Frequency Analysis of a Linear Elastic Structure Carrying a Chain of Oscillators
Publication: Journal of Engineering Mechanics
Volume 125, Issue 5
Abstract
In this technical note we analyze the free vibration of M undamped oscillators attached to an arbitrarily supported, linear elastic structure. Using the assumed-modes method with N component modes, the frequency equation governing the free vibration for this combined system is typically obtained as the characteristic determinant of a generalized eigenvalue problem of size (N + M) × (N + M). In this note we will show that by algebraically manipulating the generalized eigenvalue problem associated with free vibration, we can reduce it to a simple secular equation consisting of the sum of N terms, the roots or natural frequencies of which can be obtained either numerically or graphically. In addition, the resultant secular equation lends itself to the solution of an inverse problem that cannot be easily solved by analyzing the original generalized eigenvalue problem.
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Published In
Journal of Engineering Mechanics
Volume 125 • Issue 5 • May 1999
Pages: 587 - 591
History
Published online: May 1, 1999
Published in print: May 1999
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