Energy bands of a periodic viaduct in out-of-plane vibration: Coupling with a half-space

Abstract

In this study, the periodic viaduct is used as an example to introduce a new type of phononic crystal structure: the "open"-type phononic crystal structure. A numerical model for analysis of the energy band of a periodic viaduct undergoing out-of-plane vibration is developed in this study. The most remarkable characteristic of the proposed model for the energy band of the periodic viaduct is that it can take into account the coupling between the periodic viaduct and the half-space soil. The viaduct considered in this study is assumed to be a regularly periodic arrangement of unit cells along its longitudinal direction. For simplicity, each unit cell is assumed to be consisted of a pile foundation, a pier and a horizontal beam. To obtain the compliances for the pile foundations, the pile-soil interaction problem is solved by the fictitious pile method first. Using the transfer matrix method and the obtained compliances for the pile foundations, the impedances for the piers are obtained. Based on the Bloch theorem and the transfer matrix method, the nonlinear polynomial eigenvalue equation for the periodic viaduct is derived using the impedance of the piers. Utilizing the obtained nonlinear eigenvalue equation, the approximate linear eigenvalue equation for the periodic viaduct is obtained and numerical results for the energy bands of the periodic viaduct are presented. Numerical results of this paper show that for the out-of-plane vibration of the periodic viaduct, there are three kinds of lattice waves propagating in the periodic viaduct. Moreover, in a low frequency range, all three lattice waves are evanescent, which will lead to the localization of lattice waves in the periodic viaduct.