非经典阻尼系统的精确解

提出了一种求解非经典阻尼系统的通用的解析方法,分别给出了多自由度非比例阻尼系统的自由振动和强迫振动的实数解的表达式.自由振动归结为求解一个线性代数方程组,把系统分为亚临界阻尼情况、退化阻尼情况和部分退化阻尼情况分别进行了讨论.对于强迫振动,研究了系统的稳态解和瞬态解,求解过程也归结为求解代数方程组.在几个算例中,把得到的精确解和数值计算结果进行了比较,两者吻合得很好.该方法为非比例阻尼系统的求解提供了一条有效的途径.

Exact solution of non classical damping systems

An analytical method to solve the non-classical damping system is presented. Real exact solutions of the free vibration and forced vibration of multi-degree-of-freedom systems with non-proportional viscous damping are given respectively. In virtue of solving simple linear algebraic equations,the solutions of the free vibration in sub-critical damping, entirely and partially degenerate damping may be obtained.For the forced vibration, the problem of solving the steady-state and transient vibration can be turned into solving the linear algebraic equations too. The examples show that the analytical solutions obtained by this method agree well with the solutions obtained by the numerical method.Thus,this method is very effective to analyze the non- proportional damping system.