轴向力影响下大阻尼梁高频能量流响应解析模型

Analytical Model of Vibrational Energy Flow with High Frequency for a High Damping Beam under Axial Force

针对轴向力作用下大阻尼梁的高频振动问题,基于能量流分析方法构建高频动响应解析预报模型。推导梁结构的能量传递方程和能量损失方程,结合功率平衡方程构建轴向力影响下大阻尼梁的能量密度控制方程。以简支梁为典型算例,分析结构的能量密度响应,研究轴向力和结构阻尼损耗因子对高频能量流响应的影响。数值结果表明:提出的能量流响应解析模型渐进一致逼近基于波动分析法的经典模型解,可以准确预示轴向力作用下大阻尼梁的高频弯曲振动响应。随着梁结构轴向载荷和阻尼损耗因子的增加,能量密度自激励点向两端约束边界衰减速度提高。但是,梁结构的弯曲振动总能量随轴向载荷单调增加,而随阻尼损耗因子单调减小。

The high frequency vibration problem of large damping beams with axial load applied is studied. An analytical model for prediction of the high frequency vibration response of the beam is developed based on the vibrational energy flow method. The energy transmission equation and the energy loss equation of the beam structure are formulated.Combined with the power equilibrium equation, the energy density governing equation of the beam is derived. Taking the simply supported beam as a typical example, the energy density distribution is obtained by the proposed analytical model.The effects of axial force and structural damping loss factor on the resulting energy density are also investigated. It is found that the obtained energy density by the presented analytical model can asymptotically approach the results by the wave analysis based classical model. Hence, the presented analytical model can be employed to predict high frequency bending vibration of beams with high damping under constant axial loads. It is also observed that the larger axial force and structural damping loss factor make energy density attenuate more quickly from the driving point to the boundary. The resulting total energy increases with the increasing of the axial force, while decreases with the increasing of structural damping loss factor.