In this paper, a procedure to analytically develop an approximate nonlinear solution for the prototypic nonlinear mass-spring-damper system based on multi-dimensional convolution expansion theory is offered. An analytical nonlinear step response is also conducted to characterize the overall system response. The developed analytical step response provides an illumination for the source of differences between nonlinear and linear responses such as initial departure time, differences in settling times and steady value, and non-symmetric response. Feasibility of the proposed implementation is assessed by a numerical example. The developed kernel-based model shows the ability to predict, understand, and analyze the system behavior beyond that attainable by linear-based model.
Analytical Response for the Prototypic Nonlinear Mass-Spring-Damper System
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Omran, A, & Newman, B. "Analytical Response for the Prototypic Nonlinear Mass-Spring-Damper System." Proceedings of the ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, Volume 5. Istanbul, Turkey. July 12–14, 2010. pp. 43-52. ASME. https://doi.org/10.1115/ESDA2010-24153
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