Modal analysis of a lattice type metamaterial by modeling cell structures using Euler–Bernoulli beams

Abstract

Metamaterials have superior properties compared to materials found in nature and allow the tailoring of static and dynamic characteristics of the cell structures. In this study, the vibration characteristics of the sandwich plate systems composed of lattice beam structures are investigated and their behavior under various loading conditions is determined. In this context, a matrix-based solution method is developed to calculate the natural frequencies of the structure by assuming lattice elements as individual Euler–Bernoulli beams. The same structures are also analyzed with a commercial finite-element solver (ANSYS) to compare the results. In order to verify the results and determine the applicability of the proposed approach, an experimental study is conducted. Unit cell structures are additively manufactured with Stereolithography (SLA) and experimental modal analysis is performed using impact testing. Also, the amount of deflections on the structures under various loading conditions is determined experimentally by performing three-point bending tests on the plates. It has been concluded that approximate vibration characteristics of lattice-type metamaterial structures with various unit cell geometries can be determined in a short time by utilizing the matrix-based method without the need for any commercial software or performing complex experiments.