Dynamic response of axially functionally graded beam with longitudinal-transverse coupling effect

This study investigates the dynamic response of an axially functionally graded (AFG) beam with longitudinal-transverse coupling effect. The beam is acted by a moving transverse harmonic load and a moving longitudinal harmonic load simultaneously. Both the classical beam theory (CBT) and the Timoshenko beam theory (TBT) are employed and written in a unified form. The system of equations of motion is obtained using Lagrange's equations. The nonlinear formulations of the longitudinal-transverse coupling AFG beams are presented. These formulations are solved using the Newmark method in conjunction with a direct iteration procedure; subsequently, the free and forced dynamic behavior characteristics of the AFG beams are investigated. A comparison of the results obtained using the TBT and CBT is performed. The nonlinear effects caused by different excitation frequencies and amplitudes both in the transverse and longitudinal directions of the moving loads on the dynamic responses of the AFG beam are discussed. Further, different nonlinear dynamic behaviors of the AFG beam caused by different longitudinal-transverse coupling coefficients are revealed. The numerical results indicate that the longitudinal-transverse coupling effect plays an important role in the dynamic behavior of the AFG beam. (C) 2018 Elsevier Masson SAS. All rights reserved.