含复阻尼振动系统的对偶原则及其数值方法研究

Dual Principle of Oscillation Systems with Complex Damping and Its Numerical Method

研究了运用复阻尼理论时应遵循的对偶原则 ,针对激励力无法用解析表达式写出的多自由度复阻尼振动系统 ,提出了按三角插值法和常数项法配置对偶项的方法 ,分析了含复阻尼振动系统运动方程的数值解及其稳定性 ,结合弹性连杆机构动力学分析方法 ,以铝基阻尼合金材料的曲柄摇杆机构为实例 ,按复阻尼理论对其动力学特性进行了分析计算 ,所得结果表明所提方法是正确的。

In describing the dissipative capacity of structural material, the complex damping theory has wide application due to the better agreement between theoretic analysis and experiment. However, difficulty exists in solving the vibration equation with complex damping. In this paper the dual principle of complex constitutive theory is developed. Dual term configuration methods based on trigonometric interpolate and constant term methods are put forward, in view of the situation that the exciting forces cannot be expressed analytically in a multi-degree of freedom system. For solving the complicated vibration equations containing complex damping, a numerical method using iteration procedure to improve the solution accuracy is adopted. Furthermore, the numerical stability and improvement measures are discussed. As an example, the dynamic properties of a crank-rocker mechanism with damping alloy parts are analyzed. The results show that the presented method is correct.