Nature of stationarity of the natural frequencies at the natural modes in the Rayleigh-Ritz method

A variational formulation of the Rayleigh-Ritz method to obtain approximate natural frequencies and natural modes is presented. The stationarity of the natural frequencies with respect to the arbitrary coefficients in the linear combination of the assumed deflection shapes, and also at the natural modes is investigated. It is concluded that the natural frequencies are stationary and need not always be minimum, with respect to the arbitrary coefficients; however, they are minimum with respect to the natural modes. This may provide a means of checking the accuracy of the computed natural frequencies obtained by using energy techniques such as the Rayleigh-Ritz, Galerkin, and finite element methods. (C) 1997 Academic Press Limited.