一般阻尼结构的模态阻尼优化设计

研究了一般阻尼结构的模态阻尼优化设计方法。该方法主要包含两方面的内容，一方面是在给定阻尼器个数和系数的条件下，研究如何找到最佳的安装位置，使结构的某几阶模态阻尼比达到最大；另一方面是在给定某几阶模态阻尼比的目标值的条件下，确定最佳安装位置和阻尼器系数．使结构的模态阻尼比达到指定的目标值。从模态阻尼与结构参数的关系式出发，利用类似于kronecker积展开的方法，导出模态阻尼比对于附加阻尼器的位置灵敏度表达式，从而确定阻尼器的最佳安装位置。对于第二类问题，通过拟牛顿法中的Broyden方法进行迭代，最终确定阻尼器的系数。本文方法简单，易于与有限元方法结合应用到工程实际结构。文中的算例证明了本文方法的可靠性和有效性。

Modal damping optimization for general damped structures

A modal damping optimization method for general damped structures is developed in this paper. The aim of this method is that by attaching dampers at the optimal locations and fixing the optimal damping coefficients of the structures, the modal damping factors of the systems are made to be at the given target values. Based on the relationship between modal damping factors and structure parameters, the expressions of the location sensitivities of modal damping factors relative to the dampers are derived, and through which the optimal locations of the dampers of the structures are ultimately determined. And by using Broyden iterative method, the appropriate damping coefficients are then obtained. The advantage of the method is that it can be easily applied to engineering structures which can be discreted by finite-element-method. Finally, the validity of the method is demonstrated through numerical examples presented in the present paper.