结构非比例阻尼矩阵的建模和识别

Modeling and Identifying of Non-Proportional Damping of Structures

阻尼是结构动力学分析的重要参数 ,对阻尼矩阵的估计一直是动力学建模的难点。通常的做法是假设结构中的阻尼满足某种数学模型 ,然后利用实验数据对模型参数进行识别。本文针对目前工程上普遍接受的非比例阻尼模型—— Liang模型 ,在粘性阻尼振动系统的实空间解耦方法的基础上 ,通过类似于矩阵 Kronecker积和列展开的方法 ,建立了非比例阻尼矩阵的识别方法及在实验模态不完备情况下的数值迭代算法。文中算例表明了本文方法是正确和可行的。

Damping of structures is an important factor in structural dynamic analysis. It is very difficult to describe the damping property of the structures precisely. The common method to get damping model is to identify the parameters of the mathematical damping model by using the test mode information. The proportional damping matrix is one of the most useful damping models used in the numerical calculation for structural vibration, but cannot well represent the real phenomenon caused by damping pro-perty in structures. The non-proportional damping model is developed and improved during the past decades. A method is developed to identify the non-proportional damping matrix of structures. The damping matrix is based on “Liang’s damping model” which can correctly simulate the real structural damping more. Based on the test mode information, the uncoupled modal damping and modal stiffness can be obtained by using the decoupling method in real subspace. Then the proportional and the non-proportional parts of the damping matrix can be identified from the uncoupled modal damping and modal stiffness. A numerical example proves the feasibility of the method.