Bounds on the natural frequencies of laminated rectangular plates with extension-twisting (and shearing–bending) coupling

Abstract

Anti-symmetric angle-ply laminates are widely believed to uniquely possess Extension-Twisting (together with Shearing–Bending) coupling behavior. The results in this article serve to dispel this misconception by presenting solutions for both standard laminates, containing combinations of angle plies (±45°) and cross plies (90° and/or 0°), and angle-ply laminates, containing only±45° ply orientations; chosen to reflect current industrial design practice, and also because they serve to produce hygro-thermally curvature-stable properties in some standard laminate configurations, i.e., with immunity to the thermal distortions that generally arise in this class of mechanically coupled laminate as a result of the high temperature curing process.Details of the algorithm used to develop the definitive list of laminate stacking sequences, with up to 21 plies, are given first. Closed form natural frequency solutions for each of these sub-groups are then presented, identifying significant differences in the frequency spectrum bounds across a range of aspect ratios, with respect to the ubiquitous anti-symmetric angle-ply designs.