多激励下结构反共振频率的计算和配置

Computation and assignment of antiresonant frequency of structure under multiple excitation forces

反共振频率是指结构在激励力作用下,某个自由度的振动响应为零的频率,其在结构的局部振动控制中具有重要意义。提出了一种结构在多激励作用下反共振频率的计算方法,并基于该计算方法和部分特征结构配置方法实现了结构在多激励作用下反共振频率的配置。基于结构的质量阵、刚度阵和激励力向量构造出一个线性矩阵,该矩阵的特征值即为多激励作用下结构的反共振频率。分别以线性面载荷激励的矩形板和多个激励下的弹簧质量系统为例,计算了反共振频率,并使用质量阵/刚度阵修改方法和附加简单振子方法配置了结构的反共振频率。数值结果验证了计算方法和配置方法的准确性。

Anti-resonance is of great significance in the local vibration control of structures.Generally,the antiresonance frequency refers to the frequency at which the vibration response of a degree of freedom is zero when a structure is subjected to an excitation force.In this paper,a method for computing the antiresonance frequency under multiple excitation forces is proposed.And the anti-resonance frequency can also be assigned with the calculation method and methods of partial eigenvector assignment.A linear ma-trix is constructed with the mass matrix,the stiffness matrix and the excitation force vector,so that the eigenvalue of the linear ma-trix is the antiresonance frequency under multiple excitation forces.In this paper,the antiresonance frequencies are calculated for a rectangular plate excited by linear surface loads and a spring-mass system under multiple excitations.In addition,the antiresonance frequency of the structures is assigned by structural modification and attaching a simple oscillator.Numerical results verify the accu-racy of the calculation method and configuration method.