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research-article

Analysis of Dynamic Behavior of the Finite Elastic Metamaterial-Based Structure with Frequency Dependent Properties

[+] Author and Article Information
Xiaohui Shen

School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907, USA; Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA
shen128@purdue.edu

C T Sun

School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907, USA
sun@purdue.edu

Miles Barnhart

Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA
mvbxcf@mail.missouri.edu

Guoliang Huang

Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA
huangg@missouri.edu

1Corresponding author.

ASME doi:10.1115/1.4038950 History: Received June 27, 2017; Revised January 04, 2018

Abstract

For practical applications of the elastic metamaterials, dynamic behavior of finite structures made of elastic metamaterials with frequency dependent properties are analyzed theoretically and numerically. First, based on a frequency dependent mass density and Young's modulus of the effective continuum, the global dynamic response of a finite rod made of elastic metamaterials is studied. It is found that due to the variation of the effective density and Young's modulus, the natural frequency distribution of the finite structure is altered. Furthermore, based on the spectral approach, the general wave amplitude transfer function is derived before the final transmitted wave amplitude for the finite layered metamaterial structure with decreasing density is obtained using the mathematical induction method. The analytical analysis and finite element solutions indicate that the increased transmission wave displacement amplitude and reduced stress amplitude can be controlled by the impedance mismatch of the adjacent layers of the layered structure.

Copyright (c) 2017 by ASME
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