A methodology for direct identification of characteristic wave-types in a finite periodic dual-layer structure with transverse connection

In a companion paper the phenomenon of flexural-longitudinal wave coupling in an infinite dual-beam periodic structure with transverse connection is investigated. The remarkable finding obtained that there was such a periodic structure which conveyed fundamentally three symmetric and three antisymmetric characteristic coupled waves. In this paper, a methodology is proposed to realize the direct identification of characteristic waves from the responses of a finite periodic structure. This represents a considerable departure from traditional methods, in which the assumption of infinite dimension of a periodic structure is implied. It is the inverse process of the traditional studies which obtain characteristic wave-types based on the assumption and then continue the studies with the wave-types. A general expression for the individual transition matrix of one periodic element is defined and derived from two adjacent junction-mobilities of a finite periodic structure. A common transition matrix for all elements is then constructed using responses based on the mathematical analysis of the relations between responses or junction-mobilities, individual transition matrices and characteristic wave-types. Finally, a specific experimental structure and approach was designed to extract the characteristic waves from the responses. All the symmetrical and antisymmetrical characteristic wave-types, except the pairing of near-field wave-types, are extracted from the common transition matrix of the finite periodic structure, demonstrating the feasibility of the method presented.