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 isproposed to study the dynamics of axially moving orthotropic rectangular plates subjectedto linearly varying in-plane stresses. the finite element method (fem) with higher orderinterpolation functions is rst used to discretize the spatial partial derivatives with respectto the coordinate direction of the plate. the dierential quadrature method (dqm) isthen employed to discretize the resulting system of ordinary dierential equations. linearlyvarying uniform and non-uniform distributed load conditions are considered on two oppositeedges of the plate. comparisons are made with existing numerical and analytical solutionsin the literature. it is revealed that the proposed mixed method is highly accurate andecient. finally, the dimensionless complex frequencies of the axially moving orthotropicplate with dierent boundary conditions under the linearly varying in-plane stresses arecalculated by the proposed mixed method. the curves for the real and imaginary parts ofthe rst three dimensionless complex frequencies versus the dimensionless axially movingspeed are obtained. the eects of material properties of the plate, variation of in-planestresses, and the dimensionless moving speed on the stability of the orthotropic plate areinvestigated.