Theoretical investigation of the simultaneous resonance of a cylindrical bubble under triple-frequency acoustic excitation

IF 3.5 3区工程技术 Journal of Hydrodynamics Pub Date : 2025-02-20 DOI:10.1007/s42241-025-0107-1

Jia-xin Yu, Zhi-hao Liu, Jin-xin Luo, Xiang-qing Zhang, Zheng-gui Li, Yu-ning Zhang

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Abstract

In the present paper, the simultaneous resonance of a cylindrical bubble under triple-frequency acoustic excitation is investigated theoretically. Specifically, based on the multi-scale method, the dimensionless oscillation equations and the second-order analytical solutions of the primary-subharmonic-subharmonic (PRI-SUB-SUB), primary-superharmonic-superharmonic (PRI-SUPER-SUPER) simultaneous resonances are obtained. Based on the analysis of the frequency response, the nonlinear dynamic behavior of the cylindrical bubble and its influencing factors are analyzed. The primary conclusions include: (1) Under triple-frequency acoustic excitation, the frequency response of PRI-SUB-SUB presents a single peak, and that of PRI-SUPER-SUPER presents two peaks. (2) The polytropic exponent affects both the peak value and position of the resonance peak in the frequency response. (3) The unstable region in frequency response curve of the simultaneous resonance is significantly affected by the total amplitude and equilibrium radius, presenting a positive correlation.

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三频声激励下圆柱形气泡同步共振的理论研究

本文从理论上研究了三频声激励下圆柱形气泡的同时共振。具体而言，基于多尺度方法，得到了原-次谐波-次谐波（PRI-SUB-SUB）、原-超谐波-超谐波（PRI-SUPER-SUPER）同步共振的无量纲振荡方程和二阶解析解。在频率响应分析的基础上，分析了圆柱气泡的非线性动力特性及其影响因素。初步结论如下：(1)在三频声激励下，PRI-SUB-SUB的频率响应呈单峰，PRI-SUPER-SUPER的频率响应呈双峰。(2)多向性指数对频率响应中共振峰的峰值和位置都有影响。(3)同时共振频率响应曲线的不稳定区域受总振幅和平衡半径的显著影响，呈正相关关系。

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来源期刊

Journal of Hydrodynamics MECHANICS-

自引率

12.00%

发文量

2374

审稿时长

4.6 months

期刊介绍： Journal of Hydrodynamics is devoted to the publication of original theoretical, computational and experimental contributions to the all aspects of hydrodynamics. It covers advances in the naval architecture and ocean engineering, marine and ocean engineering, environmental engineering, water conservancy and hydropower engineering, energy exploration, chemical engineering, biological and biomedical engineering etc.