Free vibration analysis of elastic metamaterial circular curved beams with locally resonant microstructures

In this study, in-plane free vibration of elastic metamaterial circular curved beams is investigated. The beams are made of three-dimensional periodic arrangement of the coated spherical particles embedded in a matrix. The two-step homogenization method is utilized to obtain the effective material properties of the beams. The Euler-Bernoulli curved beam theory with the assumption of an inextensible centerline is used to derive the governing equation of motion of the beams. Also, the finite element method (FEM) is utilized to compute natural frequencies of the beams. First, the numerical results are compared with those computed in the literature and also calculated via commercial FEM software, and then, a parametric study is performed to examine the influences of various design parameters on the natural frequencies of the curved beams. The obtained results show that the metamaterial curved beams can be used in diverse future applications.

Automated summary

This study investigates the in-plane free vibration of elastic metamaterial circular curved beams. The effective material properties of the beams are obtained through the two-step homogenization method. The governing equation of motion is derived using the Euler-Bernoulli curved beam theory. The results show that the metamaterial curved beams have diverse future applications.