Skip to Main Content
Vibration of Continuous Systems, 2nd Edition
book

Vibration of Continuous Systems, 2nd Edition

by Singiresu S. Rao
March 2019
Intermediate to advanced content levelIntermediate to advanced
816 pages
24h 41m
English
Wiley
Content preview from Vibration of Continuous Systems, 2nd Edition

6Solution Procedure: Eigenvalue and Modal Analysis Approach

6.1 INTRODUCTION

The equations of motion of many continuous systems are in the form of nonhomogeneous linear partial differential equations of order 2 or higher subject to boundary and initial conditions. The boundary conditions may be homogeneous or nonhomogeneous. The initial conditions are usually stated in terms of the values of the field variable and its time derivative at time zero. The solution procedure basically involves two steps. In the first step, the nonhomogeneous part of the equation of motion is neglected and the homogeneous equation is solved using the separation‐of‐variables technique. This leads to an eigenvalue problem whose solution yields an infinite set of eigenvalues and the corresponding eigenfunctions. The eigenfunctions are orthogonal and form a complete set in the sense that any function images that satisfies the boundary conditions of the problem can be represented by a linear combination of the eigenfunctions. This property constitutes what is known as the expansion theorem. In the second step, the solution of the nonhomogeneous equation is assumed to be a sum of the products of the eigenfunctions and time‐dependent generalized coordinates using the expansion theorem. This process leads to a set of second‐order ordinary differential equations in terms of the generalized coordinates. These equations ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Applied Structural and Mechanical Vibrations, 2nd Edition

Applied Structural and Mechanical Vibrations, 2nd Edition

Paolo L. Gatti
Structural Vibration

Structural Vibration

C.Y. Wang, C.M. Wang

Publisher Resources

ISBN: 9781119424147Purchase book