Abstract This paper presents a robust Wide Strip Transition Matrix (WSTM) method for analyzing the vibration behavior of a restrained orthotropic plate subjected to in-plane compression and resting on Winkler-Pasternak foundations. This study highlights the complexity of the mathematical analysis of this advanced plate, which has significant applications across various engineering fields, including aerospace panels, composite bridge decks, pavements, and machine foundations. WSTM integrates analytical nodal lines and wide strips into transition matrices via Winkler-Pasternak foundation coupling, yielding a lower-order eigenvalue problem across a limited number of wide strips. This process achieves superior modal accuracy compared to other advanced analytical and numerical methods, while significantly reducing computational costs and processor memory. The innovation of the WSTM lies in integrating the wide strip concept with a precise transition matrix derived directly from the modal ordinary differential equations, based on the plate's partial differential equation of motion. The numerical results are obtained by employing the WSTM method as an initial value algorithm that utilizes an improved transition matrix operating on panels divided into wide strips. Compared to numerical methods like finite element, finite difference, or finite strip methods, the proposed approach eliminates the need for extensive element formulation and the solution of large systems of algebraic equations. The advantages of the present method are discussed, and its convergence, stability, and accuracy are demonstrated. The findings strengthen the reliability of predicting dynamic responses and stability limits. This evidence, in turn, enables the optimized design of plate-like structural components in engineering applications. .
Sheikh et al. (Mon,) studied this question.