求解含缺陷一维周期结构动力响应的高效算法

An efficient algorithm for the dynamic responses of one-dimensional periodic structures with defects

基于周期结构的动力特性和群理论,建立了一种高效求解含缺陷一维周期结构动力响应的数值方法。在求解结构动力响应时,高效求解结构对应的线性代数方程组最为关键。采用凝聚技术,可减小结构对应线性代数方程组的规模。基于周期结构动力系统中线性代数方程组的特性,通过一个小规模含缺陷结构和一维周期结构的响应分析,可得到含缺陷一维周期结构的动力响应。同理,一维周期结构的动力响应可通过一系列小规模结构的响应分析得到,且小规模结构的动力响应可基于群理论高效求解。数值算例表明,本文算法有较高的求解效率。

Based on the dynamic properties in periodic structure and group theory,an efficient numerical method for computing the dynamic responses of the one-dimensional periodic structures with defects is proposed.Efficiently solving the linear algebraic equations corresponding to the structure is a key issue for computing the dynamic responses.By using a condensation technique,the scale of the linear algebraic equations corresponding to the structure is reduced.By using the properties of the linear algebraic equations of the periodic systems,the solution of the dynamic response of a one -dimensional periodic structure with defects can be converted into that of the response analysis of a small-scale structure with defects and that of a one -dimensional periodic structure.Subsequently,the solution of the one-dimensional periodic structure can be converted into solutions of a series of small-scale structures.Then,the linear algebraic equations corresponding to the small-scale structures can be efficiently solved by group theory.Numerical examples are presented to demonstrate the efficiency of the proposed method.