On normal modes of vibrating 1-D mechanical systems with discontinuous properties
Journal
Mechanics of Advanced Materials and Structures
Journal Volume
19
Journal Issue
4
Pages
265-270
Date Issued
2012
Author(s)
Abstract
A fundamental solution for the problem describing the longitudinal vibration of the rod with viscous damping has been found. A theoretical approach for 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 the 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.
Type
journal article