Modal Analysis of General Plate Structures

Abstract

A general analytical method, referred to as the Fourier spectral element method, is presented for the dynamic analysis of plate structures consisting of any number of arbitrarily oriented rectangular plates. The compatibility conditions between any two adjacent plates are generally described in terms of three-dimensional elastic couplers with both translational and rotational stiffnesses. More importantly, all plates involved can be arbitrarily restrained along any edges in contrast to the commonly imposed condition: each plate has to be simply supported along, at least, one pair of parallel edges. Thus, plate structures here are not limited to Levy-type plates as typically assumed in other techniques. The flexural and in-plane displacement fields on each plate are analytically expressed as accelerated Fourier series expansions and the expansion coefficients are considered as the generalized coordinates to be determined using the familiar Rayleigh–Ritz technique. The accuracy and reliability of the present method are validated by both finite element analysis (FEA) and experimental data for box structures under various boundary conditions.

An exact spectral-dynamic stiffness method for free flexural vibration analysis of orthotropic composite plate assemblies – Part I: Theory

“…However, when using this method, there is no guarantee that no natural frequency of the structure will be missed and the method may become computationally expensive and very difficult in achieving high accuracies, particularly in the high frequency range. Besides, the assembly procedure in this method seems to be quite tedious and cumbersome [28,29]. The superposition method on the other hand, pioneered by Lamé [38] and extensively used by Gorman in plate vibration problems (see his review paper [39]), has been shown to be an accurate and efficient method.…”

“…However, different admissible functions should be chosen for different boundary conditions so that the formulation using the Rayleigh-Ritz method is not unique. Recently, a Fourier-series based analytical method (FSA) was proposed by Li and his co-authors [26][27][28][29] for plates with general boundary supports. In the FSA, a fictitious Fourier cosine series was used to satisfy first the elastic BC and then the GDE to form the final eigenvalue system expressed in terms of separate stiffness and mass matrices.…”

“…These include the Rayleigh-Ritz method [22][23][24][25], Fourier series-based analytical method [26][27][28][29] and superposition method [30][31][32] amongst others [33][34][35][36]. The Rayleigh-Ritz method has been frequently used [22][23][24][25] because of its flexibility and conceptual simplicity [37].…”

Hypersonic Aeroelastic Response of Elastic Boundary Panel Based on a Modified Fourier Series Method

“…Li et al [21] summarized the modified Fourier series method (MFSM) and proposed a complete set of analytical solutions for the transverse vibration of rectangular plates with general elastic boundary supports. Later on, the MFSM has been applied to solve many problems of plates with elastic boundary restraints, such as free vibration of two elastically coupled rectangular plates [22], modal analysis of general plate structures [23], and modeling analysis of elastically restrained panel [24]. This method is also used well in triangular plates [25], blades [26], circular plates [27], confocal annular elliptic plates [28], and so on.…”

A modal-spectral model for flanking transmissions

“…Most of these methods require the assumption of some geometry simplification. But recent formulations try to extend their use to more general structures, for example composed of rectangular plates [41,42,43].…”