Theoretical approach for determination of normal modes of vibrating mechanical systems with discontinuous properties

0328795 - ÚT 2010 RIV PT eng C - Conference Paper (international conference)
Fedorchenko, Alexander I. - Stachiv, Ivo - Wang, A. B.
Theoretical approach for determination of normal modes of vibrating mechanical systems with discontinuous properties.
Proceedings IRF' 2009. Porto: Faculty of Engineering, University of Porto, 2009 - (Gomes, J.; Meguid, S.), S1503-PO286. ISBN 978-972-8826-21-5.
[International Conference on Integrity, Reliability and Failure /3./. Porto (PT), 20.07.2009-24.07.2009]
R&D Projects: GA AV ČR(CZ) IAA200760801
Institutional research plan: CEZ:AV0Z20760514; CEZ:AV0Z10100521
Keywords : normal modes * laplace transform * resonance
Subject RIV: BI - Acoustics

In this paper a fundamental solution of the problem describing the longitudinal vibration of the rod with viscous damping has been found. A theoretical approach for the determination of normal modes of vibrating one-dimensional mechanical systems with 3-stepwise constant properties has been put forward. The transcendental equation has been derived from the solution in Laplace image space and its roots are natural frequencies. The equation relates thickness of layers and elastic moduli; it makes possible experimental measurement of thin film thickness and elastic moduli. The physical interpretation of the natural frequencies by introducing an “effective” speed of the wave propagation has been proposed.
Permanent Link: http://hdl.handle.net/11104/0175011