A Novel Energy Flow Model for High-Frequency Vibration Analysis of Beams in a Thermal Environment

Abstract

As an exceedingly important issue in vibro-acoustic community, the thermal effects can significantly affect the dynamic behaviors of the structures. The previous studies are mainly performed using the deterministic methods which are infeasible at high frequencies. Energy flow analysis (EFA) is a recent method for high-frequency structural analysis. However, until now the thermal effects are neglected in EFA studies. In this paper, a novel EFA model is developed to predict the high-frequency response of beams in a thermal environment. The wavenumber related with the axial membrane force arising from thermal stresses is considered in the derivation, and then the thermal stress effect is incorporated in the EFA governing equation in terms of effective damping loss factor. In addition, the effect of temperature-dependent material properties is included in the EFA formulation. The proposed EFA model is validated against the modal analysis for a simply supported beam for various frequencies and damping loss factors, and good agreements are found. The results indicate that the thermal effects can affect spatial distributions and levels of the energy density, and the vibrational response of beam increases with temperature.