"Theoretical approach for determination of normal modes of vibrating mechanical systems with discontinuous properties" . "Stachiv, Ivo" . "Proceedings IRF' 2009" . . "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 \u201Ceffective speed of the wave propagation has been proposed."@en . . "Wang, A. B." . . . . . "P(IAA200760801), Z(AV0Z10100521), Z(AV0Z20760514)" . . "[A8292ED0E027]" . "Theoretical approach for determination of normal modes of vibrating mechanical systems with discontinuous properties" . "RIV/61388998:_____/09:00328795!RIV10-AV0-61388998" . . "3"^^ . . "8"^^ . . "1"^^ . . "Porto" . "Porto" . "Theoretical approach for determination of normal modes of vibrating mechanical systems with discontinuous properties"@en . . "normal modes; laplace transform; resonance"@en . "346161" . . "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 \u201Ceffective speed of the wave propagation has been proposed." . . "Faculty of Engineering, University of Porto" . "RIV/61388998:_____/09:00328795" . "978-972-8826-21-5" . . . "Theoretical approach for determination of normal modes of vibrating mechanical systems with discontinuous properties"@en . "2009-07-20+02:00"^^ . "Fedorchenko, Alexander I." . . . .