Thermal effect on the dynamic response of axially functionally graded beam subjected to a moving harmonic load

Dynamic response of an axially functionally graded (AFG) beam under thermal environment subjected to a moving harmonic load is investigated within the frameworks of classical beam theory (CBT) and Timoshenko beam theory (TBT). The Lagrange method is employed to derive the equations of thermal buckling for AFG beam, and then with the critical buckling temperature as a parameter the Newmark-β method is adopted to evaluate the dynamic response of AFG beam under thermal environments. Admissible functions denoting transverse displacement are expressed in simple algebraic polynomial forms. Temperature-dependency of material constituent is considered. The rule of mixture (Voigt model) and Mori-Tanaka (MT) scheme are used to evaluate the beam's effective material properties. A ceramic-metal AFG beam with immovable boundary condition is considered as numerical illustration to show the thermal effects on the dynamic behaviors of the beam subjected to a moving harmonic load.