Rayleigh's optimization approach for the approximate solution of integral equations for vibration problems
Abstract
Lord Rayleigh's optimization concept when solving integral equations by means of the Ritz method is used to determine the fundamental frequency coefficient of several vibrating systems. Instead of using a specific trial function with undetermined coefficients, polynomial expressions containing a powerlaw term with an undetermined exponent are used. Since the calculated eigenvalue constitutes an upper bound, by minimizing it with respect to the undetermined exponent, one is able to improve the value of the frequency coefficient.
 Publication:

Journal of Sound Vibration
 Pub Date:
 May 1990
 DOI:
 10.1016/0022460X(90)90775U
 Bibcode:
 1990JSV...139...63L