自由阻尼梁高频能量流响应的解析模型

针对自由阻尼梁的高频振动问题，基于波动理论提出了大阻尼复合结构的能量流解析模型。利用等效复刚度方法确定了完全自由阻尼梁结构的等效弯曲刚度和损耗因子，基于能量流分析方法构建了结构的能量密度控制方程，求解了结构的高频能量流响应。分析了弯曲波在阻尼结构耦合处的能量传递特性，构建了局部自由阻尼梁的高频能量流解析模型，预测了大阻尼耦合结构的高频振动特性。数值结果表明，提出的能量流解析解与经典的时空平均波动解一致逼近，因而能够精确地预测自由阻尼梁等大阻尼复合结构的高频能量流响应。

Analytical model of high-frequency energy flow response for a beam with free layer damping

An analytical energy flow model based on wave theory is proposed to predict the vibration of large damping composite structures such as a beam with free layer damping in the high-frequency range. Using the equivalent complex stiffness model, both equivalent flexural stiffness and structural loss factor of a beam with free layer damping are obtained. Then the corresponding energy density equation is derived for a beam with full free layer damping by energy flow analysis. By analyzing the energy transfer char-acteristic at the interface of damping treatment, an analytical model for the energy flow response of a beam with partial free layer damping is developed to predict the vibrating characteristics of the coupled large damping structure. Various numerical analyses show that the energy density obtained by the proposed model is in a good agreement with that by the classic wave model with time-and space-average treatment. Consequently, the present model can be employed to accurately predict the structural energy flow response to high-frequency excitation for large damping composite structures such as a beam with free layer damping.