Applying the methods of BCOP and matrix exponential in the vibration analysis of multi-span composite plates under opposing moving inertia loads

Abstract

The dynamic response of multi-span composite plates excited by moving inertia loads is scrutinized within this study. The masses are traveling on a two-lane trajectory in opposing direction with constant velocity. Two major types of opposing moving masses are comprehensively assessed here, including a case that two masses start to move in opposing direction simultaneously, and the other position when the second mass starts to move in the opposite direction just the first one left the plate. All case studies are presented for two cases of boundary conditions SFSF and SSSS. The complete solution of governing differential equations for the structure is achieved by a novel combination of two methods as Boundary Characteristic Orthogonal Polynomials (BCOP) and the robust numerical procedure of matrix exponential. Utilizing the features of orthogonal polynomials through the BCOP method, the natural frequencies would be extracted by proceeding a free vibration analysis. Having established the state-space formulation for the problem, the temporal response of equations would be derived using an iterative numerical procedure based on the matrix exponential functions. A comprehensive parametric study is conducted through numerical examples to show that the important parameters such as mass ratio, aspect ratio, velocity parameter as well as the parameter of the distance between lanes how could affect the dynamic behavior of FRP plates, under two-lane opposing moving masses. By introducing a conversion factor, the effect of inertia terms on the dynamic behavior of composite plats is evaluated.