This study determines the eigenvalues, eigenvectors, and nodal patterns of a class of orthotropic plates whose geometry is governed by the equation
(x/a)α + (y/b)β = 1,
where the parameters a, b, a, and a permit the plate geometry to vary over a range which includes the rhombus, circle, ellipse, square, and rectangle.
Variable thickness, inplane forces, and mixed or discontinuous boundary conditions are also considered. The following assumptions have been employed:
i). plate is thin with respect to other dimensions,
ii). deflections are small,
iii). rotary inertia and shear are neglected.
The method of analysis employed is the Rayleigh-Ritz energy technique using xy-polynomials as the approximated deflection. Eigenvalues and eigenvectors were computed by the method of reductions, and the evaluation of double integrals was achieved by the numerical procedure of Gauss-Legendre quadratures.
The validity of the analysis was checked by comparison with known solutions for rectangular orthotropic plates, and isotropic plates with variable thickness, in-plane forces, and mixed or discontinuous boundary conditions. It was found that the calculated frequencies and nodal patterns were in good agreement with existing data
