Vibration of a prestressed orthotropic rectangular thin plate via singular perturbation technique (Q1086023)

The method of matched asymptotic expansions is used in investigating the vibration of a highly prestressed rectangular thin plate exhibiting natural material orthotropy. When the bending rigidity is small compared to the applied in plane loading, analytical results which are correct to \(O(\epsilon^ 2)\) (where \(\epsilon^ 2\) denotes a normalized bending rigidity) are presented for various boundary conditions including the fully clamped case. To leading order solution in \(\epsilon\), the eigenvalues of an ideal orthotropic membrane are obtained. The first order solutions in \(\epsilon\) show the influence of bending stiffness and material orthotropy on the eigenvalue, while torsional rigidity affects the eigenvalues to second order in \(\epsilon\). In particular, \textit{K. Hutter} and \textit{V. O. S. Olunloyo}'s results are recovered for the special case of isotropic material properties [e.g. ibid. 63-77 (1979; Zbl 0397.73058)].