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

This paper proposes an efficient algorithm for computing the dynamic responses of one-dimensional periodic structures and periodic structures with defects. It uses the symmetric property of the periodic structure and the energy propagation feature of the dynamic system to analyze the algebraic structure of the matrix exponential corresponding to one-dimensional periodic structures and periodic structures with defects. By using the special algebraic structure of this matrix exponential and the precise integration method, an efficient and accurate algorithm is proposed for computing the matrix exponential corresponding to one-dimensional periodic structures or periodic structures with defects. Hence an efficient method is presented for computing the dynamic responses of one-dimensional periodic structures and periodic structures with defects. It is accurate, efficient and saves memory.