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Received Nov 11, 2017; Revised Feb 22, 2018; Accepted Mar 29, 2018
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1. Introduction
The sector, annular, and circular plates are typical structural components used in engineering widely. The flexural vibration of sector, annular, and circular plates has been studied by researchers and design engineers with considerable interest. A number of investigations [1–5] have been devoted to flexural vibrations of structures, maybe because the flexural vibration has lower resonant frequencies and a decisive role in terms of fluid-structure coupling. However, the vibrations of structures also contain in-plane parts, which often appear in high frequency motions and large coupled structures. When the sound radiation and energy transmission of coupled structures are considered, the importance of in-plane vibration is nonnegligible. Consequently, it is of great significance to obtain deep in-plane vibration comprehensions of sector, annular, and circular plates.
Xing and Liu [6] applied a Rayleigh quotient variational principle to study the free in-plane vibration for rectangular plate. In the paper, all classical boundary restraints which included two various kinds of simple supports were taken into consideration. Bercin and Langley [7] analyzed the in-plane vibration problem of plate structures by adopting the dynamic stiffness technique and classical finite element assembled technique. Nefovska-Danilovic and Petronijevic [8] also used this method to investigate the in-plane free vibration of arbitrarily restrained isotropic rectangular plate. Gorman [9] used the method of superposition to solve the problem of free in-plane vibration of plates; then he used this method to solve in-plane vibration of Levy-type plates [10] which have a pair of simply supported opposite edges at least. Andrianov et al. [11] adopted homotopy perturbation method to study the in-plane vibration of rectangular plate. Chen et al. [12] applied Chebyshev-Lagrangian approach to study in- and out-of-plane vibration of plate with cutout. Mohazzab and Dozio [13] used the spectral collocation method to analyze in-plane vibration of isotropic skewed geometrical plates. Some other efforts [14–18] have also been devoted to the in-plane vibration problem of plate structures.
It is needed to point out that a great majority of existing investigations in aforementioned issues are restricted within...