Journal
PHYSICS LETTERS A
Volume 381, Issue 13, Pages 1111-1117Publisher
ELSEVIER
DOI: 10.1016/j.physleta.2017.01.036
Keywords
Acoustic metamaterial; Helmholtz resonator; Nonlinear effects; Perturbation method
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Funding
- National Natural Science Foundation of China [61571222, 11104142, 11474160]
- Natural Science Foundation of Jiangsu Province, China [BK20161009]
- Six Talent Peaks Project of Jiangsu Province, China,
- Qing Lan Project of Jiangsu Province, China
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We theoretically investigate the nonlinear effects of acoustic wave propagation and dispersion in a cylindrical pipe with periodically arranged Helmholtz resonators. By using the classical perturbation method in nonlinear acoustics and considering a nonlinear response up to the third-order at the fundamental frequency, the expressions of the nonlinear impedance Z(NHR) of the Helmholtz resonator and effective nonlinear bulk modulus B-neff of the composite structure are derived. In order to confirm the nonlinear properties of the acoustic metamaterial, the transmission spectra have been studied by means of the acoustic transmission line method. Moreover, we calculate the effective acoustic impedance and dispersion relation of the system using the acoustic impedance theory and Bloch theory, respectively. It is found that with the increment of the incident acoustic pressure level, owing to the nonlinearity of the Helmholtz resonators, the resonant frequency coo shifts toward the lower frequency side and the forbidden bandgap of the transmission spectrum is shown to be broadened. The perturbation method employed in this paper extends the general analytical framework for a nonlinear acoustic metamaterial. (C) 2017 Elsevier B.V. All rights reserved.
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