Static, free and forced vibration of functionally graded (FG) sandwich beams excited by two successive moving harmonic loads

Abstract

This paper examines static, free and forced vibration of functionally graded (FG) sandwich beams under the action of double moving harmonic loads travelling with constant velocities using Timoshenko beam theory (TBT). Three different sandwich beam models with various cross-sectional shape and various boundary conditions are considered. It is assumed that in FG part of sandwich beams, the material properties vary continuously through the thickness of the beam according to simple power-law form. The problem is formulated based on the energy approach. For this purpose, the unknown displacement functions are approximated by using the simple polynomials together with the auxiliary functions for satisfying the essential boundary conditions. The equations of the motion are obtained by using the Lagrange's equations, and solved with the help of the implicit time integration method of Newmark-. In this study, the effects of the different sandwich beam models, boundary conditions, gradient index, the velocity, excitation frequency and the phase angles of the two successive harmonic loads, and the distance between the loads on the mechanical behavior of sandwich beams are discussed in detail. At the same time, extensive static and free vibration results are presented to check the reliability of the present formulation. Good agreement is observed. (C) 2016 Elsevier Ltd. All rights reserved.