Wen L. Li

TL;DR: In this paper, the displacement solution is expressed as a two-dimensional Fourier series supplemented with several one-dimensional series, which is capable of representing any function (including the exact displacement solution) whose third-order partial derivatives are (required to be) continuous over the area of the plate.

TL;DR: In this article, the in-plane vibration problem of a rectangular plate with elastically restrained edges is solved using an improved Fourier series method in which the inplane displacements are expressed as the superposition of a double Fourier cosine series and four supplementary functions in the form of the product of a polynomial function and a single cosine-series expansion.

TL;DR: In this paper, a general analytical method is derived for the vibration analysis of rectangular plates with elastic edge restraints of varying stiffness, and the displacement solution is sought simply as a linear combination of several one-and two-dimensional Fourier cosine series expansions.

TL;DR: The vibrations of circular, annular, and sector plates are traditionally considered as different boundary value problems and often treated using different solution algorithms and procedures as mentioned in this paper, and the vibrations of these plates are considered as boundary value functions.

TL;DR: In this paper, an analytical method is derived for determining the vibrations of two plates which are generally supported along the boundary edges, and elastically coupled together at an arbitrary angle by four types of coupling springs of arbitrary stiffnesses.