A separation-of-variable dynamic stiffness method for the free vibration of thin orthotropic rectangular plates with general homogeneous boundary conditions

• General SOV-type plate to elastically restrained boundaries. • Closed-form DSM for orthotropic rectangular plates. • W–W algorithm avoids direct eigenvalue solving. • Explicit closed-form J0 term for the W–W algorithm. • Mode shapes computed for arbitrary boundary conditions. A separation-of-variable dynamic stiffness method (SOV-DSM) is proposed for the free vibration analysis of an thin orthotropic rectangular plate with general homogeneous boundary conditions. Firstly, the extended SOV solution satisfying Rayleigh’s principle is extended to handle arbitrary boundary conditions and then applied to develop closed-form dynamic stiffness formulations. Then, an enhanced Wittrick–Williams (W-W) algorithm is used to solve the eigenvalue problem rather than solving the highly nonlinear eigenvalue equations. The J 0 count problem involved in applying the W-W algorithm is addressed by providing an explicit and closed-form expression for the J 0 term based on the characteristics of the SOV solution. Furthermore, a numerical technique is provided to calculate the mode shape of the plate with any arbitrary boundary conditions. The accuracy of the proposed method is validated through numerical experiments by comparison with other analytical solutions.