Dynamic stiffness formulation for transverse and in-plane vibration of rectangular plates with arbitrary boundary conditions based on a generalized superposition method

Dynamic stiffness formulation for isotropic and orthotropic plates with point nodes

“…Liu and Banerjee [40] generalized the approach presented in [38] when they investigated the free vibration behaviour of orthotropic plates. Recently, Wei et al [41] made a noteworthy contribution when they formulated the dynamic stiffness matrix for transverse and in-plane vibration of rectangular plates with arbitrary boundary conditions. Their work differs from the work described in [38,42,43] in that the choice of the trigonometric function to describe the series solution was somehow different, which yielded slightly different results.…”

“…( 42) into Eqs. (41) and changing the order of summation for the double series, we obtain after some algebraic transformations, the first part of equations of the infinite linear system which connects the Fourier coefficients to the boundary values of the plate as follows…”

A modified Fourier-Ritz method for free vibration of rectangular plates with elastic constrains

“…Bert and Devarakonda (2003) used the Galerkin method to find the solution of rectangular plates with S-S-S-S boundary conditions, however, it was difficult to ensure the closedness of the solution under the condition of transverse shear deformation. Wei et al (2020) used the generalized superposition method to reduce the size of the stiffness matrix, and obtained a homogeneous solution to the vibration control equation of a rectangular plate, and proved its effectiveness, accuracy and convergence through examples. Banerjee et al (2015) and Liu and Banerjee (2016) derived the dynamic stiffness matrix of a rectangular plate by solving the biharmonic equation, so as to more accurately obtain the natural frequency and vibration mode of free vibration of the rectangular plate, and proved its accuracy by selecting modal vibration samples, but complex symbolic calculation was required.…”