Journal
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
Volume 43, Issue 2, Pages 167-184Publisher
SHANGHAI UNIV
DOI: 10.1007/s10483-021-2808-9
Keywords
nonlinear elastic wave metamaterial; nonreciprocal transmission; three-dimensional (3D) elastic wave; initial stress; O343; 5
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Funding
- National Natural Science Foundation of China [11922209, 11991031, 12021002]
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This work investigates the three-dimensional propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses. Analytical solutions for the fundamental wave and second harmonic with the quasi-longitudinal and quasi-shear modes are derived. Band gaps with initial stresses are obtained based on the transfer and stiffness matrices using the Bloch theorem. The tunability of nonreciprocal transmission by initial stress is discussed.
In this work, the three-dimensional (3D) propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated. The analytical solutions of the fundamental wave and second harmonic with the quasi-longitudinal (qP) and quasi-shear (qS(1) and qS(2)) modes are derived. Based on the transfer and stiffness matrices, band gaps with initial stresses are obtained by the Bloch theorem. The transmission coefficients are calculated to support the band gap property, and the tunability of the nonreciprocal transmission by the initial stress is discussed. This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.
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