16 Investigation of Nonlinear Dynamic Phenomena Applying Real-Time Hybrid Simulation 131 of real-time hardware and software necessary for simulation and control. For an engineer, RTHT is attractive, because an isolated physical component can be tested under realistic conditions, since all components eliminated from physical tests are collected in a virtual model. This model is running in a real time simulation and is interacting with the physical component. For a fundamental demonstration of the practicability of RTHT of nonlinear dynamic systems, both, the physical and the simulation model are kept simple. The former consists of a rigid mass, the latter of a nonlinear spring damper element. If the models are coupled in accordance with all boundary conditions, a nonlinear single degree of freedom oscillator of Duffing type is obtained. Although the Duffing oscillator can be used to demonstrate several nonlinear effects, all experiments are restricted to time periodic forcing. This restriction results from limitations of the developed transfer system, which must possess a highly accurate tracking performance for reliable results. The transfer system’s main components are an electrodynamic shaker and an iterative learning control algorithm, which is particularly appropriate for periodic processes. The hybrid simulation technique presented allows easy modification of the simulation model’s nonlinearities and shows excellent agreement with all simulations. The efficiency of the proposed system is confirmed for different periodic forcings, and all results underline that the method presented enables developments, which are hardly possible with traditional methods, or only at the price of a significantly greater effort. References 1. Saouma, V., Sivaselvan, M.: Hybrid Simulation: Theory, Implementation and Applications. Taylor & Francis Ltd., London (2008) 2. Bursi, O.S., Wagg, D.: Modern testing techniques for structural systems. In: Dynamics and Control, CISM International Centre for Mechanical Sciences, vol. 502. Springer-Verlag Wien, New York (2008) 3. Hochrainer, M.J.: Real-time hybrid testing: challenges and experiences from a teaching point of view. In: Mains, M., Dilworth, B. (eds.) Topics in Modal Analysis & Testing, Conference Proceedings of the Society for Experimental Mechanics Series, vol. 9. Springer, New York (2019) 4. Ahmadizadeh, M., Mosqueda, G., Reinhorn, A.M.: Compensation of actuator delay and dynamics for real-time hybrid structural simulation. Earthq. Eng. Struct. Dyn. 37(1), 21–42 (2008) 5. Chen, C., Ricles, J.M.: Analysis of actuator delay compensation methods for real-time testing. Eng. Struct. 31(11), 2643–2655 (2009) 6. Bartl, A., Mayet, J., Karamooz Mahdiabadi, M., Rixen, D.J.: Multi-DoF interface synchronization of real-time-hybrid-tests using a recursiveleast-squares adaption law: a numerical evaluation. In: Proceedings of the 34th IMAC, A Conference and Exposition on Structural Dynamics, 2016 7. Virgin, L.N.: Introduction to Experimental Nonlinear Dynamics. Cambridge University Press, Cambridge (2000) 8. Ziegler, F.: Mechanics of Solids and Fluids, 2nd edn. Springer, New York, Vienna (1998) 9. Hochrainer, M., Schattovich, P.: Real-time hybrid simulation of an unmanned aerial vehicle. In: Dynamics of Coupled Structures, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-319-54930-9_4, 2017 10. Maghareh, A., Silva, C.E., Dyke, S.J.: Servo-hydraulic actuator in controllable canonical form: identification and experimental validation. Mech. Syst. Signal Process. 100, 398–414 (2018) 11. Guan, F.-G., Xiong, W., Wang, H.-T.: Adaptive random control of a two-axis redundantly actuated electro-hydraulic shaking table. J. Vib. Control. 22(16), 3455–3469 (2014) 12. Zhang, R., Lauenstein, V., Phillips, B.: Substructure real-time hybrid simulation with a small-scale uni-axial shake table. In: 6th International Conference on Advances in Experimental Structural Engineering, August 1–2, 2015, University of Illinois, Urbana-Champaign, USA (2015) 13. Plummer, A.R.: Model-based motion control for multi-axis servohydraulic shaking tables. Control. Eng. Pract. 53, 109–122 (2016) 14. Wang, Y., Gao, F., Doyle, F.J.: Survey on iterative learning control, repetitive control, and run-to-run control. J. Process Control. 19, 1589–1600 (2009) 15. Bristow, D.A., Baron, K.L., Alleyne, A.G.: Iterative learning control. In: Levine, W.S. (ed.) The Control Handbook. CRC Press, Boca Raton, FL (2010)
RkJQdWJsaXNoZXIy MTMzNzEzMQ==