| Abstract: | The complementary variational principle has been used to derive the differential equations and the associated boundary conditions of the vibrating plate in terms of bending moments. It is shown that in this formulation, the plate possesses an infinite number of zero frequency modes in which the plate remains in a state of constant strain under a set of self-equilibrating bending moments. In applying the Rayleigh Ritz procedure for the non-zero frequency modes of the plate, it is shown that it the assumed functions are orthogonal to only a finite number of zero frequency modes, then one may obtain frequencies which are lower than the true frequencies of the plate. An iliustrative example is given in the paper. |
