Simplification through regression analysis on the dynamic response of plates with arbitrary boundary conditions excited by moving inertia load

Dynamic response of a thin rectangular plate traversed by a moving inertia load with arbitrary boundary condition is investigated through this paper. The inertia effect of mass is considered and relevant formulation is established based on the full-term of acceleration, employing the method of Boundary Characteristic Orthogonal Polynomials, BCOP. To acquire the complete solution of partial differential equations governing on the plate, the Galerkin method is used to separate the temporal function from the spatial one. The problem is formulated in the state space and applying the numerical method of Matrix Exponential the complete solution would be achieved. In the numerical studies, a comprehensive parametric study is performed for both cases of loading when inertia effect is included or neglected. Several mass and aspect ratios for the plate with major types of boundary conditions CCCC, SSSS, CFCF and SFSF are accounted for presenting the results. Dynamic amplification factor against velocity parameter is scrutinized within many graphs alongside with a time history analysis of dynamic deflection for the plate's mid-span. Investigating on the dynamic response concludes to the critical boundary condition upon moving mass. By introducing a conversion factor, the margin of inertia and the critical velocity where happened would be achieved, then through a regression analysis a curve fitting model of polynomials is proposed. Corresponding coefficients testify the goodness of fit for such regression which are reported within tables. Referring to this simplified model of conversion factor pertaining to the specific boundary condition, it would be possible to handle the problem in moving load case without undertaking the complexities arisen from inertia contribution into the formulation. Having derived the factor from simplified model which has been calculated for a specific mass and velocity ratio, then multiplying into the moving load response, the complete solution for moving mass would be achieved.