Abstract
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 (qS1 and qS2) 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.
Highlights
Phononic crystals consist of two or more materials periodically, and can generate band gap of elastic waves[1,2,3,4,5]
Liang et al.[21,22] studied an acoustic diode consisting of a linear phononic crystal and a nonlinear layer to show the nonreciprocal transmission of the acoustic wave
We find that the initial stress σ101 makes the central frequency of the nonreciprocal transmission change and the gap width increase about 0.2 MHz
Summary
Phononic crystals consist of two or more materials periodically, and can generate band gap of elastic waves[1,2,3,4,5]. Elastic wave metamaterial is a new concept proposed in recent years, which brings extraordinary phenomena[8,9,10,11,12,13,14,15]. These periodic structures have the ability to control the wave propagation and vibration, which results in some advanced devices in practice. Combining the band gap in the linear phononic crystal and material nonlinearity breaks the reciprocity theorem of elastic waves. The effects of the initial stresses on propagation behaviors are discussed
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