结构阻尼时域本构模型及其应用

阻尼合金作为一种新型结构功能材料在不少领域已获应用，由于其阻尼值较大且随频率呈复杂交化关系，传统的线性粘性阻尼理论或经典的非频变结构阻尼理论难以精确地描述其耗能行为。本文应用粘弹性阻尼理论，根据阻尼合金储能模量和损耗因子在频域的实测数据．应用最优化方法拟合出标准线性体模型中的本构参数；根据积分形式的三参量本构关系和变形体虚功原理，推导出了有限元形式的动力学方程；讨论了三参数初值的选取；对包含卷积积分的有限元动力学方程通过数学推导将其化为三阶线性微分方程组，再转化为标准状态变量方程，应用数值求解。数值计算实例证明了所提方法的正确和有效性。

Structural damping time domain constitution and its application

As a kind of new structural and functional material, the damping alloy has been applied in many areas. Because the internal damping of damping alloy is high and varies nonlinearly with the vibration frequency, it is difficult to describe its energy dissipation behavior accurately by the viscous damping theory or classical structural damping model with constant loss factor. In this paper, the standard three parameters model of viscoelastic mechanics is introduced as the constitutive equation for damping alloy. Based on the experimental data of energy storage module and loss factor for a specific kind of damping alloy in a given frequency span, these three parameters are confirmed in using an optimization algorithm. The finite element dynamic equations are derived through the established three parameters constitution in integral form and the virtual work principle. The established finite element equations containing convolution integration are transformed into third order ordinary differential equations, and then to be transformed into standard state variable model. Numerical examples are given to show the effectiveness of the present method in studying dynamic characteristics of structure and machines containing damping alloy components.