Extended analytical strip method for free vibration analysis of rectangular thin plates with arbitrarily varying parameters along one edge

Thin plates with properties varying along a single in-plane axis arise in many engineering applications, yet their analysis is often hindered by variable-coefficient governing equations that challenge existing analytical methods. This study presents an extension of the analytical strip method (ASM) for the free vibration analysis of rectangular thin plates with varying material properties and thickness along one edge. Unlike previous ASM formulations that treat only stepped plates and homogeneous laminates, the proposed approach can model arbitrarily varying thickness, density, and material properties. The governing differential equation is derived under the local Kirchhoff–Love assumptions, reduced via separation of variables and employing Lévy-type solution in the simply supported direction, and is discretized into strips along the varying axis. Within each strip, exponential trial functions yield closed-form homogeneous solutions. Continuity conditions across inter-strip boundaries enforce kinematic and load smoothness; while clamped, simply supported, or free boundary conditions (or combinations thereof) apply at the two outer longitudinal edges of the boundary strips. Three numerical examples are presented in order to validate the method. One example is chosen from the literature and the others are designed so as to have analytical solutions despite strong nonlinearities. The results, benchmarked against finite element and analytical solutions, demonstrate rapid convergence and excellent accuracy for plates with variable material properties and thickness, even with relatively much smaller number of elements.