CLOSED-FORM APPROXIMATION OF VIBRATION MODES OF RECTANGULAR CANTILEVER PLATES BY THE VARIATIONAL REDUCTION METHOD

Exact vibration results for a cantilever plate using the thin isotropi c plate bending theory are not known. The best separable function appr oximation of the vibration mode can be obtained by reducing the plate partial differential equation to two simultaneous ordinary differentia l equations and their boundary conditions. Imposing the boundary condi tions, this analysis can be simplified to the solution of four non-lin ear algebraic equations in four unknown modal parameters. An investiga tion of the theoretical and numerical aspects of this vibration analys is of the cantilever plate is presented, and the results show that the modal parameters are sometimes imaginary. The strong dependence of th e vibration frequencies and modal parameters on the Poisson ratio is a characteristic feature of plates with free edges. (C) 1996 Academic P ress Limited