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Abstract

Based on the Bloch theory and the flexural wave propagation theorem, the model for calculating the vibration response, sound radiation power and radiation efficiency of an acoustic metamaterial plate is established. The modal analysis of a bare pate and the plate attached to periodical lateral local resonators are developed to investigate the vibration regulation. In addition, the patterns of the sound radiation power and radiation efficiency of the plate attached to periodical lateral local resonators versus frequency are studied. The results show that 1) in a specific frequency range, the mean square velocity and the sound radiation power are far lower than those of the bare plate, which is due to the resonance of the lateral local resonator; 2) unlike the vibration response and sound radiation power, the radiation efficiency of the plate attached to periodical lateral local resonator is higher than that of the bare plate. The investigation of the plate attached to lateral local resonator in this paper lays a solid foundation for the practical engineering in the field of vibration suppression and noise reduction.

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Authors and contacts

Corresponding author:Wang Ting,wang_ting@hust.edu.cn

Funds:Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 52001131) and the Fundamental Research Funds for the Central Universities, China (Grant No. 3102020HHZY030008)

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参数名称	参数符号	参数取值
平板杨氏模量	E	$2.1 \times {10^{11}}{\kern 1 pt} {\kern 1 pt} {\text{Pa}}$
平板密度	$\rho $	$7850{\kern 1 pt} {\kern 1 pt} {\text{kg}}/{{\text{m}}^3}$
平板泊松比	$\nu $	0.3
平板厚度	h	0.003 m
垂向振子刚度	k₁	$1 \times {10^4}\;{\text{N}}/{\text{m}}$
垂向振子质量	m₁	0.005 kg
侧向振子刚度	k₂	$0.5 \times {10^4}\;{\text{N}}/{\text{m}}$
侧向振子质量	m₂	0.002 kg
四杆机构几何参数比	L/D	1
空气密度	${\rho _0}$	$1.25\;{\text{kg}}/{{\text{m}}^3}$
空气中声速	c	$343\;{\text{m}}/{\text{s}}$

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模态阶数	1	2	3	4	5	6	7
频率/Hz	75.8	164.6	214.6	303.3	312.6	445.8	451.4

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模态阶数	1	2	3	4	5	6	7
频率/Hz	70.8	147.8	179.9	200.95	201.7	206.3	206.4

模态阶数	7—11	12—130	131	132	133	134	135
频率/Hz	207.1—207.9	208.1—208.9	217.8	223.7	234.3	259.3	260.6

模态阶数	136	137	138	139	140—260	261	262
频率/Hz	267.9	268.0	269.1	269.9	270.0—271.1	278.6	282.0

模态阶数	263	264	265	266	267
频率/Hz	288.3	329.8	336.9	456.9	462.2

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Vol. 70, Issue 21 - 2021-11-05

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