功能梯度耦合梁的能量辐射传递模型

A radiative energy transfer model for functionally graded coupled beams

研究的目的是将能量辐射传递方法(RETM)拓展应用于功能梯度材料(FGM)耦合梁的高频振动响应分析。在RETM理论中,FGM耦合梁的振动响应由能量密度和功率流强度表示,振动波场由激励点实源产生的直接场与边界虚源产生的反射场叠加而成。由FGM梁微元的能量平衡推导了能量密度及功率流强度的核函数,利用耦合处的力平衡以及位移连续性推导了能量传递系数,根据边界功率流平衡确定了边界虚源强度。数值算例计算结果与波传播分析方法(WPA)的解析解进行对比,验证了所建立模型的正确性。最后,分析了梯度指数n对FGM耦合梁能量传递系数以及高频振动响应的影响,发现n的影响主要集中在n 0~1。

The purpose of this study is to extend the radiative energy transfer method(RETM)to the analysis of high-frequency vibration response of functionally graded material(FGM)coupled beams.In the RETM theory,the vibration response of FGM coupled beams was expressed by the energy density and power flow intensity.The vibration wave field is composed of the direct field generated by the real source of the excitation point and the reflection field generated by the virtual sources at the boundary.The kernel functions of energy density and power flow intensity were derived from the energy balance of the FGM beam element.The energy transfer coefficients between the FGM coupled beams were derived from the force balance and displacement continuity at the coupling point.The intensities of the boundary virtual sources were determined by the boundary power flow balances.Numerical results were compared with the analytical solutions calculated by the wave propagation analysis(WPA)method to verify the correctness of the proposed model.Furthermore,the influence of the gradient index n on the energy transfer coefficients and high-frequency vibration response was discussed.Simulation results show that the influence of n is mainly concentrated in the range of 0 to 1.