ANALYSIS OF VIBRATION BY THE WAVE-PROPAGATION METHOD AND BOLOTINS METHOD FOR A RECTANGULAR THIN-PLATE WITH AT LEAST ONE SIDE ROLLER-SUPPORTED

The wave method of Keller and Rubinow [Ann. Phys. 9, 24-75 (1960)], an d Bolotin's method [in: J.R.M. Radds, ed., Problems of Continuum Mecha nics, SIAM, Philadelphia (1961), pp. 56-68], two asymptotic methods fo r the estimation of eigenvalues of boundary value problems, are shown to be equivalent for the case of a rectangular Kirchhoff thin plate, e ach edge of which is clamped, simply-supported or roller-supported. Th e wave method is then used to calculate the eigenfrequencies for those cases for which the eigenfunctions are not obtainable by separation o f variables. Finally, the same eigenfrequencies are computed numerical ly by discretization using the Legendre-tau method. The asymptotic res ults and the numerical results are seen to be in good agreement, even near the low end of the spectrum.