additionally, vibrafuge testing was conducted by combining random vibration loading using the APAs with centrifuge acceleration at various G levels.
18 M. Khan et al. Fig. 3.3 Test instrumentation layout Fig. 3.4 Free-free modal and centrifuge test setup 3.3.1 Modal Testing Prior to modal testing, the test subassembly was instrumented with 18 triaxial accelerometers, although a total of 22 degrees of freedom (DOF) were measured due to channel count limitations. Figure 3.3 shows the accelerometer orientation and layout. Hammer testing was performed in the free-free configuration as well as on the centrifuge to determine the effects of the fixture boundary condition. Figure 3.4 shows the two modal testing setups and Fig. 3.5 provides a close-up of the beam instrumentation. Modes up to 2 kHz were obtained for each configuration and results for modes common to both tests are summarized in Table 3.1. Results are quite similar between the two tests, with low frequency errors and high MAC values, with only a
3 Model Validation for Combined Inertial Acceleration and Vibration Environments 19 Fig. 3.5 Close-up of beam tip with instrumentation Table 3.1 Free-free and centrifuge modal test results Testmode Free-free freq. (Hz) Centrifuge freq. (Hz) Freq. % difference MAC 1 3.94 16.59 321.48 0.9102 2 79.31 84.03 5.95 0.9743 3 209.32 211.89 1.23 0.9700 4 216.40 217.69 0.60 0.9619 5 220.85 222.54 0.77 0.9982 6 266.78 261.25 −2.08 0.9989 7 522.82 522.94 0.02 0.9931 8 541.33 541.83 0.09 0.9915 9 556.45 556.31 −0.02 0.9980 10 616.10 623.31 1.17 0.9984 11 765.66 766.63 0.13 0.9962 12 955.13 954.23 −0.09 0.9979 13 986.23 984.67 −0.16 0.9876 14 1014.49 1014.40 −0.01 0.7292 15 1021.59 1019.86 −0.17 0.7037 16 1050.26 1048.76 −0.14 0.9891 17 1784.08 1775.57 −0.48 0.9977 18 1816.19 1813.22 −0.16 0.9139 19 1855.25 1852.00 −0.18 0.9991 few exceptions. Modes 14 and 15 had a lower MAC mostly due to the low-quality fits obtained for the centrifuge data. In addition, damping was also observed to be much higher for many modes on the centrifuge, which is likely due to the rubber sheets between the fixture and centrifuge arm. In addition to the two modal tests presented here, the APAs were also used to extract modal parameters and results were compared to the initial modal tests. Table 3.2 compares selected bending modes for the cantilever beam extracted with each modal testing method. Here, the free-free and centrifuge results are from the hammer testing. Lopp et al. discusses details on the APA modal testing and parameter extraction in [6], so details are not covered here.
20 M. Khan et al. Table 3.2 Modal results comparison Test mode Description Free-free freq. (Hz) Free-free damp (%) Centrifuge freq. (Hz) Centrifuge damp. (%) APA5G freq. (Hz) APA 5G damp. (%) APA 100G freq. (Hz) APA 100G damp. (%) 1 1st beam vertical bending 79 0.4 84 2.0 75.3 2.4 – – 2 1st beam lateral bending 267 1.1 261 2.1 – – – – 3 2nd beam vertical bending 616 2.1 623 3.3 623 3.2 – – 4 3rd beam vertical bending 1784 1.1 1776 1.2 1788 1.4 1472.4 2.55
3 Model Validation for Combined Inertial Acceleration and Vibration Environments 21 Fig. 3.6 Selected measurements from 100 G vibrafuge run 3.3.2 Vibrafuge Testing Vibrafuge testing was conducted using a low-level random vibration input provided by the APAs combined with centrifuge inertial acceleration. Vibration levels of 1 GRMS (flat PSD profile from 50 Hz to 2 kHz) were applied alongside various acceleration levels ranging from 5 to 100 G. In addition to measuring the centrifuge levels and responses at the accelerometer locations outlined in Fig. 3.3, electrical contact between the beam tip and support block was measured to confirm contact status. Figure 3.6 shows an example of the type of measurements obtained during testing. 3.4 Finite Element Analysis As advanced vibrafuge test capabilities mature, modeling and simulation has also been developing to improve predictive capability. Once the experimental characterization for the cantilever beam assembly was complete, model validation was performed using finite element (FE) modeling. Both modal and random vibration data were utilized to calibrate and validate the model and assess vibrafuge analysis capabilities. An FE model of the cantilever beam subassembly on the reaction mass and angle bracket was created using the CUBIT meshing software [7]. Meshing was performed using quadratic 10-noded tetrahedral (TET10) elements. Accelerometers were explicitly modeled as cubes to account for the additional mass loading on the cantilever beam and remainder of the structure. In addition, the centrifuge arm was not modeled for simplicity. In the experiment, thick polyurethane rubber was placed between the angle bracket and centrifuge arm, so free-free boundary conditions were chosen instead of fixing the bottom surface of the angle bracket. Uniform modal damping values used in the simulation were obtained from test data for all available test modes and 2% otherwise. An image of the FE model is shown in Fig. 3.7. Model calibration and updating to linear modal test data was performed using the FE model, followed by a preloaded SIERRA/SM to SIERRA/SD coupled analysis, updated modal analysis, and random vibration analysis.
22 M. Khan et al. Fig. 3.7 Finite element model Table 3.3 Model calibration results Test 1 mode Description Test 1 freq. (Hz) Model 1b mode Model 1b freq. (Hz) Freq. error % MAC 2 1st beam bending (Z) 79 1 79 −1.0 0.998 3 Subassembly rocking (Y) 209 2 206 −1.7 0.984 4 Subassembly torsional 216 3 217 0.4 0.956 5 Subassembly torsional 221 4 221 0.2 0.967 6 1st beam bending (Y) 267 5 260 −2.4 0.993 7 Subassembly bending (Z) 523 6 514 −1.6 0.928 8 Subassembly bending (Y) 541 7 548 1.2 0.989 9 Subassembly axial 556 8 555 −0.2 0.898 10 2nd beam bending (Z) 616 9 642 4.3 0.997 14 Actuator mode 1014 19 1004 −1.0 0.988 17 3rd beam bending (Z) 1816 31 1759 −3.1 0.988 3.4.1 Modal Analysis Linear modal analysis was performed for the structure and model calibration was conducted with the free-free test data. Additionally, preloaded modal analysis was done to include the effects of the inertial acceleration. SIERRA/SM was used to apply the acceleration and preload the cantilever beam, followed by modal analysis with SIERRA/SD. Model Calibration First, SIERRA/SD was used to calibrate the model to the off-centrifuge free-free data listed in Table 3.1. The FE model was updated by making slight adjustments to the tip mass and beam material properties based on a preliminary analysis. The resulting calibrated mode shapes and frequencies for selected modes of interest are summarized in Table 3.3 and the MAC plot in Fig. 3.8. The full MAC plot with all test shapes is provided for reference in the Appendix Fig. 3.20. Results from the calibration were excellent, with frequency errors below 5% and MAC values above 0.9 for all modes of interest. The local cantilever beam modes are especially important since the centrifuge acceleration is expected to greatly influence the beam tip dynamics. Figure 3.9 shows the beam bending modes up to 2 kHz. Furthermore, there are certain modes of the entire assembly that also affect the beam, and these are highlighted in Fig. 3.10. Other additional FE mode shapes are provided for reference in the Appendix Fig. 3.22.
3 Model Validation for Combined Inertial Acceleration and Vibration Environments 23 Fig. 3.8 Free-free MAC Once calibration to free-free data was complete, the modes from the calibrated model were compared to data from the on-centrifuge hammer test, using the MAC plot shown in Fig. 3.11. The full MAC plot with all test shapes is provided for reference in the Appendix Fig. 3.21 Most FE modes match well even to the on-centrifuge data, although the frequency error is slightly higher. The two modes that have a lower correlation are subassembly and local actuator modes at 523 Hz and 1014 Hz in the test. Still, the FE model is generally a good match to the on-centrifuge test data, so it was utilized for subsequent analyses. Preloaded/Handoff Modal After the initial model calibration, a preloaded modal analysis was done to evaluate the subassembly dynamics under applied inertial acceleration. An explicit SIERRA/SM analysis was used to preload the cantilever beam at different acceleration levels. The updated preloaded contact state was handed off to SIERRA/SD, and follow-on modal analyses was completed. Figure 3.12 shows the resulting contact force and von Mises stresses for the 100 G preload case. The preloaded modal analysis in SD determines contact based on the resulting contact force from the SM simulation, which is set at a threshold value. Normal contact with frictionless transverse slip was enabled for the post-handoff SIERRA/SD solution. In addition, the model tangent stiffness matrices in SD are updated based on the resulting inertial preload solution from SM. One of the consequences of the updated contact state is the drastic change in the beam dynamics. At 100 G, the free end of the cantilever beam approaches more of a pinned condition due to the applied inertial acceleration that forces the tip into the support block. This results in the elimination of the first and second bending modes of the beam, which was seen in the test data. The FE model also showed that the third bending mode of the beam drops in frequency, which was once again observed in the test results. The FE preloaded model with updated contact was able to reproduce this change and Fig. 3.13 shows the comparison for the mode. The effect of this updated bending mode is more apparent in the random vibration results, which are discussed in the following section.
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