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

Document Type: Article


1 Young Researchers and Elite Club, Karaj Branch, Islamic Azad University, Karaj, P.O. Box 31485-313, Iran

2 Mechanical Engineering Department, K. N. Toosi University of Technology, Tehran, P.O. Box 19395-1999, Iran


A high order accurate mixed finite element-differential quadrature method is proposed to study the dynamics of axially moving orthotropic rectangular plates subjected to linearly varying inplane stresses. The finite element method (FEM) with higher order interpolation functions is first used to discretize the spatial partial derivatives with respect to a co-ordinate direction of the plate. The differential quadrature method (DQM) is then employed to discretize the resulting system of ordinary differential 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 efficient. Finally, the dimensionless complex frequencies of the axially moving orthotropic plate with different boundary conditions under the linearly varying inplane stresses are calculated by the proposed mixed method. The curves for the real and imaginary parts of the first three dimensionless complex frequencies versus the dimensionless axially moving speed are obtained. The effects of material properties of the plate, variation of inplane stresses, and the dimensionless moving speed on the stability of the orthotropic plate are investigated.


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