The low-frequency resonant radiation characteristics of cylindrical liquid cavity with opening at both ends
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摘要:
为研究两端开口圆柱形液腔的低频谐振辐射特性, 建立了其在低频近似条件下的分布参数模型, 由电−力−声类比得到了等效振动模型, 给出了无声负载下的谐振频率表达式。随后利用“长度等效方法”建立了液腔在辐射条件下的自辐射等效模型和声场辐射等效模型, 给出了液腔的修正长度、谐振频率及指向性函数, 并讨论了弹性壁条件下的情况。结合有限元法研究了刚性(弹性)壁条件下, 圆管结构特征参量对液腔一阶谐振频率的影响规律, 给出了自辐射等效模型满足求解精度的条件, 并利用压电效应激励液腔一阶谐振, 讨论了其声场辐射特性。对比结果表明: 液腔一阶谐振频率的等效模型计算值与有限元仿真值符合较好, 误差低于5%; 液腔的修正长度为4
a /π , 液腔在一阶谐振下近似呈“∞”型指向性。此模型将两端开口圆柱形液腔类比为“液体圆棒”, 即可将液腔视作液腔类水声换能器结构的一部分, 提供了从分布参数模型角度分析此类换能器工作机理与辐射特性的理论支撑。Abstract:In order to study the low-frequency resonant radiation characteristics of the cylindrical liquid cavity with opening at both ends, the distribution parameter model under low-frequency approximation conditions is established. The equivalent vibration model is obtained from the electroacoustic analogy, and the resonant frequency expression without any load is given. Then the “length equivalent method” is used to establish the self-radiation equivalent model and the acoustic field radiation equivalent model of the liquid cavity under radiation conditions. The corrected length, resonant frequency and directivity function of the liquid cavity are given, and the situation under elastic wall conditions is also discussed. Combined with the finite element method, the influence of the characteristic parameters of the circular tube structure on the first-order resonant frequency of the liquid cavity under the condition of rigid (elastic) wall is studied, and the condition that the self-radiation equivalent model met the solution accuracy is given. At last, the piezoelectric effect is used to stimulate the first-order resonance of the liquid cavity, and its acoustic field radiation characteristics are discussed. The comparison results show that the equivalent model calculation value of the first-order resonant frequency of the liquid cavity is in good agreement with the finite element simulation value, and the error is less than 5%. The corrected length of the liquid cavity is 4
a /π , and the liquid cavity shows approximately “∞” type directivity under the first-order resonance. This method compares the cylindrical liquid cavity with the opening at both ends to a “liquid rod”, which can be regarded as a part of the structure of a transducer containing a liquid cavity. It can provide a theoretical support for analyzing the working mechanism and radiation characteristics of such transducers from the perspective of distributed parameter model.-
Key words:
- Liquid cavity /
- Distributed parameter model /
- Resonant frequency /
- Directivity
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表 1 圆柱形液腔的结构特征参量
圆管材质 开口半径$a$ (m) 圆管长度$l$ (m) 圆管厚度$t$ (m) 水的密度${\rho _0}$ (kg/m3) 水的流体声速${c_0}$(m/s) 水的体积弹性系数${K_s}$(Pa) 铝 0.098 0.258 0.007 998.2 1481.4 2.19 × 109 
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表 2 不同边界条件下液腔一阶谐振频率等效模型计算值与有限元仿真值对比
边界条件 流体声速 (m/s) 自辐射
修正
长度$\Delta l$ (m)圆管有效
长度${l_{\rm e}}$ (m)自辐射等效模型计算值 (Hz) 有限元仿
真值 (Hz)误差 (%) 等效振动模型
计算值 (Hz)刚性壁条件 1481.4 0.1248 0.3828 1935.1 1983.5 −2.44 2133.7 弹性壁条件 1081.4 1412.6 1422.7 −0.71 1557.6
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表 3 不同圆管材质下液腔一阶谐振频率等效模型计算值与有限元仿真值对比
圆管
材质杨氏
模量 (GPa)刚性壁条件 弹性壁条件 流体声
速
(m/s)等效模型计
算值 (Hz)有限元
仿真
值 (Hz)误差
(%)流体声速
(m/s)等效模型计算
值 (Hz)有限元
仿真
值
(Hz)误差
(%)铝 70 1481.4 1935.1 1983.5 −2.44 1081.4 1412.6 1422.7 −0.71 钛合金 116 1198.0 1564.9 1610.1 −2.81 结构钢 200 1295.8 1692.6 1761.5 −3.91
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表 4 液腔一阶谐振频率等效模型计算值和两种有限元仿真值的对比
边界条件 自辐射等效模型计算值 (Hz) 特征模态
有限元仿真值 (Hz)压电激励
有限元仿真值 (Hz)刚性壁条件 1935.1 1983.5 2050.0 弹性壁条件 1412.6 1422.7 1427.0
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