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Realizing passive direction-bias for mechanical wave propagation using a nonlinear metamaterial

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Abstract

The possibility of realizing amplitude-activated passive direction-bias in longitudinal elastic wave propagation using a nonlinear acoustic metamaterial is demonstrated. Applying the method of multiple scales, approximate analytical solutions are derived for the dispersion curve and bandgap shifts due to the presence of nonlinear hardening local oscillators within the metamaterial using its lumped parameter effective-mass model. The configuration for a structural waveguide consisting of a tuned combination of a nonlinear and a linear acoustic metamaterial that takes advantage of these shifts to produce amplitude-activated direction-bias in propagation was postulated and verified using discrete element simulations. A numerical routine to generate root profile geometries that enable contact-based hardening response in tip-loaded cantilever beam resonators was developed and implemented. Utilizing a hybrid fabrication process involving additively manufactured and machined components, a prototype test article was constructed. Experiments using a structural waveguide test rig verify the existence and extent of bandgaps and provide evidence for the passive direction-bias phenomenon. Follow-on investigations on configurations with different types of nonlinearities could pave the way for development of additional passive acoustic wave manipulation devices with enriched dynamics.

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Acknowledgements

This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.

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Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Oklahoma State University, 218, Engineering North, Stillwater, OK, 74078, USA

    Prateek P. Kulkarni & James M. Manimala

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  1. Prateek P. Kulkarni
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  2. James M. Manimala
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Correspondence to James M. Manimala.

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Appendix: List of symbols

Appendix: List of symbols

m :

Mass

k :

Stiffness

\({k}_{{n}}\) :

Nonlinear stiffness parameter

u :

Displacement

\(\omega \) :

Frequency

\(\alpha \) :

Mass ratio

\(\beta \) :

Stiffness ratio

\(\tau \) :

Non-dimensionalized time

\(\varepsilon \) :

Perturbation parameter

\(\varGamma \) :

Nonlinearity parameter

q :

Wave number

\(\mu \) :

Non-dimensionalized wave number

L :

Lattice length

\({A}_{1 }\) :

Amplitude of harmonic wave solution

D*:

Transmissibility

AM:

Acoustic metamaterial

LRAM:

Locally resonant acoustic metamaterial

NLAM:

Nonlinear acoustic metamaterial

DBWG:

Direction-biased wave guide

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Kulkarni, P.P., Manimala, J.M. Realizing passive direction-bias for mechanical wave propagation using a nonlinear metamaterial. Acta Mech 230, 2521–2537 (2019). https://doi.org/10.1007/s00707-019-02415-w

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  • DOI: https://doi.org/10.1007/s00707-019-02415-w

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