热梯度环境下梁高频振动的能量流模型

Energy flow model for high-frequency vibration of beams in thermal-gradient environment

航空航天领域中的结构常由于高速飞行时的气动加热等因素在内外表面形成明显的温度差异,结构内部也常因此存在温度的梯度分布。为分析含有温度梯度的梁在高频激励下的动力学响应,建立了热梯度梁的能量流模型。首先通过求解热传导方程得到了梁内的温度场。然后考虑温度场对材料属性的影响,确定了梁的物理中性层以消除拉伸-弯曲变形耦合。基于哈密顿原理建立了梁的弯曲变形控制方程,进而得到了梁弯曲变形的波动频散关系。进一步推导得到了周期平均与局部空间平均后梁振动能量密度与能量流之间的关系,通过任意微元体内的能量平衡关系得到了热梯度环境下梁的能量流模型。与基准解的对比表明,建立的能量流模型能得到热梯度梁在高频激励下较为准确的振动能量分布情况。

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.