Radiative energy transfer model for high frequency vibration of functionally graded beams in thermal environment

A simple and efficient energy flow model is developed by radiative energy transfer method (RETM) to predict the high frequency vibration response of functionally graded(FG) beams in thermal environment. The Timoshenko beam theory is applied to derive the motion governing equations. Thermal effects are incorporated into the dynamic model through the temperature dependent material properties and the thermal stresses. The wavenumber and group velocity associated with thermal stress are included in the energy governing equation. By introducing the artificial springs to simulate different boundary conditions, the energy conversion relationship of the two waves at boundaries are deduced. The response of FG beam loaded by a high-frequency harmonic force is described by energy density and energy flow intensity. They are composed of energy rays from the real source at the load point and energy rays reflected from the imaginary sources at the boundaries. Numerical simulations are performed in various forms of thermal environments to verify the proposed model. The RETM results are compared with those obtained by the wave propagation approach under different parameters, and good consistencies are observed. Numerical results show that the vibrational energy density of FG beams are affected by thermal effects and can be reduced by optimising the gradient factors.