Bounds on the natural frequencies of laminated rectangular plates with Extension–Bending coupling

Abstract

Extension–Bending coupling behaviour is believed to arise uniquely in anti-symmetric Cross-ply laminates. The results in this article serve to dispel this misconception by presenting solutions for both Cross-ply laminates and Standard laminates, defined as containing combinations of angle plies and cross plies, for a range of different sub-sequence symmetries. Details of the algorithm used to develop the definitive list of laminate stacking sequences with up to 21 plies are presented. Finally, natural frequency factor envelopes are developed, which identify significant differences in the bounds, across a range of aspect-ratios, between Standard laminate configurations and the previously assumed Cross-ply designs.