Multi-mass-spring model and energy transmission of one-dimensional periodic structures

This paper deals with a classical problem on a linear elastic lattice. A multi-mass-spring model is proposed to build the unit cell. Based on this multi-mass-spring model, a detailed investigation on the band of frequency gaps of one-dimensional periodic structures is conducted. A unified formulation to study the band structures of one-dimensional periodic structures is obtained. To determine the bound frequencies of the bands of frequency gaps, a very simple method without investigating the dispersion curves is proposed based on the modal analytical method. The method presented in this paper is applicable to general cases and is much more convenient than that proposed by other related investigations. In addition, the dynamic property of a finite periodic structure is investigated from the view of energy input, energy distribution, and interactions between the external excitation and the finite periodic structure, from which the energy flow pattern is illustrated clearly.