基于行波法的多板耦合结构振动功率流研究

通过引入局部坐标,离散波幅系数矩阵,组装状态向量矩阵,建立了离散板的行波法通用表达式,该表达式的提出可以将行波法的研究对象由简单结构推广到多板耦合结构。自编行波法MATLAB程序计算结构的稳态响应,将行波法半解析结果与有限元数值结果进行对比,验证了提出的行波法通用表达式计算多板耦合结构的有效性、高效性。应用行波法分别求解经典薄板理论和Mindlin板理论的振动控制方程,计算耦合结构的主动功率流和被动功率流,结果表明:在全频范围内,面内剪切和旋转惯量对主动功率流和被动功率流有很大影响,在进行功率流主动控制时应尽可能采用厚板理论。损耗因子的增加可以有效减少共振频率范围附近的被动功率流峰值,但对其他频率范围内的被动功率流峰值影响不大。

Vibration power flow of multi-plate coupled structures based on traveling wave approach

The general expressions of the traveling wave approach for a discrete plate were established, by introducing local coordinates, discrete wave amplitude coefficient matrix, and assemble state vector matrix. These general expressions led to that the study object of the traveling wave approach was extended from simple plates to multi-plate coupled structures. Structural steady vibration responses calculated with the self-compiled program of the traveling wave approach were compared with the numerical results with the finite element method. This traveling wave approach semi-analytical solution was verified to be effective and convenient. Based on the classical thin plate theory and Mindlin plate theory, respectively, the traveling wave method was used to compute active power flow and passive power flow of multi-plate coupled structures. The calculated results showed that within the whole frequency range, shear and rotary inertia inplane have a great influence on active power flow and passive power flow; when conducting active power flow control, using the thick plate theory is recomended as far as possible; increase in loss factor can effectively reduce the peak value of passive power flow near the frequency range of resonances, but this influence is not large within the other frequency range. 