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<p>In this work, the phenomenon of low frequency vibration absorption of a metamaterial-based structure consisting of a base structure as a beam attached with distributed spring-mass-damper subsystems acting as local resonators is presented. The current work examines the behavior of the system from an overall mass view point for the deployment of light-weight structures in automotive and aerospace applications. The base structure is modelled as Euler–Bernoulli beam having a large radius of curvature. The nonlinear dynamic model of the system is derived using extended Hamilton’s principle incorporating geometric nonlinearities. The free vibration analysis is performed and the influence of different parameters such as number of absorbers, absorber-beam mass ratio and location of absorbers on the bandgap phenomenon is investigated. Further, the nonlinear response of metamaterial beam under parametric excitation is investigated, and its ability to vibration attenuation is examined. The coupled governing equations are discretized using Galerkin’s principle and the method of multiple scales is used to obtain closed form steady state solutions. The system exhibits spring softening behavior and multiple vibration amplitudes along with shifting of response curve away from the resonant frequency, leading to effective vibration attenuation. The optimum range of number of absorbers, location of absorbers and absorber-beam mass ratio is established and the results obtained through nonlinear analysis of the system are in line with those of linear regime. Furthermore, it is demonstrated that by keeping vibration absorbers at the terminal end, absorber mass ratio between 0.2 and 0.3 range and number of absorbers between 5 and 10 leads to the widest bandwidth around tuning frequency. The linear results have been validated through FEA and numerical simulations, and close agreement is achieved for nonlinear outcomes. The obtained results in this study shall be helpful in designing lightweight metamaterial structures for engineering applications in automotive and aerospace industries.</p>

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Dynamic Response and Vibration Attenuation of Elastic Metamaterial Beam Under Parametric Excitations

  • 期刊论文

  • 发表日期：

    2026年4月27日

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  • Pravesh Kumar

摘要

In this work, the phenomenon of low frequency vibration absorption of a metamaterial-based structure consisting of a base structure as a beam attached with distributed spring-mass-damper subsystems acting as local resonators is presented. The current work examines the behavior of the system from an overall mass view point for the deployment of light-weight structures in automotive and aerospace applications. The base structure is modelled as Euler–Bernoulli beam having a large radius of curvature. The nonlinear dynamic model of the system is derived using extended Hamilton’s principle incorporating geometric nonlinearities. The free vibration analysis is performed and the influence of different parameters such as number of absorbers, absorber-beam mass ratio and location of absorbers on the bandgap phenomenon is investigated. Further, the nonlinear response of metamaterial beam under parametric excitation is investigated, and its ability to vibration attenuation is examined. The coupled governing equations are discretized using Galerkin’s principle and the method of multiple scales is used to obtain closed form steady state solutions. The system exhibits spring softening behavior and multiple vibration amplitudes along with shifting of response curve away from the resonant frequency, leading to effective vibration attenuation. The optimum range of number of absorbers, location of absorbers and absorber-beam mass ratio is established and the results obtained through nonlinear analysis of the system are in line with those of linear regime. Furthermore, it is demonstrated that by keeping vibration absorbers at the terminal end, absorber mass ratio between 0.2 and 0.3 range and number of absorbers between 5 and 10 leads to the widest bandwidth around tuning frequency. The linear results have been validated through FEA and numerical simulations, and close agreement is achieved for nonlinear outcomes. The obtained results in this study shall be helpful in designing lightweight metamaterial structures for engineering applications in automotive and aerospace industries.