A review of the classic analysis of the deformations of a square unsymmetric cross-ply laminate cooled from its curing temperature to a lower temperature is first presented. The analysis is based on a Rayleigh-Ritz approach and variations of the total potential energy. The dependency of the cooled shape on the dimensions of the laminate, specifically its side-length-to-thickness ratio, is discussed. In particular, the tendency of the laminate to cool to a saddle shape or one of two cylindrical shapes, depending on its dimensions, is discussed. Attention then turns to an analysis of the linear vibration characteristics of the laminate. A Rayleigh-Ritz approach and Hamilton's principle are utilized by extending the approximate displacement fields from the cooling analysis to the vibratory situation. Interest centers on the lowest natural frequency and the associated mode shape. It is shown that the linear vibration characteristics depend strongly on whether the static shape considered is the saddle or cylindrical configuration. The overall behavior of the natural frequencies and mode shapes for the stable static configurations appears to agree fairly well with that observed from a finite-element analysis. Agreement for the unstable saddle configuration is not as satisfactory.
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