Analysis of Anisotropic Plates

Abstract

An energy formulation and solutions are presented for the analysis of plane anisotropic rectangular plates with various boundary condi tions. The formulation includes linear theory stability analysis, the calculation of natural frequencies and mode shapes, and analysis of displacement due to lateral loads. In-plane loadings are included in all of these formulations. The Ritz technique is used to find the minimum of energy expressions using a series expansion of beam mode shape functions. Several numerical and experimental results are presented and compared.

Modal Vibration Damping of Anisotropic FRP Laminates Using the Rayleigh–ritz Energy Minimization Scheme

“…A detailed account of the method for isotropic plates has been given by Young [16], and that for anisotropiclaminated plates by Ashton and Waddoups [14] and Ashton and Whitney [13]. An outline of the application of the Rayleigh-Ritz method to modal vibration of anisotropiclaminated plates, together with its utilization in computing the modal damping of such plates, is given here.…”

“…Following the work of Young [16] and Ashton and Waddoups [14] in using Bernoulli-Euler-type beam functions with free and/or clamped end conditions, the functions X ði;mÞ ðxÞ and Y ðj;nÞ ðyÞ can be conveniently represented in the following general form:…”

“…Generally, however, the (natural) boundary conditions of a free edge in a plate are not completely satisfied by the use of the corresponding free-end beam functions. Nevertheless, experimental evidence tends to suggest that this has only a marginal effect on the results [14,17]. Equation (25) can be written in the matrix form…”

“…The latter method has been used by various authors [5,9] to compute the modal damping of laminated plates, and good correlation with experimental values have been reported. However, the Rayleigh-Ritz method involves considerably less computation than the FE method, and it would be advantageous on that account alone to use this method where possible [14,15]. It is the aim of the present work to use the Rayleigh-Ritz method to compute the modal damping of anisotropic-laminated plates, and to compare the theoretical results with values obtained experimentally, and with those obtained by the FE method.…”

Free Vibrations of Unsymmetrically Laminated Anisotropic Plates with Clamped Edges

“…Vibrations of generally anisotropic plates have been analyzed by Waddoups and Ashton [3][4][5]. Using the Rayleigh-Ritz approach, their analyses were formulated to use the characteristic beam functions tabulated in [6] .…”