Complete vibration band gap characteristics of two-dimensional periodic grid structures

Abstract

In this article, the spectral element method combined with Bloch theorem is applied to calculate complete vibration band gap characteristics of two-dimensional periodic grid structures, which is verified by structural vibration transmission results based on spectral element method and finite element method. According to the differential equation of motion, complete spectral stiffness matrix of beam element is established at first, then stiffness matrix of grid structure can be obtained by coordinate transformation and assembly method, so as to form governing equation of motion based on Bloch boundary conditions. The band gap characteristics of periodic structures can be calculated by solving motion equation. Through band gap distribution analysis of two-dimensional periodic grid structures, the dispersion relations of different unit arrangements and effects of material and structural parameters on band gap characteristics are obtained which can be applied to acoustic design or vibration and noise reduction areas.