包裹型幂指厚度声子晶体设计与宽频减振特性模拟

Design of wrapped phononic crystals with exponentially-varying thickness and simulation of broadband vibration reduction characteristics

摘要

针对船舶设备及板结构的宽频减振难题，本文弥补传统声子晶体低频带隙窄、带隙覆盖率低的不足，提出一种融合局部共振与声学黑洞(ABH)效应的包裹型幂指厚度轻质声子晶体结构。该结构在幂指数变厚度对称钢板内嵌入空心铅散射体；借助有限元法求解其能带结构与振动传输特性，分析减振性能。结果表明：该结构在 0～1400 Hz 内存在两条完全带隙，总带宽 1158.68Hz(覆盖率为 82.76%)，振动传输损耗最高达 125dB；带隙机理为空心散射体扭转效应与声学黑洞的能量汇聚作用发生耦合，同时受基体刚度梯度的调控；增大幂指数高度 h_A或散射体高度 h₂可拓宽带隙，而增加幂指数长度 l_A会使带隙变窄；声子晶体夹芯板模型的振动衰减峰值约为 180dB，较非幂指数结构提升约 20dB，证实了幂指数厚度设计在宽频减振中的显著优势。本文设计的声子晶体及声子晶体夹芯结构为船舶宽频振动控制问题提供了新思路。

Abstract

Aiming at the problem of broadband vibration damping of ship equipment and plate structures, this paper overcame the drawbacks of conventional phononic crystals characterized with narrow low-frequency bandgaps and low band-gap coverage, and proposed a lightweight wrapped phononic crystal structure with exponentially-varying thickness that integrated local resonance and acoustic black hole (ABH) effects. The structure embedded hollow lead scatterers in symmetric steel plates with exponentially-varying thickness. The finite element method was adopted to calculate its band structure and vibration transmission characteristics, and the vibration reduction performance was analyzed. Results show that the structure possesses two complete bandgaps within 0～1400 Hz, with a total bandwidth of 1158.68Hz (band-gap coverage of 82.76%), and the maximum vibration transmission loss reaches 125dB. The bandgap mechanism involve coupling between hollow scatterer torsion and acoustic black hole (ABH) structure energy convergence, along with matrix stiffness gradient regulation. Increasing the exponential height h_A or scatterer height h₂ can broaden the bandgap, whereas increasing the exponential length l_A narrows the bandgap width. The vibration attenuation peak of the phononic crystal sandwich plate model is approximately 180dB, which is about 20dB higher than that of the non-exponential structure. This verifies the remarkable advantages of the exponentially-varying thickness design in broadband vibration attenuation. The phononic crystal and its sandwich structure designed in this paper provide a new idea for broadband vibration control of ships.

关键词

包裹型声子晶体 / 幂指厚度 / 局部共振机理 / 声学黑洞效应 / 宽频减振 / 有限元模拟

Key words

wrapped phononic crystal / power-exponent thickness / local resonance mechanism / acoustic black hole effect / broadband vibration reduction / finite element simulation

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基金资助

国家重点研发计划重点专项(2024YFE0101200)