Modeling and experimental study of non-reciprocal acoustic energy transfer in vibro-acoustic Duffing oscillator

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Abstract

Mechanisms for the nonreciprocal transmission of acoustic energy and the construction of non-reciprocal vibro-acoustic systems have been subjects of intense research in recent years. An experimental study of acoustic nonreciprocal transmission in an experimental system with a nonlinear membrane and two acoustic cavities of different sizes is reported. The membrane can be simplified into a Duffing oscillator, and the asymmetry of the frequency response function of this oscillator is used to realize the non-reciprocal transmission of acoustic energy. The asymptotic solution of the frequency response function of the nonlinear membrane is obtained by the complexification-averaging method. The theoretical simulation results accord well with the experimental results. The results show that the experimental system has a maximum non-reciprocal quantity of 9.1 times in theory, 4.3 times in the experiment, and the normalized frequency bandwidth of the jump phenomenon region is up to 0.56. The research results reveal the mechanism of non-reciprocal transfer of acoustic energy in the experimental system and demonstrate a new way to realize the asymmetric transfer of acoustic energy in an acoustic system with an air medium.

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Authors and contacts

Corresponding author:Lu Huan-Cai,huancailu@zjut.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant Nos. 51875522, 51975525), and the International Science and Technology Cooperation Foundation for “One-Belt and One-Road” of Zhejiang Province, China (Grant No. 2018C04018).

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参数名称	符号
上声腔边长	${L_1}$
下声腔边长	${L_2}$
上声腔体积	${V_1}$
下声腔体积	${V_2}$
薄膜半径	$R$
薄膜厚度	$h$
薄膜面积	${S_{\rm me} }$
薄膜质量	${m_{\rm me} }$
薄膜表面附加空气质量	${m_{\rm{a}}}$
实验测得薄膜的一阶共振频率	${f_1}$
无预应力的薄膜共振频率	${f_0}$
薄膜密度	${\rho _{\rm me} }$
薄膜杨氏模量	$E$
薄膜线性刚度	${k_1}$
薄膜立方非线性刚度	${k_3}$
薄膜泊松比	$\upsilon $
薄膜阻尼系数	$ \eta $
薄膜中心点横向位移	${\dot q_{\rm me} }$
薄膜平均速度	${\bar v_n}$
空气声速	$ {c_0} $
空气密度	${\rho _{\rm{a}}}$
激励频率	${\omega _{\rm{S}}}$
源强幅值	${Q_{\rm{s}}}$
非互易量	$NR$

DownLoad: CSV

参数名称	符号	数值	单位
上声腔边长	${L_1}$	0.2	m
下声腔边长	${L_2}$	0.3	m
薄膜半径	$R$	0.017	m
薄膜厚度	$h$	1×10^–4	m
薄膜密度	${\rho _{\rm me} }$	980	kg/m³
薄膜杨氏模量	$E$	2.1	MPa
薄膜泊松比	$\upsilon $	0.49
实验测得的薄膜线性固有频率	$ {f_1} $	77	Hz
薄膜立方非线性刚度	${k_3}$	3.50×10⁶	N/m³
薄膜阻尼系数	$ \eta $	8×10^–5	s^–1
空气声速	$ {c_0} $	340	m/s
空气密度	${\rho _{\rm{a}}}$	1.29	kg/m³

DownLoad: CSV

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Vol. 71, Issue 10 - 2022-05-20

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