Free Vibration Analysis of Rectangular Plates

Estimates for Divergence Velocities of Axially Moving Orthotropic Thin Plates

“…Free vibrations of classical rectangular plates, which are not moving axially, have been discussed in the book by Gorman (1982). The case of orthotropic plates, specifically, has been studied by Biancolini et al (2005) Tension inhomogeneities and their effects on the divergence instability of moving plates have been studied in Banichuk et al (2013a).…”

On the free vibrations of a rectangular plate with two opposite sides simply supported and the other sides attached to linear springs

“…Thus, the results obtained by the Rayleigh-Ritz method are approximate. Gorman in [4] and [5] succeeded in solving approximately free vibration problems of plates for various geometries and boundary conditions. Compared to the Rayleigh-Ritz method, the superposition technique in [4] and [5] allows one to obtain an analytical form of the solution which satisfies the governing differential equation and the boundary conditions.…”

“…In [2] Leissa gives a survey of research on rectangular plate problems up to 1970. For a further overview up to beginning of this century the reader is referred to [4]- [9].…”

Vibration of plate on foundation with four edges free by finite cosine integral transform method

“…The chosen functions normally do not satisfy both the governing differential equations and boundary conditions. Gorman used the superposition technique to solve approximately free vibration problems of plates for various geometries and boundary conditions, like in Gorman (1980) and Gorman (1982). A set of static beam functions was used to determine the natural frequencies of elastically restrained plates, like in Bapat et al (1988) and Zhou (1996).…”