A spectral collocation solution for in-plane eigenvalue analysis of skew plates

• Free in-plane vibration of skew plates is studied.
• The solution is obtained using the spectral collocation method.
• Plates with various skew angles, aspect ratios and boundary conditions are analyzed.
• The method has a high rate of convergence and degree of accuracy.
• Design guidelines related to the plate geometrical parameters are provided.

Free in-plane vibration analysis of isotropic plates with skew geometry is carried out using the spectral collocation method. The mathematical formulation of the discretized spectral solution is expressed in a concise matrix form which can be directly and easily coded in modern mathematical software packages. A rather comprehensive set of plate cases with various skew angles, aspect ratios, and boundary conditions is presented, with the aim of both showing the rate of convergence and degree of accuracy of the adopted method and providing useful design guidelines related to the effect of the plate geometrical parameters on the fundamental in-plane frequency value.