基于傅里叶级数展开的多跨耦合板功率流研究

Power flow analysis of a multi-span coupled plate using Fourier series expansion

提出了一种基于傅里叶级数展开求解水平多跨耦合板振动响应的解析方法。建立了多跨耦合板模型,使用傅里叶级数对单点激励力和未知耦合弯矩进行了表达,并利用耦合边的角速度连续性条件,实现了耦合边耦合弯矩的求解以及各子板任意点响应的计算。根据功率流理论,得到了激励点输入功率流以及各耦合边传递功率流的计算公式。取三跨耦合板模型作为理论仿真对象,使用ANSYS有限元软件验证了理论模型的正确性。利用获得的理论模型,分析了阻尼和激励点位置对结构输入和传递功率流的影响,结果表明对激励板进行阻尼处理以及在板的中心位置激励,能有效抑制结构功率流的输入和传递。

An analytical method solving the vibration response of a multi-span coupled plate using Fourier series expansion was proposed.A model for a multi-span coupled plate was built,Fourier series expansions of a point excitation force and the unknown coupled moment were obtained,based on angular velocity continuity conditions of coupling sides,their coupled moments could be achieved,and then it was convenient to solve the vibration response of any point of all sub-plates.According to the power flow theory,the expressions of the input power flow of the excitation point and the transferred power flow of the coupling sides were deduced.A three-span coupled plate model was taken as a theoretical simulation object,and checked with the finite element software ANSYS.Using this theoretical model,the effect of damping and excitation locations on the input power flow and the transferred one was analyzed.The results indicated that the damping-treatment on the excited plate and the excitation at the center of the plate can effectively suppress the input and transferred power flows.