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Abstract
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In this thesis, the dynamic behavior of micro-curved beams under concentrated moving load based on the modified strain gradient theory (MSGT) and modified couple stress (MCST) in conjunction with the first-order shear deformation theory of beams is investigated. In order to use a systematic and efficient method for discretization of the governing equation which has the capability to implement the different boundary conditions and dynamic loadings, in the spatial domain, the finite element method is employed. For this purpose, two-noded elements with six degrees of freedom per node, are used. The equations of motion of an arbitrary element of the microbeam are deived by employing Hamilton's principle in polar coordinate system. After performing the assembling process of the stiffness and mass matrices of the elements and imposing the boundary conditions, the resulting sytem of equations of motion are discretized in time domain by applying Newmark's method and transformed into a system of algebraic equations. To avoid the shear locking phenomenon, the reduced Guass integration is used to calculate the elements of the stiffness matrix corresponding to the transverse shear strain. In orderto verify the correctness of the formulation and the accuracy of method of solution, after showing the convergence behavior of the method, the results are compared with the other existing results in open literature, and also with exact solution. Then, the effects of the ratio of thickness to length scale parameter, length-to-thickness ratio, speed of moving load, opening angle of microbeam and boundary conditions on the dynamic behavior of micro-curved beams under the moving force are studied.
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