ABSTRACT
The exact analysis for the vibration of systems of many degrees of freedom is generally difficult and its associated calculations are laborious. Even with high-speed digital computers that can solve equations of many DOF, the results beyond the first few normal modes are often unreliable and meaningless. In many cases, all the normal modes of the system are not required, and an estimate of the fundamental and a few of the lower modes is sufficient. For this purpose, Rayleigh's method and Dunkerley's equation are of great value and importance. This chapter examines the Rayleigh method in light of the matrix techniques and shows that the Rayleigh frequency approaches the fundamental frequency from the high side. The Ritz method is essentially the Rayleigh method in which the single shape function is replaced by a series of shape functions multiplied by constant coefficients.
