Journal of Sound and Vibration最新文献_第8页

Numerical mode matching (NMM) method for efficient simulation of elastic/acoustic waves in multilayered heterogeneous structures 数值模式匹配（NMM）方法在多层非均质结构中有效模拟弹性/声波

IF 4.9 2区工程技术 Q1 ACOUSTICS

Journal of Sound and Vibration

Pub Date : 2026-03-17 Epub Date: 2025-12-12 DOI: 10.1016/j.jsv.2025.119608

An Qi Ge , Jie Liu , Mingwei Zhuang , Qing Huo Liu

Metasurfaces, a common type of vertically multilayered heterogeneous structure, effectively modulate elastic wave propagation by controlling its phase and magnitude. Simulation of the relationship between geometric design parameters and wave phase is crucial for elastic metasurface design, but it typically demands large-scale parametric sweeps in 3D numerical simulations, leading to high computational costs. To accelerate the computation, this work proposes a general Numerical Mode Matching (NMM) method for elastic/acoustic wave propagation in vertically multilayered heterogeneous structures. The method decomposes a complex 3D problem into a series of 2D inhomogeneous waveguide eigenvalue problems, solved using the spectral element method (SEM), and a 1D layered medium problem solved analytically using a recursive procedure. The formulation ensures the continuity of displacement and traction at layer interfaces, incorporating solid-fluid coupling with linear-slip boundary conditions. The efficiency and accuracy of the proposed NMM method are demonstrated through several numerical examples. Additionally, a 3D metasurface based on a solid-fluid coupled multilayered resonant unit cell is designed using the NMM method, showcasing its capability to enable functionalities such as wave steering and focusing. The results indicate that the proposed method significantly reduces computational costs while maintaining high accuracy, making it a powerful tool for simulating elastic waves in multilayered heterogeneous structures, particularly in metasurface design.

超表面是一种常见的垂直多层非均质结构，它通过控制弹性波的相位和幅度来有效地调制弹性波的传播。几何设计参数与波相关系的模拟对于弹性超表面设计至关重要，但在三维数值模拟中通常需要大规模的参数扫描，导致计算成本很高。为了加快计算速度，本文提出了一种用于弹性/声波在垂直多层非均质结构中传播的通用数值模式匹配（NMM）方法。该方法将复杂的三维问题分解为一系列二维非均匀波导特征值问题，用谱元法（SEM）求解，用递归方法解析求解一维层状介质问题。该公式考虑了固流耦合和线性滑移边界条件，保证了层间界面位移和摩擦力的连续性。通过数值算例验证了该方法的有效性和准确性。此外，采用NMM方法设计了基于固流耦合多层谐振单元电池的三维超表面，展示了其实现波转向和聚焦等功能的能力。结果表明，该方法在保持较高精度的同时显著降低了计算成本，是模拟多层非均质结构中弹性波的有力工具，特别是在超表面设计中。

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引用次数: 0

Vibration of a mistuned bladed disk under fluctuating rotor speed 转子转速波动下失谐叶片盘的振动

IF 4.9 2区工程技术 Q1 ACOUSTICS

Journal of Sound and Vibration

Pub Date : 2026-03-17 Epub Date: 2025-12-03 DOI: 10.1016/j.jsv.2025.119600

Alok Sinha

This paper deals with the stability and forced response of a bladed disk under fluctuating rotor speed which leads to time varying blades’ stiffnesses. Inevitable small variations in blades’ stiffnesses due to manufacturing tolerances result in time-varying mistuning. Using the method of slowly varying parameters, stability conditions are obtained analytically and verified by numerical solution of governing differential equations. The stabilizing effects of random and alternate mistuning are investigated in the presence of time varying blades’ stiffnesses. For stable bladed disks with time-varying random mistuning and with constant random mistuning, statistical distributions of the peak maximum amplitude are generated via Monte Carlo simulations at 0.1% and 1% damping ratios.

本文研究了转子转速波动导致叶片刚度时变的叶片盘的稳定性和强迫响应问题。由于制造公差导致叶片刚度不可避免的微小变化导致时变失谐。采用慢变参数法，解析得到了系统的稳定条件，并通过控制微分方程的数值解进行了验证。研究了叶片刚度随时间变化时随机失谐和交替失谐的稳定效果。对于具有时变随机失谐和恒定随机失谐的稳定叶片盘，通过蒙特卡罗模拟得到了0.1%和1%阻尼比下最大振幅峰值的统计分布。

引用次数: 0

An iterative tension-based transfer matrix method for dynamic analysis of periodic cables 基于迭代张力传递矩阵法的周期索动力分析

IF 4.9 2区工程技术 Q1 ACOUSTICS

Journal of Sound and Vibration

Pub Date : 2026-03-17 Epub Date: 2025-12-06 DOI: 10.1016/j.jsv.2025.119601

He Zhang, Yihui Guo, Tengxin Lin, Linjie Yao, Yuhui Zhou

Periodic structure-based vibration control has emerged as a novel strategy for engineering structures, yet its implementation in cable systems faces critical analytical challenges. In this study, we propose an updated Transfer Matrix (TM) methodology that resolves two fundamental limitations in existing approaches: (1) modeling inaccuracies caused by discontinuities in non-uniform cables, and (2) the failure of conventional TM methods due to deformation-dependent transfer matrices. To resolve the first limitation, a segmented catenary element method is proposed, integrating the State-Space Approach (SSA) with the catenary element method. This framework enables the discretization of periodic cable systems into uniform segments, each governed analytically by the hyperbolic equilibrium equations derived from catenary theory. For the second limitation, explicit equations relating transfer matrices to dynamic tension are first derived; then an iterative dynamic tension approach is developed to update the deformation-dependent transfer matrices. By employing the Joint Coupling Matrix (JCM) method to construct the global transfer matrix, the closed-form solution for the vibration responses can be derived. The accuracy of the updated TM method is verified through comparisons between frequency response curves obtained from the updated TM method and those from the Finite Element Method (FEM). The updated TM method is then employed to evaluate the performance of the periodic structure-based vibration mitigation strategy in periodic cable systems, revealing the effectiveness of this approach under different combinations of structural periodic parameters and load conditions. The results provide a theoretical foundation and practical guidance for optimizing periodic cable configurations to achieve enhanced vibration mitigation performance in civil engineering applications.

基于周期性结构的振动控制已成为工程结构的一种新策略，但其在索系统中的实施面临着严峻的分析挑战。在本研究中，我们提出了一种更新的传递矩阵（TM）方法，该方法解决了现有方法的两个基本局限性：(1)非均匀电缆的不连续引起的建模不准确性；(2)由于变形相关的传递矩阵而导致传统的TM方法失效。针对第一个局限性，提出了一种将状态空间法与接触网元法相结合的分段接触网元方法。该框架使周期电缆系统离散成均匀的部分，每个部分由从悬链线理论导出的双曲平衡方程解析控制。对于第二个限制，首先推导了传递矩阵与动态张力的显式方程；然后提出了一种迭代动态张力法来更新变形相关传递矩阵。采用联合耦合矩阵（JCM）法构造整体传递矩阵，推导出振动响应的封闭解。通过与有限元法得到的频率响应曲线的比较，验证了改进后的TM法的精度。利用改进后的TM方法，对周期性索系的周期性结构减振策略进行了性能评估，揭示了该方法在不同结构周期参数和荷载条件组合下的有效性。研究结果为优化周期拉索结构以提高土木工程中的减振性能提供了理论基础和实践指导。

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引用次数: 0

Accounting for dielectric losses in piezoelectric shunt tuning 压电分流调谐中介电损耗的计算

IF 4.9 2区工程技术 Q1 ACOUSTICS

Journal of Sound and Vibration

Pub Date : 2026-03-17 Epub Date: 2025-12-05 DOI: 10.1016/j.jsv.2025.119598

Jens D. Richardt , Boris Lossouarn , Jan Høgsberg , Jean-François Deü

Effective vibration reduction of mechanical structures by piezoelectric shunt damping requires a precise design of the electrical shunt circuit. In this context, the influence of dielectric losses on the accuracy of shunt calibration is analyzed. Numerical analysis of an SDOF structure shows that dielectric losses can result in a significantly increased vibration amplitude when not accounted for in the calibration of a resonant shunt. To address this, a new correction method based on impedance matching is proposed, enabling the use of existing tuning expressions not accounting for dielectric losses. It is demonstrated numerically and experimentally that the influence of dielectric losses is more pronounced for low electromechanical coupling factors. The proposed correction method is shown to provide an accurate correction for the influence of dielectric losses on the shunt tuning.

利用压电并联阻尼实现机械结构的有效减振，需要精确设计并联电路。在此背景下，分析了介电损耗对分流校准精度的影响。对SDOF结构的数值分析表明，在谐振分流器的校准中，如果不考虑介质损耗，会导致振动幅值的显著增加。为了解决这个问题，提出了一种新的基于阻抗匹配的校正方法，可以使用现有的不考虑介电损耗的调谐表达式。数值和实验结果表明，当机电耦合系数较低时，介质损耗的影响更为明显。所提出的校正方法对介电损耗对分流调谐的影响提供了精确的校正。

引用次数: 0

Sommerfeld effect of non-ideal double-body vibration system driven by AC motor 交流电机驱动非理想双体振动系统的索默菲尔德效应

IF 4.9 2区工程技术 Q1 ACOUSTICS

Journal of Sound and Vibration

Pub Date : 2026-03-17 Epub Date: 2025-12-05 DOI: 10.1016/j.jsv.2025.119573

Xiaozhe Chen , Baitong Zhou , Vladislav Sorokin

In this paper, the Sommerfeld effect in a non-ideal vibrational system with two degrees of freedom driven by an AC motor is investigated. The interaction between the AC motor and the vibration system is explored, leading to the development of a dynamical model and the establishment of the governing differential equations of motion. Subsequently, the motion coupling is considered by the analysis of the electromagnetic torque of the AC motor. The first-order approximate solution of the equations is then obtained by using the averaging method, and the torque balance equation is derived. Based on this torque balance condition, the characteristics of the Sommerfeld effect in the system are analyzed. The existence of multiple steady-state motions in the system is confirmed by experimental results for both sweep and fixed-frequency excitations, which are supported by the theoretical analysis. Furthermore, the occurrence of the Sommerfeld effect is identified through the parameters of the AC motor, which are monitored by the programmable logic controller. It is noted that in engineering applications, the electrical input and unbalanced mass of the AC motor can be utilized for the suppression of the Sommerfeld effect in vibrating systems.

本文研究了由交流电机驱动的非理想二自由度振动系统中的索默菲尔德效应。探讨了交流电机与振动系统之间的相互作用，建立了交流电机的动力学模型并建立了控制运动微分方程。然后，通过分析交流电机的电磁转矩，考虑了运动耦合。然后用平均法求出方程的一阶近似解，推导出力矩平衡方程。在此转矩平衡条件下，分析了系统中索默菲尔德效应的特性。扫描激励和定频激励的实验结果证实了系统中存在多重稳态运动，理论分析也支持了这一结论。此外，通过交流电机的参数来识别索默菲尔德效应的发生，并由可编程逻辑控制器监控这些参数。值得注意的是，在工程应用中，交流电机的电输入和不平衡质量可用于抑制振动系统中的索默菲尔德效应。

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引用次数: 0

Hybrid nonlinear energy sink, a tunable device for vibration mitigation : Theorical and experimental demonstration 混合非线性能量阱——一种可调减振装置：理论与实验论证

IF 4.9 2区工程技术 Q1 ACOUSTICS

Journal of Sound and Vibration

Pub Date : 2026-03-17 Epub Date: 2025-12-09 DOI: 10.1016/j.jsv.2025.119577

Louis Mesny , Sébastien Baguet , Roberto Alcorta , Alireza Ture Savadkoohi , Claude-Henri Lamarque , Simon Chesné

Hybridization is a powerful and recent technology that combines passive and active components to enhance system performance. The central idea behind this approach is to improve the responsiveness and adaptability of the passive energy absorption mechanism by integrating a control law supported by actuator/sensor pairs. This combination enables the system to dynamically adapt itself to varying excitation conditions, thereby significantly improving overall performance. Meanwhile, nonlinear energy sinks (NES) are well known for their frequency robustness. The weak point of a nonlinear energy sink lies in its activation threshold, i.e.: the absorber is inactive at low or high levels of external force applied to the primary structure. Additionally, under a significant shift in the primary structure’s natural frequencies, the absorber becomes ineffective or inactive. Furthermore, the reactivity of passive absorbers may be insufficient depending on the application. For these reasons, a new device for vibration mitigation called the hybrid nonlinear energy sink is introduced. The latter is designed to overcome the limitations of passive linear and nonlinear absorbers and hybrid linear absorbers. It enhances the non-linear passive energy sink by integrating sensor-actuator pairs and a specially designed control law to modify the system dynamics in real time. This ensures that the absorber remains effective even when external conditions change. This paper presents theoretical and experimental demonstrations of this new device, applied to a one-storey building. By introducing control laws within the hybrid nonlinear energy sink, it becomes possible to adjust its parameters, e.g., the nonlinear stiffness, to shift the activation threshold and ensure consistent performance of the absorber in real-time.

杂交是一项强大的最新技术，它结合了无源和有源组件来提高系统性能。该方法的核心思想是通过集成执行器/传感器对支持的控制律来提高被动能量吸收机构的响应性和适应性。这种组合使系统能够动态地适应不同的激励条件，从而显着提高整体性能。同时，非线性能量汇（NES）具有频率鲁棒性。非线性能量吸收的弱点在于它的激活阈值，即：吸收器在低或高水平的外力作用于主要结构时不活跃。此外，在主要结构的固有频率发生重大变化的情况下，吸收器变得无效或不活跃。此外，被动吸收剂的反应性可能因应用的不同而不足。基于这些原因，提出了一种新的减振装置——混合非线性能量汇。后者是为了克服被动线性和非线性吸收器以及混合线性吸收器的局限性而设计的。它通过集成传感器-执行器对和特殊设计的控制律来实时修改系统动力学，从而增强非线性无源能量吸收。这确保吸收器即使在外部条件发生变化时仍然有效。本文介绍了这种新装置的理论和实验证明，并应用于一个单层建筑。通过在混合非线性能量吸收器中引入控制规律，可以调整其参数，例如非线性刚度，以移动激活阈值并确保吸收器的实时一致性能。

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引用次数: 0

Vibration characteristics of integrally mistuned turbine blisks with hard-coating and bladed multi-packet shrouds 整体失谐涡轮硬涂层叶片多包叶冠的振动特性

IF 4.9 2区工程技术 Q1 ACOUSTICS

Journal of Sound and Vibration

Pub Date : 2026-03-17 Epub Date: 2025-12-09 DOI: 10.1016/j.jsv.2025.119607

Wensai Ma , Bin Bai , Xiang Li , Xinye Li , Shichuan Wang , Gang Chen

To effectively address vibration issues in aero-engine blisks, this study establishes a lumped parameter dynamic model (LPDM) of mistuned integrally turbine blisk with hard-coating and bladed multi-packet shrouds (MITB-HC-BMPSs), systematically investigating the variation laws of modal and vibration characteristics under different mistuning strengths. There are two configurational models on the LPDM considering blade stiffness mistuning, that is, Style 1 (MITB-HC without BMPSs) and Style 2 (MITB-HC-BMPSs). The BMPSs are introduced to connect adjacent blades, forming coupled groups to enhance inter-blade stiffness coupling. The effects of HC and BMPSs on natural frequencies, modal localization, and resonant responses are analyzed, with solutions validated against existing literature. Results show that mistuning has negligible influence on natural frequencies but significantly induces modal shape and forced response localization, with severity increasing as mistuning strength rises. Notably, the hybrid system of HC and BMPSs demonstrates superior vibration reduction: compared with single measures, it more significantly weakens vibration localization. The HC reduces system stiffness and dissipates vibrational energy, while BMPSs enhance structural coupling to mitigate stiffness heterogeneity. This study furnishes both theoretical foundation and engineering guidance for the vibration-damping optimization design of ITB with composite material structures in aero-engines.

为有效解决航空发动机叶片振动问题，建立了硬涂层多包叶冠失谐整体涡轮叶片（MITB-HC-BMPSs）的总参数动力学模型（LPDM），系统研究了不同失谐强度下的模态和振动特性变化规律。考虑叶片刚度失谐的ldm有两种构型模型，即1型（MITB-HC不带bmps）和2型（MITB-HC- bmps）。引入bmps连接相邻叶片，形成耦合组，增强叶片间刚度耦合。分析了HC和bmps对固有频率、模态局部化和共振响应的影响，并根据现有文献验证了解决方案。结果表明，失谐对固有频率的影响可以忽略不计，但会显著诱导模态振型和强迫响应局部化，且随失谐强度的增加，影响程度逐渐增大。值得注意的是，HC和bmps的混合系统具有更好的减振效果：与单一措施相比，它更明显地减弱了振动的局部化。HC降低了系统刚度并耗散了振动能量，而bmps增强了结构耦合以减轻刚度非均匀性。本文的研究为航空发动机复合材料结构ITB减振优化设计提供了理论基础和工程指导。

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引用次数: 0

Theoretical corrections for measured sound pressure of hydrophones in vibrating liquid column 振动液柱中水听器实测声压的理论修正

IF 4.9 2区工程技术 Q1 ACOUSTICS

Journal of Sound and Vibration

Pub Date : 2026-03-17 Epub Date: 2025-11-27 DOI: 10.1016/j.jsv.2025.119536

Limu Qin , Gen Zhang , Jie Zhou , Bohan Shen , Wen He

The measured sound pressure of hydrophones (MSPH) corresponds to the pressure averaged over hydrophones effective sensitive area (ESA) due to hydrophones integrating properties, which is theoretically equivalent to the pressure at hydrophones acoustic center and can be approximated as the pressure at hydrophones geometric center in a uniform acoustic field. An accurate analytical solution for the MSPH serves as the critical foundation for ensuring calibration precision in the vibrating liquid column absolute calibration method (VLCACM). However, the current VLCACM inadequately considers the effects of hydrophones structure, acoustic field inhomogeneity and dynamic liquid column on the MSPH, leading to compromised calibration accuracy. In this scenario, a novel MSPH analytical framework that explicitly considers hydrophone-liquid column coupling effects is presented in this paper. Firstly, an ESA integral model and a spatial averaging correction theory are developed based on the integrating properties of hydrophones to resolve the liquid column acoustic field vertical inhomogeneity. Secondly, leveraging the Jacobi-Anger expansion, a harmonic correction theory for MSPH is formulated to quantify the effect of hydrophones dynamic measurement point caused by the simple harmonic motion of the liquid column on the MSPH, with recursive relationships derived for harmonic amplitude prediction. Finally, the proposed MSPH correction framework was experimentally validated over the frequency range of 10 Hz to 2000 Hz using a dedicated vibration liquid column calibration platform—comprising an electromagnetic standard shaker and an integrated measurement and control system—paired with a 27.5 mm diameter truncated spherical piezoelectric hydrophone exhibiting a sensitivity of approximately -173.7 dB. Results demonstrate that adapting the proposed spatial averaging and harmonic correction can effectively reduce calibration errors in VLCACM.

测得的水听器声压（MSPH）对应于水听器有效敏感区（ESA）上由于水听器的积分特性而产生的平均压力，理论上等同于水听器声中心处的压力，可以近似为均匀声场中水听器几何中心处的压力。在振动液柱绝对定标法（VLCACM）中，精确的MSPH解析解是保证定标精度的关键基础。然而，目前的VLCACM没有充分考虑水听器结构、声场不均匀性和动态液柱对MSPH的影响，导致校准精度降低。在这种情况下，本文提出了一种明确考虑水听-液柱耦合效应的新型MSPH分析框架。首先，基于水听器的积分特性，建立了欧空局积分模型和空间平均校正理论，解决了液柱声场垂直非均匀性问题；其次，利用Jacobi-Anger展开，建立了MSPH的谐波校正理论，量化了液柱简谐运动引起的水听器动态测点对MSPH的影响，并推导了递推关系，预测了谐波幅值。最后，在10 Hz至2000 Hz的频率范围内，使用专用振动液柱校准平台对所提出的MSPH校正框架进行了实验验证，该平台包括一个电磁标准激振器和一个集成测量和控制系统，并与一个27.5 mm直径的截断球形压电水听器（灵敏度约为-173.7 dB）相匹配。结果表明，采用本文提出的空间平均和谐波校正方法可以有效地降低vlccm的标定误差。

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引用次数: 0

Sound propagation in slowly varying ducts 声音在缓慢变化的管道中传播

IF 4.9 2区工程技术 Q1 ACOUSTICS

Journal of Sound and Vibration

Pub Date : 2026-03-17 Epub Date: 2025-11-30 DOI: 10.1016/j.jsv.2025.119572

Thomas J. White, Raphaël C. Assier, William J. Parnell

This paper analyses the propagation of acoustic waves through slowly varying lined ducts via a Wentzel-Kramers-Brillouin (WKB) approach. It is assumed that the curvature of the duct boundary can be related to a small parameter, ϵ, and slowly varying modes can be defined as solutions to the Helmholtz equation. The duct lining is approximated by a surface impedance boundary condition applied at the fluid-duct interface. It is assumed that slowly varying modes exist in the duct and do not reflect or change eigenstate as they propagate. Posing a WKB ansatz, the known leading order asymptotic solution is recovered and corrected to first order, more accurately representing the normal boundary condition, and addressing errors in the pressure field. It is found that, when compared with numerical simulations performed using COMSOL, this solution is unsatisfactory when there are multiple highly cut-on modes for a given frequency. This is due to modal coupling, which is especially prevalent at low frequencies. It is possible to account for the coupling whilst retaining a WKB approach, by defining a coupled mode solution, where the acoustic field is projected over a set of propagating modes which satisfy the true boundary condition. This approach is implemented to

O (ϵ)

and validated against full numerical simulations performed in COMSOL.

本文用温策尔-克莱默斯-布里渊（WKB）方法分析了声波在缓慢变化的管道中的传播。假设管道边界的曲率可以与一个小参数相关联，并且可以将缓慢变化的模态定义为亥姆霍兹方程的解。管道衬砌由流体-管道界面处的表面阻抗边界条件近似表示。假设在管道中存在缓慢变化的模式，并且在传播时不反射或改变本征态。提出WKB解，将已知的前阶渐近解恢复并修正为一阶解，更准确地表示了正常边界条件，并解决了压力场中的误差。结果表明，当给定频率下存在多个高导通模态时，与COMSOL进行的数值模拟相比，该方法不能令人满意。这是由于模态耦合，这是特别普遍的低频。在保留WKB方法的同时，可以通过定义耦合模式解决方案来解释耦合，其中声场投影在一组满足真实边界条件的传播模式上。这种方法被实现到O（御柱），并在COMSOL中进行了完整的数值模拟验证。

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引用次数: 0

Stress-controlled magnetoacoustic conversion efficiency of SH waves: Theoretical analysis and experimental validation 应力控制的SH波磁声转换效率：理论分析与实验验证

IF 4.9 2区工程技术 Q1 ACOUSTICS

Journal of Sound and Vibration

Pub Date : 2026-03-17 Epub Date: 2025-12-14 DOI: 10.1016/j.jsv.2025.119613

Wenbo Cao , Bin Wu , Ren Liu , Xiang Gao , Xiucheng Liu

The magnetostrictive effect is an intrinsic property of ferromagnetic materials and physically allows the generation of multimodal ultrasonic guided waves. Among ultrasonic guided waves, Shear Horizontal (SH) waves are the advantageous carrier for ultrasonic nondestructive testing due to their mode purity. However, the influence of stress on the Magnetoacoustic Conversion Efficiency (MCE) is not considered in the conventional SH wave excitation theory, so it fails to reveal the intermodulation mechanism of axial stress and magnetoacoustic coupling effect. In this paper, the nonlinear modulation of magnetostrictive SH wave amplitude by the stress in the elastic interval was quantified by establishing a force-magnetic-acoustic multi-field coupling model. Theoretical analysis and experimental results revealed the high stress sensitivity of MCE curve. Under a low magnetic field intensity, with the increase in stress, the normalized amplitude of SH waves decreased firstly and then increased. Under a high magnetic field intensity, the amplitude of SH waves exhibited a monotonically increasing behavior. The proposed model successfully decoupled the dynamic interaction between stress and magnetostrictive SH waves, thus offering a theoretical framework for stress detection based on the magnetostrictive effect.

磁致伸缩效应是铁磁材料的固有特性，在物理上允许多模态超声导波的产生。在超声导波中，剪切水平波因其模式纯度高而成为超声无损检测的有利载体。然而，传统的SH波激励理论没有考虑应力对磁声转换效率的影响，未能揭示轴向应力与磁声耦合效应的互调机制。本文通过建立力-磁-声多场耦合模型，量化了弹性区间应力对磁致伸缩SH波振幅的非线性调制。理论分析和实验结果表明，MCE曲线具有较高的应力敏感性。在低磁场强度下，随着应力的增大，SH波的归一化振幅先减小后增大。在高磁场强度下，SH波振幅呈现单调递增的特征。该模型成功地解耦了应力与磁致伸缩SH波之间的动态相互作用，从而为基于磁致伸缩效应的应力检测提供了理论框架。

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引用次数: 0