Dynamic Analysis of Functionally Graded Sandwich Plates under Multiple Moving Loads by Ritz Method with Gram–Schmidt Polynomials

Abstract

This paper investigates the dynamic behavior of functionally graded sandwich plates under multiple moving loads. The first-order shear deformation theory of plates is adopted with the effects of shear deformation and rotary inertia included. By using Lagrange’s equations, the equations of motion for the dynamic behavior of the plate are derived. Then they are solved by the Ritz and Newmark time integration methods for the free and forced vibrations of the plates with different boundary conditions. To guarantee that all terms in the admissible functions can cope with the essential boundary conditions, the Gram–Schmidt procedure is used to generate the shape functions for the Ritz method. The influences of several factors on the dynamic response of the plates, such as layer thickness ratio, boundary condition, velocity, excitation frequency, phase angle, etc., are examined and discussed in detail. The numerical study indicates that the dynamic deflection has initial fluctuated growth in the low range of moving load velocity before reaching the peak at the critical velocity, which is followed by the considerable decrease in magnitude. Besides, the gaps or distances between the moving loads also play an important role in predicting the dynamic deflections of the plate when subjected to more than one moving loads.