Chapter 13 Damping Identification and Model Updating of Boundary Conditions for a Cantilever Beam Nimai Domenico Bibbo and Vikas Arora Abstract Model updating is a crucial tool for dynamically loaded structures as natural frequencies and damping can have a vital impact on normal operation and fatigue life. Finite element models always deviate from experimentally obtained results due to variations in mass and stiffness and the lack of a damping matrix. Thus, it is vital for many large structures, that the dynamic properties be determined experimentally and subsequently apply model updating to “tune” the finite element model. In this paper, model updating techniques are tested on a small cantilever beam where the fixed boundary condition is assumed to be flexible and the main source of damping. The methods are tested using both simulated data and experimental data for updating the stiffness and damping matrices. The results of the analytical model are compared both before and after updating with its experimental counterpart. The model updating procedure follows a two-step process. In step one the stiffness matrix is updated using the iterative eigensensitivity approach where selected stiffness related parameters, in this case the boundary conditions, are updated based on the sensitivities to eigenfrequencies and mode shapes. In the second step, the damping of the structure is updated. Keywords Model updating · Damping identification · Modal expansion/Reduction · Simulated model updating · Experimental model updating 13.1 Introduction The advent of the finite element method [1] has brought about the ability for more advanced and refined analysis of engineering structures. Stress distributions and modal properties can be analyzed for geometry far more complex than what is possible otherwise. The benefit of this is the ability to create structures optimized to the environmental factors they are subjected to. There is however one caveat, a finite element model is only ever as good as the users ability to capture the physical properties of the system. The stiffness and mass of a system are often fairly well known, however differences often exist due to production tolerances, joints and boundary conditions. These differences can significantly impact modal results and stress distributions. With the advances in experimentally measuring modal parameters [2], methods were in turn developed to update finite element models using the results from experimental analysis. Development started in the 1960/1970s, however much of the use and further development first came around in the 1990s with the increasing performance of computational hardware. These early methods and the model updating procedure is well described in [3]. The updating of mass and stiffness matrices can generally be split into two categories, direct updating methods and iterative updating methods. The direct methods have the advantage of updating the mass and stiffness matrices in one step and are able to match the experimentally obtained results very accurately. However for this article, only the iterative methods are of interest as the direct methods update the system matrices without consideration of the physical connectivity of the finite element model. Using iterative methods, updating parameters are selected where it is thought that error in the finite element model exists. This could be joints, boundary conditions, youngs modulus, density, etc. Many iterative methods exist, one of the most popular being the inverse eigensensitivty approach [4] which utilizes the eigenvalues and modeshapes of a N. D. Bibbo ( ) Department of Technology and Innovation, University of Southern Denmark, Odense, Denmark Lindø Offshore Renewables Center, Munkebo, Denmark e-mail: ndbi@iti.sdu.dk V. Arora Lindø Offshore Renewables Center, Munkebo, Denmark © The Society for Experimental Mechanics, Inc. 2021 A. Linderholt et al. (eds.), Dynamic Substructures, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-47630-4_13 139
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