摘要
建立了常曲率壳结构的能量辐射传递模型,以预测高频径向点激励下结构的能量响应。基于Donnell-Mushtari薄壳理论推导了常曲率壳的振动控制方程,获得了波传播特性参数。利用驻项法近似求得了弯曲波输入功率辐射强度的方向函数。根据能量密度控制方程求得了能量密度和功率流强度的核函数。结构内部任一点的能量由实源产生的能量和边界虚源产生的能量叠加求得。数值算例计算了三种典型常曲率壳结构的能量响应,并与模态叠加法和振动传导法的计算结果进行了对比,验证了模型的准确性。最后讨论了频率、曲率半径及阻尼对常曲率壳结构能量响应的影响。结果表明:曲率半径和激励频率均会影响壳结构波传播特性和能量分布特征,x和y方向曲率半径差距越小,弯曲波传播的方向性越小;曲率半径越小,结构平均能量密度越大;频率越高,弯曲波传播的方向性越小,结构能量密度衰减速度越快。
Here,an energy radiation transfer model for a constant curvature shell structure was established to predict structure energy response under high-frequency radial point excitation.Based on Donnell-Mushtari thin shell theory,the vibration governing equation of a constant curvature shell was derived and wave propagation characteristic parameters were obtained.Directional function of input power radiation intensity of bending wave was approximately obtained using the stationary term method.According to energy density control equation,kernel functions of energy density and power flow intensity were obtained.Energy at any point inside shell structure was obtained by superimposing energy generated by real sources and energy generated by virtual sources at boundary.Energy responses of 3 typical constant curvature shell structures as numerical examples were calculated,and the results were compared to those obtained with the modal superposition method and vibration conduction method to verify the correctness of the proposed model.Finally,effects of excitation frequency,curvature radius and damping on energy response of constant curvature shell structure were discussed.The results showed that both curvature radius and excitation frequency can affect wave propagation characteristics and energy distribution features of shell structures;the smaller the difference between curvature radii in x and y directions,the smaller the directionality of bending wave propagation;the smaller the curvature radius,the larger the structure average energy density;the higher the excitation frequency,the smaller the directionality of bending wave propagation and the faster the decay rate of structural energy density.
作者
张宏宇
代成浩
黄进安
陈海波
ZHANG Hongyu;DAI Chenghao;HUANG Jin’an;CHEN Haibo(CAS Key Lab of Mechanical Behavior and Design of Materials,University of Science and Technology of China,Hefei 230027,China)
出处
《振动与冲击》
北大核心
2025年第9期88-98,共11页
Journal of Vibration and Shock
基金
国家自然科学基金(11772322
12172350)。
