Dynamic analysis of arbitrarily restrained stiffened plate under moving loads

This paper develops a unified method for the vibration analysis of stiffened plate subjected to moving loads traveling along arbitrary paths. The stiffened plate is modeled as the main/secondary built-up structure in which the plate is selected as the main structure, whereas the stiffeners treated as the beam are selected as the secondary structures. The stiffeners are allowed to be arbitrarily distributed in terms of the number, length, location and orientation. The connection joint between the plate and beam is described by considering the motion compatibility conditions at the interface on the basis of the first order shear deformation theory (FSDT). Both the torsion, bending and warping of the stiffeners are taken into account. To deal with the spatial discretization of the displacement field, the displacements of plate are expressed as the expansions of Chebyshev polynomials of the first kind (CPOFK). Penalty function method using artificial springs is used to realize the various boundary conditions. Afterward, the finite-dimensional governing equations of motion are obtained by means of the Lagrange's equation. To improve the computational efficiency, the mode reduction technique is used to obtain the reduced-order dynamic model. The first-order generalized- time integration scheme is then employed to solve the reduced-order governing equations of motion in time domain. The convergence and accuracy of the presented method are verified by comparing with Finite Element Method (FEM) and published literature. Finally, the effects of stiffeners, boundary condition, moving speed and inertia interaction on the dynamic response of stiffened plate are examined by parametric studies.