Summary
A first known investigation on the vibratory characteristics of pretwisted composite symmetric laminates with trapezoidal planform is presented. A governing eigenvalue equation is derived based on the Ritz minimization procedure. This formulation shows that bending and stretching effects of these symmetric laminates are coupled by the presence of twisting curvature. For the solution method, a set of orthogonally generated shape functions is employed to approximate the transverse and in-plane displacements. These functions are generated through a proposed recurrence formula. During the orthogonalization process, a basic function is introduced to ensure the satisfaction of the essential boundary conditions. This proposed method is applied to determine the vibration response of the titled problem. The effects of angles of twist and laminated layers upon the vibration frequencies are examined. Convergence tests for selected examples are presented in which the accuracy of the results is established. It has been found that an increase in the angle of twist also strengthens the torsional stiffness of the laminated plates and therefore results in higher twisting frequencies. The present solutions, where possible, are verified by comparison with data of simplified examples that are available in the literature.
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Lim, C.W., Liew, K.M. Vibration of pretwisted cantilever trapezoidal symmetric laminates. Acta Mechanica 111, 193–208 (1995). https://doi.org/10.1007/BF01376930
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DOI: https://doi.org/10.1007/BF01376930