Design of Quasi-isotropic Rectangular Plates for Optimizing the Fundamental Mode of Bending Vibration

Abstract

This study is the first work to demonstrate that quasi-isotropic laminated composite plates can be optimized for bending vibration through appropriate stacking-sequence design. A quasi-isotropic plate is defined as a laminated composite plate exhibiting isotropic in-plane stiffness. Owing to this constraint, such plates have traditionally been excluded from stacking-sequence optimization. The present work clarifies why optimization remains feasible despite the in-plane isotropy requirement and outlines a systematic procedure for maximizing or minimizing the fundamental natural frequency with respect to ply orientation angles while preserving isotropic in-plane behavior. Numerical results are provided for square and rectangular plates under various classical boundary conditions, and the corresponding maximum and minimum fundamental frequencies are identified. In particular, the ratio of maximum to minimum fundamental frequency is evaluated; for example, it reaches 2.17 for a cantilevered quasi-isotropic square plate.