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The anti-plane vibration of a quartz plate with an additional partial non-uniform mass layer for acoustic wave sensing

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Abstract

The anti-plane vibration of a quartz plate having an additional partial non-uniform mass layer is solved by ignoring the effect of small c 56 in comparison with other elastic constants. This analysis is based on the trigonometric series solution, and the convergence is examined. Numerical simulation is conducted for several different types of layers of different thicknesses using linear, cosine, and quadratic functions. The frequency spectrums, in addition to the length and mass fraction of the layer, are discussed separately. Compared with the homogeneous mass layer, the non-homogeneous layer with greater inertia leads to earlier appearance of the higher modes and more modes trapped under the same condition. Especially, there is no energy trapping in the plate with a fully covered uniform mass layer. However, this kind of energy trapping can be obtained again when the surface is non-uniform for some cases.

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Authors and Affiliations

  1. State Key Laboratory for Mechanical Structure Strength and Vibration, School of Aerospace, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Peng Li & Feng Jin

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  1. Peng Li
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  2. Feng Jin
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Correspondence to Feng Jin.

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Li, P., Jin, F. The anti-plane vibration of a quartz plate with an additional partial non-uniform mass layer for acoustic wave sensing. Acta Mech 224, 1397–1414 (2013). https://doi.org/10.1007/s00707-013-0812-7

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  • DOI: https://doi.org/10.1007/s00707-013-0812-7

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