Analytical dispersion curves and bandgap boundaries for quadrilateral lattices

Abstract

The two-dimensional quadrilateral lattice structures are the most common periodic structures in industrial engineering application. This paper investigates the Bragg bandgap mechanism of classical quadrilateral periodic lattice structures. The explicit expressions of dispersion relations are obtained analytically and those with the eigenmodes corresponding to the same dispersion relation solution are connected to form the band structure. Unlike the existing works, it is the first to connect dispersion curves with the same eigenmodes, which explains the bandgap formation and transmission loss more reasonably. Four kinds of two-dimensional quadrilateral lattice structures are investigated to discuss the effects of shear force and mid-masses. The analytic expressions of bandgap boundaries are obtained and the influence of parameters including the mass ratio, tensile stiffness ratio and shear stiffness ratio on the bandgap boundaries is discussed.