High accuracy mixed finite element-differential quadrature method for free vibration of axially moving orthotropic plates loaded by linearly varying in-plane stresses

A high order accurate mixed nite element-dierential quadrature method is proposed to study the dynamics of axially moving orthotropic rectangular plates subjected to linearly varying in-plane stresses. The Finite Element Method (FEM) with higher order interpolation functions is rst used to discretize the spatial partial derivatives with respect to the coordinate direction of the plate. The Dierential Quadrature Method (DQM) is then employed to discretize the resulting system of ordinary dierential equations. Linearly varying uniform and non-uniform distributed load conditions are considered on two opposite edges of the plate. Comparisons are made with existing numerical and analytical solutions in the literature. It is revealed that the proposed mixed method is highly accurate and ecient. Finally, the dimensionless complex frequencies of the axially moving orthotropic plate with dierent boundary conditions under the linearly varying in-plane stresses are calculated by the proposed mixed method. The curves for the real and imaginary parts of the rst three dimensionless complex frequencies versus the dimensionless axially moving speed are obtained. The eects of material properties of the plate, variation of in-plane stresses, and the dimensionless moving speed on the stability of the orthotropic plate are investigated.