Wave propagation properties of rotationally symmetric lattices with curved beams.

Abstract

In this study, we design a type of rotationally symmetric lattice with curved beams and investigate the wave propagation properties of the structure. The analytical model of the structure is established to obtain the mass and stiffness matrices first. Because the dimensions of the mass and stiffness matrices will become very large if the structure is meshed with a number of small elements, we introduce the symplectic solution method to overcome the above difficulties of solving the eigenvalue problem. The effects of geometrical parameters and slenderness ratios on the distributions of bandgaps and variations of group velocities are investigated. We also numerically investigate the dynamic wave dispersion behavior and the transient responses of displacement and transmission coefficients in lattices subjected to excitations. Excellent agreement is obtained between the results obtained by the symplectic solution method and numerical simulations. The special wave-attenuation property of this type of structure is demonstrated and validated through experimental testing. The measured transmission coefficients in lattices with different geometrical parameters and slenderness ratios are in good agreement with the numerical simulations. The work provides a method for calculating wave behaviors in lattices and obtains lower bandgaps and directional wave propagation.