基于能量辐射传递法的功能梯度板高频振动响应分析

Analysis on the high-frequency vibration response of a functionally graded plate based on the radiative energy transfer method

该研究的目的是将能量辐射传递法(radiative energy transfer method,RETM)推广到功能梯度板模型中,以预测结构的高频振动响应。基于一阶剪切变形理论推导了功能梯度板的振动控制方程,获得了波传播特性参数。在该方法中,结构内部的能量响应由激励产生的直接场与边界虚源产生的反射场叠加得到。在临界频率以下,能量响应由一种传播波控制;而在临界频率以上,由三种传播波控制。数值算例结果与模态叠加法和功率流分析进行了对比,验证了RETM在计算不同物理参数下功能梯度板高频振动响应的准确性。研究了不同厚度下剪切变形和转动惯量对能量响应的影响,讨论了材料梯度因子、结构阻尼和激励频率对高频振动能量的影响。结果表明,材料梯度因子的变化会导致结构波传播特性和能量分布特征的变化,越大能量的衰减速度越快,衰减幅度越大。

The purpose of this study is to generalize the radiative energy transfer method(RETM) to a functionally graded plate model to predict the high-frequency vibration response of structures.Based on the first-order shear deformation theory,the vibration governing equation of the functionally graded plate was derived and the wave propagation characteristics were obtained.In the method,the energy inside the structure was obtained by superposition of the direct field generated by the real source and the reflection field generated by the boundary virtual sources.Below the critical frequency,the energy response was controlled by a propagating wave;while above the critical frequency,the energy response was controlled by three propagating waves.The numerical results were compared with those calculated by the modal superposition method and power flow analysis to verify the accuracy of RETM in calculating the high-frequency vibration response of the functionally graded plate with different physical parameters.The influences of shear deformation and rotational inertia of the plates with different thickness on the energy response were studied.The effects of material graded factor,structural damping and excitation frequency on high frequency vibration energy were discussed.The study shows that the change of material graded factorwill lead to the change of mechanical properties of the plate,and the higher theis,the faster the energy attenuation rate and the greater the attenuation range will be.