耦合梁中高频抖动的行波分析与主动控制

为研究中高频扰动下耦合梁结构的动力学响应与主动控制，基于Timoshenko梁理论，考虑梁中转动惯量和剪切变形的影响，采用行波方法分别建立梁结构纵向运动、弯曲运动的单元模型与结点散射模型，进而获得耦合梁的行波动力学模型及其精确的中高频抖动响应；引入“功率流”的分析思想，并以此为目标函数，优化得到了最优控制力的大小与相位，然后对结构施加最优控制力，实现耦合梁结构的功率流主动控制。在此基础上，进行数值仿真分析，并与Euler-Bernoulli梁理论计算结果进行对比。结果表明，采用行波方法计算耦合梁结构的动力学响应准确可靠；Timoshenko梁模型较Euler-Bernoulli梁模型在中、高频段更为精确，且更接近工程实际；功率流主动控制可以明显降低耦合梁结构全频域内的抖动，验证了基于行波方法功率流主动控制的正确性与有效性。

Travelling Wave Analysis and Active Control of Jitter in the Median and High Frequency Regions for Coupled Beam

To study dynamic response and active control of coupled beam structure under the influence of disturbance in the median and high frequency regions, based on the Timoshenko beam theory, considering the influence of rotatory inertia and shear deformation of beam, the member models of the longitudinal, bending motion and the junction scattering model are established by travelling wave method for beam structure, respectively. Then the travelling wave kinetic model of coupled beam is built and the accurate dynamic response is obtained in the median and high frequency regions. The thought of “power flow” is introduced, which is used as the objective function, and optimized control force amplitude and phase are obtained by optimization algorithm, which are applied to the coupled beam structure. Ultimately, active control of power flow for coupled beam structure is realized. On this basis, the numerical simulation is made, and simulation results are compared with those obtained by Euler-Bernoulli beam theory. The results show that the dynamic response of coupled beam structure by travelling wave method is accurate and reliable; Timoshenko beam model is more accurate than Euler-Bernoulli beam model in the median and high frequency regions, and is more closer to practical engineering；Active control of power flow can efficiently reduce the jitter of the coupled beam structure in the whole frequency domain, and it proves that active control of power flow by travelling wave method is correct and valid.