Transient vibration analysis of a completely free plate using modes obtained by Gorman's superposition method

Abstract

This paper shows that the transient response of a plate undergoing flexural vibration can be calculated accurately and efficiently using the natural frequencies and modes obtained from the Superposition Method. The response of a completely free plate is used to demonstrate this. The case considered is one where all supports of a simply supported thin rectangular plate under self weight are suddenly removed. The resulting motion consists of a combination of the natural modes of a completely free plate. The modal superposition method is used for determining the transient response, and the natural frequencies and mode shapes of the plates used are obtained by Gorman's ω radian frequency of vibration

A Review of Prediction Methods for the Transient Vibration and Sound Radiation of Plates

“…The Gorman method has a lot of applications in the steadystate analysis of plates while there are still few in the plate's transient analysis [31][32][33][34][35]. A recent research conducted by Mochida and IIanko [36] has proved that this method is also effective for solving the transient vibration response of a plate with non-classical boundary conditions and has faster convergence rate than that of the Rayleigh-Ritz method.…”

Free Vibration Analysis of Shallow Shells using the Superposition-Galerkin Method

“…The boundary conditions of other edges are given by Equation (6). The in-plane displacements U and V, and out-plane displacement W of the first to fourth building blocks are expressed by Equation (7) with Equations (8) - (11), respectively. It is noted that each trigonometric term in Equations (8) -(11) satisfies the boundary conditions given by Equation (6) and with the additional polynomial terms, these equations satisfy the boundary conditions given by Equation (5).…”

“…The Superposition-Galerkin Method requires two numbers for the series summations. One is the number of driving coefficients, which is "k" in Equation (7) and the other is the number of terms in the series expansions in Equations. (8) -(11), which is "K".…”

“…The Superposition method was also utilised for the analysis of open cylindrical shells [5]. It was also shown that this method was applicable for the determination of steady state response of plates [6] and transient response of a plate [7].…”