Abstract: The structures in aerospace applications are usually exposed in extreme thermal environment due to the aerodynamic heating effect, thereby leading to the significant temperature difference between the internal and external surfaces of structures. As a result, the thermal gradient always exists inside the structures. To analyze the dynamic response of the beam exposed in thermal-gradient environment and subjected to high-frequency excitation, an energy flow model for the beams with thermal gradient is developed. The thermal field in the beam is solved by the thermal conduction equation. Considering the influences of the temperature on material properties, the physical neutral plane of the beam is determined to remove the stretch-bending coupling. The governing equations of deformation of the beam are derived using the Hamilton's principle to obtain the dispersion relation for the bending wave. Furthermore, the relationship between the energy density and energy intensity is deduced after the time-period average and local-space average. The governing equations for the energy density are attained by considering the power balance in any differential element. Compared with the benchmark solutions, the model proposed can give the accurate prediction of the vibrational energy density of the beam under the high-frequency excitation.

Key words: energy finite element method, power flow, power flow finite element method, high-frequency vibration, thermal environment