Vertical plated structures are frequently used in modern engineering applications, such as building walls, glass window facades, and even propelling missiles and rockets subjected to high gravity force. Intensive research on the dynamics and stability of vertical plates can advance the knowledge to enhance the applicability in practical engineering designs. Nevertheless, the investigation of heavy standing plates under its body forces/self-weight has hitherto received less attention, in particular for the vibration analysis.

This paper investigates the buckling and vibration of heavy standing plates with rotational elastic edge constraints. The discrete singular convolution (DSC) method is applied to derive the governing eigenvalue equation. Convergence and comparison studies are conducted to authenticate the correctness and accuracy of the DSC approach. Accurate first-known vibration solutions for elastically restrained vertical plates are presented. Moreover, the influences of elastic supporting edges and body forces/self-weight on the buckling and vibration behaviour of vertical plates are also examined.