基于声电类比的低频消音结构优化设计

Optimization design of low-frequency silencing structure based on acoustic-electric analogy

基于声电类比,设计了与电滤波器性能相似的低频消音结构,并结合传递矩阵法和模拟退火法,构造了声学结构的优化设计策略。首先,采用归一化方法,以四阶切比雪夫高通电滤波器为基准,设计了电学带阻滤波器;然后,基于声电类比,将电路中的电感电容转换为声学结构中的细管和圆柱腔,构造了消音结构原型,并利用传递矩阵法,建立其数学模型,推导声波传递损失表达式;最后,结合声学结构的数学模型和模拟退火法,以有效衰减带宽最大为目标,以消音结构的尺寸参数为变量,对原型结构进行优化设计。结果表明:基于声电类比,能获得合理的消音结构原型,克服了仅依靠经典消音结构进行设计的局限;结合推导的传递损失数学模型和模拟退火法,对消音结构原型进行参数优化,能显著提高其消音效果,表现在传递损失超过20 dB的带宽拓宽至410~2 165 Hz,是优化前带宽的202%,特别是优化后的结构克服了原型结构在466~537 Hz频率内不能实现有效消音的缺陷,获得了连续的大跨度有效带宽,且传递损失曲线平均增幅达22.8%。

Here,based on acoustic-electric analogy,a low-frequency silencing structure with similar performance to an electric filter was designed,and an optimization design strategy for acoustic structure was constructed by combining transfer matrix method and simulated annealing method.Firstly,using the normalization method,based on the fourth order Chebyshev high pass filter,an electrical band-stop filter was designed.Then,based on acoustic-electric analogy,inductance and capacitance in a circuit were converted into tubules and cylindrical cavities in an acoustic structure,and a prototype of silencing structure was constructed.Its mathematical model was established using transfer matrix method to derive the expression of sound transmission loss.Finally,combining mathematical model of acoustic structure and simulated annealing method,taking maximizing effective attenuation bandwidth as the objective and size parameters of silencing structure as variables,the optimization design was performed for the prototype structure.The results showed that based on acoustic-electric analogy,a reasonable prototype of silencing structure can be obtained to overcome the limitation of relying solely on classical silencing structure for design;combining the derived transmission loss mathematical model and simulated annealing method,parametric optimization is performed for silencing structure prototype to significantly improve its silencing effect,its bandwidth with transmission loss exceeding 20 dB is widened to 410-2165 Hz which is 202%of the bandwidth before optimization;especially,the optimized structure overcomes the defect of the prototype structure being unable to realize effective silencing in the frequency range of 466-537 Hz and obtains a continuous large-span effective bandwidth,and the average increase in transmission loss curve reaches 22.8%.