Vibrations of rectangular plates with elastically restrained edges

Ritz Vector Approach for Static and Dynamic Analysis of Plates With Edge Beams

“…As stated earlier, Warburton and Edney [8] proposed such an approach in which two Ritz vectors corresponding to two different idealized boundary conditions are considered for representing an intermediate boundary condition. Several (ideally infinite) vectors can be used in this procedure.…”

“…For simplicity, Takabatake and Nagareda [2] assume the stiffness coefficients calculated by the new formulations to be uniformly distributed over the entire length of plate edge. The assumptions made in this approach may be avoided by combining it with the method proposed by Warburton and Edney [8]. Instead of considering the stiffness coefficients to be uniformly distributed along the length, the bending and the torsion characteristics of the beam can be considered by incorporating appropriate integrals in the expressions for total kinetic and potential energies.…”

“…In this paper, we present an alternate method for static and dynamic analyses of elastic plates with edge beams. It is based on the useful insights provided by Warburton and Edney [8] as well as Takabatake and Nagareda [2], and employs static beam functions in Rayleigh-Ritz method to account for the actual bending and torsional stiffness of edge beams. The proposed approach is not based on any assumption regarding the distribution of translational and rotational stiffness imparted by the edge beams.…”

“…Takabatake and co-workers [3][4][5][6] presented the governing equations for various types of rectangular and circular plates under Kirchoff-Love hypotheses whereas Laura and Grossi [7] studied the transverse vibration of rectangular plates with elastic translational and rotational edge restraints. Warburton and Edney [8] used Rayleigh-Ritz approach in which a pair of Ritz vectors corresponding to two different idealized boundary conditions is selected for representing an intermediate boundary condition thereby avoiding the problem associated with the selection of Ritz vectors in plates with elastic edge restraints. The two Ritz vectors are then used to develop an eigenvalue problem for evaluating the fundamental frequency.…”

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

“…Leissa gave a survey of research on rectangular plate problems up to 1970, like in Warburton (1954) and Leissa (1973). The further overview up to the beginning of this century is presented in Warburton (1979) and Warburton & Edney (1984). One of the most commonly used methods in free vibration analysis of plates is the Rayleigh-Ritz energy technique, where appropriate functions associ-ated with various boundary conditions are chosen to describe the lateral deflection of the deformed plates.…”