Math models of flexible dynamic systems have been the subject of research and development for many years. One area of interest is exact Laplace domain solutions to the differential equations that describe the linear elastic deformation of idealized structures. These solutions can be compared to and complement finite order models such as state-space and finite element models. Halevi (2005) presented a Laplace domain solution for a finite length rod in torsion governed by a second order wave equation. Using similar methods Van Auken (2010, 2012) presented a Laplace domain solution for the transverse bending of an undamped uniform slender beam based on the fourth order Euler-Bernoulli equation, where it was assumed that rotary inertia and shear effects were negligible. This paper presents a new exact Laplace domain solution to the Timoshenko model for an undamped uniform non-slender beam that accounts for rotary inertia and shear effects. Example models based on the exact Laplace domain solution are compared to finite element models and to slender beam models in order to illustrate the agreement and differences between the methods and models. The method is then applied to an example model a half-car with a flexible body.
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ASME 2014 12th Biennial Conference on Engineering Systems Design and Analysis
July 25–27, 2014
Copenhagen, Denmark
Conference Sponsors:
- International
ISBN:
978-0-7918-4584-4
PROCEEDINGS PAPER
Development and Comparison of Laplace Domain Models for Non-Slender Beams and Application to a Half-Car Model With Flexible Body Available to Purchase
R. Michael Van Auken
R. Michael Van Auken
Dynamic Research Inc., Torrance, CA
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R. Michael Van Auken
Dynamic Research Inc., Torrance, CA
Paper No:
ESDA2014-20348, V002T07A018; 12 pages
Published Online:
October 23, 2014
Citation
Van Auken, RM. "Development and Comparison of Laplace Domain Models for Non-Slender Beams and Application to a Half-Car Model With Flexible Body." Proceedings of the ASME 2014 12th Biennial Conference on Engineering Systems Design and Analysis. Volume 2: Dynamics, Vibration and Control; Energy; Fluids Engineering; Micro and Nano Manufacturing. Copenhagen, Denmark. July 25–27, 2014. V002T07A018. ASME. https://doi.org/10.1115/ESDA2014-20348
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