Applied Mathematical Modelling最新文献_第8页

Vibroacoustic analysis of fluid-loaded baffled rectangular plates with nonlinear energy sinks using Chebyshev spectral method 用切比雪夫谱法分析含非线性能量汇的流载折板矩形板的振动声

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-07-01 Epub Date: 2025-12-24 DOI: 10.1016/j.apm.2025.116725

Tiantong Zhao , Tiangui Ye , Hong Yin , Minggang Wang , Guoyong Jin , Zhigang Liu

This paper introductions a Chebyshev spectral method for the vibroacoustic analysis of fluid-loaded rectangular plates incorporating nonlinear energy sinks (NES). The proposed method employs Chebyshev polynomials for the spatial discretization of both structural displacements and the radiated acoustic pressure, achieving high accuracy with relatively few degrees of freedom. An iterative approach is used to solve for the eigenpairs of a rectangular plate submerged in a heavy fluid medium, and the obtained modal components are then incorporated into the reduced-order model of the fluid-loaded rectangular plate with NES. The harmonic balance method (HBM) is employed to efficiently determine the forced nonlinear response of the system. To validate the accuracy of the proposed approach, the model is first verified for fluid-loaded baffled rectangular plates equipped with a tuned mass damper (TMD) by comparing the results with reference solutions from the literature. For NES-equipped plates, Runge-Kutta methods combined with the Rayleigh integral formula are used as a benchmark for comparison. The results demonstrate the effectiveness of the proposed methodology in capturing the vibroacoustic behavior of NES-equipped fluid-loaded plates. Results indicate that the NES effectively suppresses vibration and reduces radiated sound pressure, without introducing additional resonance peaks. However, excessive NES stiffness can weaken noise reduction despite enhanced local vibration control. These findings confirm the method’s accuracy and computational efficiency, providing a powerful tool for nonlinear vibroacoustic analysis in heavy fluid environments.

本文介绍了一种切比雪夫谱法用于含非线性能量汇的受流矩形板的振动声分析。该方法采用切比雪夫多项式对结构位移和辐射声压进行空间离散化，以相对较小的自由度实现了较高的精度。采用迭代法求解了浸没在重流体介质中的矩形板的特征对，并将得到的模态分量纳入到含流体矩形板的降阶模型中。采用谐波平衡法（HBM）有效地确定了系统的强迫非线性响应。为了验证所提出方法的准确性，首先通过将结果与文献中的参考解进行比较，对装有调谐质量阻尼器（TMD）的流载折板矩形板进行了模型验证。对于配备nes的板，采用龙格-库塔法结合瑞利积分公式作为基准进行比较。结果证明了所提出的方法在捕获配备nes的流体加载板的振动声学行为方面的有效性。结果表明，在不引入额外共振峰的情况下，NES有效地抑制了振动，降低了辐射声压。然而，过度的NES刚度会削弱降噪，尽管增强了局部振动控制。这些结果证实了该方法的准确性和计算效率，为重流体环境下的非线性振动声分析提供了有力的工具。

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引用次数: 0

Steady-state amplitude of an encapsulated gas bubble radial oscillations at resonance 被封装的气泡在共振时径向振荡的稳态振幅

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-07-01 Epub Date: 2025-12-26 DOI: 10.1016/j.apm.2025.116719

Alexander G. Petrov , Yuri V. Fedorov

Using gas microbubbles coated by a thin viscoelastic shell as ultrasound contrast agents (UCA) improves the resolution of ultrasound images of human tissues. The most interesting effects are the oscillations of encapsulated bubbles at resonance. In this case, the ratio of the oscillation amplitude of the encapsulated bubble to the external acoustic pressure is maximized, and thus, the effect of ultrasound on the inclusion is also maximized. In this regard, the present study examines the forced nonlinear oscillations of a gas bubble coated with a viscoelastic shell in a liquid when the frequency of the external acoustic pressure coincides with the undamped linear resonant frequency of the encapsulated bubble. The averaging method usage results in a formula of dependence of the encapsulated gas bubble oscillations amplitude on the amplitude of external pressure, thermophysical properties of the gas and the liquid viscosity, as on the viscoelastic parameters of the bubble shell. A good agreement of the formula with numerical calculations is demonstrated.

采用粘弹性薄壳包覆的微气泡作为超声造影剂（UCA），提高了人体组织超声图像的分辨率。最有趣的效应是被封装的气泡在共振时的振荡。在这种情况下，被封装气泡的振荡幅度与外界声压之比最大，从而超声波对包体的影响也最大。在这方面，本研究考察了当外部声压的频率与被封装的气泡的无阻尼线性谐振频率一致时，被粘弹性外壳包裹的气泡在液体中的强迫非线性振荡。采用平均法可以得到一个公式，即被封装的气泡振荡振幅与外部压力的振幅、气体的热物理性质和液体粘度的关系，以及与气泡壳的粘弹性参数的关系。计算结果与公式吻合较好。

引用次数: 0

Enhanced energy harvesting of a spinning bi-directional piezoelectric pipe conveying fluid 旋转双向压电管道输送流体的增强能量收集

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-07-01 Epub Date: 2025-12-31 DOI: 10.1016/j.apm.2025.116730

An-Xiang Zhao , Xiao-Tian Guo , Feng Liang , Yao Chen

To address the limitations of conventional piezoelectric energy harvesting, such as narrow operational bandwidth, uncontrollable band distribution, and poor material durability, this paper develops an efficient energy harvester based on a motional bi-directional piezoelectric pipe. The sandwich square pipe spins around its longitudinal axis, and a steady fluid flows inside. Two groups of piezoelectric bimorph are symmetrically arranged on the orthogonal exterior surfaces of the pipe, each connected to a resistive load circuit. The simply supported and cantilevered configurations are both considered. Numerical results demonstrate superior performance of the proposed energy harvester as follows: i) the spinning motion transforms voltage response from a unimodal to bimodal pattern, greatly improving the electricity output bandwidth; ii) the energy harvesting band can be manipulated by tuning the spinning speed; iii) the gyroscopic effect simultaneously activates voltages in both transverse directions, achieving synchronous multi-source energy output. It is also found that the voltage response to the fluid–structure interaction (FSI) effect is highly sensitive to the support condition. Additionally, the impacts of pipe length, fiber orientation angle in the face layers, and core layer property on the energy harvesting performance are investigated, clarifying comprehensive parametric regulation mechanisms.

针对传统压电能量收集技术存在的工作带宽窄、频带分布不可控、材料耐用性差等缺点，研制了一种基于双向运动压电管的高效能量收集装置。夹心方形管绕其纵轴旋转，一种稳定的流体在管内流动。两组压电双晶片对称地布置在管道的正交外表面上，每组接一个电阻负载电路。简支和悬臂结构都被考虑。数值结果表明：1)旋转运动使电压响应由单峰模式转变为双峰模式，大大提高了输出带宽；Ii)可以通过调节纺丝速度来控制能量收集带；Iii)陀螺仪效应同时激活两个横向电压，实现多源能量同步输出。研究还发现，流固耦合效应的电压响应对支护条件高度敏感。此外，还研究了管道长度、端面层纤维取向角和芯层性质对能量收集性能的影响，阐明了综合参数调节机制。

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引用次数: 0

Adaptive control of uncertain output-feedback systems with time-varying actuator faults 具有时变执行器故障的不确定输出反馈系统的自适应控制

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-07-01 Epub Date: 2026-02-06 DOI: 10.1016/j.apm.2026.116826

Zhenwei Ma , Qiufeng Wang , Binrui Wang , Baile An

This paper addresses the adaptive control problem for output-feedback nonlinear systems subject to model uncertainties and time-varying actuator faults, which frequently arise in safety-critical applications. Existing neural network-based adaptive and fault-tolerant control methods are often developed under full-state feedback or yield only semi-global stability, and rarely treat unmeasurable states, dynamic uncertainties, and time-varying actuator faults within a unified output-feedback framework. To bridge this gap, a neural network-based full-order observer is first constructed to estimate both unmeasurable states and lumped uncertainties from output measurements. On this basis, an augmented adaptive neural network control scheme with a smooth switching mechanism is proposed, which combines neural network approximation with robust compensation to guarantee the global stability of the closed-loop system. In addition, a composite fault-tolerant control strategy is devised, in which an adaptive law estimates the average effectiveness of time-varying actuator faults, while a robust term compensates for the residual time variations. A rigorous Lyapunov analysis shows that the closed-loop system is globally stable and that the tracking error can be driven into an arbitrarily small neighborhood of the origin under the combined effects of unmeasurable states, system uncertainties, and time-varying actuator faults. Two simulation case studies are conducted: a numerical study on a second-order nonlinear system verifies the effectiveness, robustness, and fault-tolerance of the proposed method; and a hardware-in-the-loop study on a single-link robot manipulator demonstrates improved tracking performance and smoother control action compared with the dynamic-gain adaptive control baseline.

本文研究了在安全关键应用中经常出现的具有模型不确定性和执行器时变故障的输出反馈非线性系统的自适应控制问题。现有的基于神经网络的自适应和容错控制方法往往是在全状态反馈或仅产生半全局稳定性的情况下开发的，很少在统一的输出反馈框架内处理不可测量状态、动态不确定性和时变执行器故障。为了弥补这一差距，首先构建了一个基于神经网络的全阶观测器来估计输出测量的不可测量状态和集总不确定性。在此基础上，提出了一种带平滑切换机制的增强自适应神经网络控制方案，该方案将神经网络逼近与鲁棒补偿相结合，保证了闭环系统的全局稳定性。此外，设计了一种复合容错控制策略，其中自适应律估计时变执行器故障的平均有效性，而鲁棒项补偿剩余的时间变化。严格的Lyapunov分析表明，在不可测量状态、系统不确定性和执行器时变故障的综合作用下，闭环系统是全局稳定的，跟踪误差可以被驱动到原点的任意小邻域内。通过两个仿真实例研究：一个二阶非线性系统的数值研究验证了所提方法的有效性、鲁棒性和容错性；通过对单连杆机器人机械臂的半实物研究表明，与动态增益自适应控制基线相比，该方法具有更好的跟踪性能和更平滑的控制动作。

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引用次数: 0

Adaptive finite-time second-order sliding mode attitude control for fixed-wing UAVs 固定翼无人机自适应有限时间二阶滑模姿态控制

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-07-01 Epub Date: 2026-01-11 DOI: 10.1016/j.apm.2026.116745

MohammadReza Ebrahimpour , Mihai Lungu , Saleh Mobayen , Rui Wang

Fixed-wing unmanned aerial vehicles are widely used in applications such as environmental monitoring, surveillance, and aerial mapping, where accurate attitude control is essential for flight stability and mission success. However, external disturbances, parametric uncertainties, and actuator dynamics with saturation and faults pose significant challenges to control performance and reliability. This paper proposes a robust and adaptive attitude-control strategy that addresses these challenges while maintaining low computational complexity. A fast finite-time second-order sliding-mode control method is designed by combining backstepping and sliding mode control techniques, providing enhanced robustness and effective suppression of chattering. The method is further augmented with an adaptive radial basis function neural network law and an auxiliary compensation system: the adaptive law updates only a single learning parameter, reducing computational load by approximately 53 % compared with conventional neural network–based adaptive methods, while the auxiliary system mitigates actuator saturation. Numerical simulations demonstrate that the proposed methods reduce tracking errors by up to 77 % relative to conventional approaches, maintain performance under severe disturbances and uncertainties, and achieve low computational overhead, highlighting their practical applicability in real-world unmanned aerial vehicle operations.

固定翼无人机广泛应用于环境监测、监视和航空测绘等领域，精确的姿态控制对飞行稳定和任务成功至关重要。然而，外部干扰、参数不确定性以及执行器的饱和和故障动力学对控制性能和可靠性提出了重大挑战。本文提出了一种鲁棒的自适应姿态控制策略，以解决这些挑战，同时保持较低的计算复杂度。将反步控制技术与滑模控制技术相结合，设计了一种快速有限时间二阶滑模控制方法，增强了鲁棒性，有效抑制了抖振。该方法进一步增强了自适应径向基函数神经网络律和辅助补偿系统：自适应律只更新单个学习参数，与传统的基于神经网络的自适应方法相比，计算负荷减少了约53%，而辅助系统减轻了执行器的饱和。数值模拟表明，与传统方法相比，所提出的方法将跟踪误差降低了77%，在严重干扰和不确定性下保持性能，并且实现了较低的计算开销，突出了其在实际无人机操作中的实用性。

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引用次数: 0

Recursive modeling and trajectory optimization of space manipulator mounted on flexible structure 柔性结构空间机械臂递归建模与轨迹优化

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-07-01 Epub Date: 2026-01-11 DOI: 10.1016/j.apm.2026.116741

Yixing Gong, Hao Wen

Manipulators mounted on flexible bases are widely used in space missions. However, their control is complicated by the dynamic coupling between the manipulator and the flexible base. The control objective of such a system is to simultaneously suppress the base’s vibrations and control the manipulator to move to its target configuration. Most existing approaches either use simplified mass-spring models that fail to capture complex dynamics or high-fidelity methods that are computationally expensive. This study focuses on manipulators mounted on large slender truss structures and presents a trajectory optimization scheme to accomplish the control task. To simplify analysis, the large slender truss is modeled as an Euler-Bernoulli beam with dynamics derived via the finite element method. For efficiency, the manipulator-truss dynamics is derived using recursive modeling. Subsequently, a trajectory optimization problem is formulated, in which the system’s implicit dynamics are employed as constraints. Afterwards, The trajectory optimization problem is subsequently transcribed into a nonlinear programming formulation and solved to generate optimal trajectories for feedback-based online tracking. Finally, numerical simulations using an Absolute Nodal Coordinate Formulation beam as reference demonstrate the effectiveness of the proposed trajectory optimization scheme, achieving the control tasks in both Absolute Nodal Coordinate Formulation- and Euler-Bernoulli-based models.

安装在柔性基座上的机械臂在航天任务中有着广泛的应用。然而，由于机械臂与柔性基座之间的动态耦合，使其控制变得复杂。该系统的控制目标是在抑制基座振动的同时控制机械手运动到目标位形。大多数现有的方法要么使用简化的质量-弹簧模型，无法捕获复杂的动力学，要么使用计算成本高的高保真方法。针对安装在大型细长桁架结构上的机械臂，提出了一种轨迹优化方案来完成控制任务。为了简化分析，将大型细长桁架建模为欧拉-伯努利梁，并通过有限元法推导其动力学。为提高效率，采用递归建模方法推导了机械臂桁架动力学。在此基础上，提出了以系统隐式动力学为约束条件的轨迹优化问题。然后，将轨迹优化问题转化为非线性规划公式求解，生成基于反馈的在线跟踪的最优轨迹。最后，以绝对节点坐标公式光束为参考的数值仿真验证了所提出的轨迹优化方案的有效性，实现了绝对节点坐标公式和基于euler - bernoulli模型的控制任务。

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引用次数: 0

A new method of specifying parameter bounds for optimization of reduced-order models and application in design of controllers 一种确定降阶模型优化参数界的新方法及其在控制器设计中的应用

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-07-01 Epub Date: 2026-01-10 DOI: 10.1016/j.apm.2026.116751

Anuj Goel , Amit Kumar Manocha , Parveen Bajaj , George Uwadiegwu Alaneme

In the present work, a new framework is proposed to design controllers using model order reduction techniques for linear time invariant complex engineering systems. The proposed model order reduction methodology employs optimization-based techniques namely ant lion optimization and moth flame optimization for which boundary conditions are systematically procured from an interim model derived using balancing free square-root algorithm. An area control coefficient is introduced to adjust the exploration range of the optimization process around the coefficients of the interim reduced-order model. The numerator as well as denominator coefficients of the desired reduced-order models are optimized to retain the performance characteristics of the original high-order systems. The effectiveness of the proposed approach is assessed based on different error metrics and unit step response plots. To validate the performance, seven benchmark systems of different pole configurations have been considered from the literature. It has been found that proposed approach provides reduced-systems with significant improvement in error and transient performance when compared to the literature work. The suggested model order reduction approach is further extended to design proportional-integral-derivative controller and fractional-order proportional-integral-derivative controller for an 84th-order benchmark system and a mechanical ventilator system respectively. The results demonstrate that the proposed model order reduction-based controller design approach achieves high-performance control with lesser steady-state error, improved time-domain specifications and robust disturbance rejection capability.

本文提出了一种利用模型降阶技术设计线性时不变复杂工程系统控制器的新框架。所提出的模型降阶方法采用基于优化的技术，即蚁狮优化和蛾焰优化，其边界条件是系统地从使用平衡自由平方根算法导出的临时模型中获得的。在中间降阶模型系数周围引入面积控制系数来调整优化过程的勘探范围。对期望的降阶模型的分子和分母系数进行了优化，以保持原高阶系统的性能特征。基于不同的误差度量和单位阶跃响应图对所提方法的有效性进行了评估。为了验证性能，从文献中考虑了七个不同极点配置的基准系统。研究发现，与文献相比，本文提出的方法在误差和瞬态性能方面提供了显著改善的简化系统。将模型降阶方法进一步推广到84阶基准系统和机械通风机系统的比例-积分-导数控制器和分数阶比例-积分-导数控制器的设计中。结果表明，所提出的基于模型阶数约简的控制器设计方法具有较小的稳态误差、较好的时域参数和鲁棒抗扰能力，实现了高性能的控制。

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引用次数: 0

Efficient simulation method of non-stationary non-Gaussian stochastic ground motions based on adaptive interpolation strategy 基于自适应插值策略的非平稳非高斯随机地震动高效模拟方法

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-07-01 Epub Date: 2026-01-10 DOI: 10.1016/j.apm.2026.116746

Xiangqian Sheng , Kuahai Yu , Wenliang Fan , Baiwan Su

The translation process-based spectral representation method is widely used to simulate the non-stationary non-Gaussian stochastic ground motions. However, the computation of the underlying evolutionary power spectral density matrix and its decomposition require substantial computational effort at discrete time-frequency points. To address this problem, this paper proposes an adaptive interpolation strategy for selecting the time-frequency interpolation points to improve the simulation efficiency. Firstly, the correlation function equations between non-Gaussian stochastic processes and the underlying Gaussian stochastic processes are constructed using Mehler's formula. A fast calculation method for the evolutionary power spectral density of the underlying Gaussian processes is introduced based on the interpolation technique. Secondly, the discrete time-frequency interpolation points are determined based on the amplitude information of the evolutionary power spectral density of the underlying Gaussian stochastic processes. The evolutionary power spectral density matrix is decomposed at these time-frequency interpolation points. The decomposed spectrum is then expressed as a sum of products of various time and frequency components. Spline interpolation is applied to these components at the discrete time-frequency points to approximate the matrix decomposition required by the spectral representation method, improving the efficiency of the decomposition. Additionally, the Fast Fourier Transform further accelerates simulation efficiency. Finally, the accuracy and efficiency of the proposed method for simulating non-stationary non-Gaussian stochastic ground motions are verified by considering the real ground motion record, stochastic vector processes, different probability distribution types, different power spectrum density types, and the number of variates.

基于平移过程的谱表示方法被广泛用于模拟非平稳非高斯随机地震动。然而，底层进化功率谱密度矩阵的计算及其分解需要在离散时频点进行大量的计算。针对这一问题，本文提出了一种选择时频插值点的自适应插值策略，以提高仿真效率。首先，利用梅勒公式建立了非高斯随机过程与底层高斯随机过程的相关函数方程；介绍了一种基于插值技术的高斯过程演化功率谱密度的快速计算方法。其次，根据高斯随机过程演化功率谱密度的幅值信息确定离散时频插值点；在这些时频插值点处对演化功率谱密度矩阵进行分解。然后将分解后的频谱表示为各种时间和频率分量的乘积和。在离散时频点对这些分量进行样条插值，逼近谱表示法所需的矩阵分解，提高了分解效率。此外，快速傅里叶变换进一步提高了仿真效率。最后，通过考虑实际地震动记录、随机矢量过程、不同概率分布类型、不同功率谱密度类型和变量数量，验证了所提方法模拟非平稳非高斯随机地震动的准确性和效率。

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引用次数: 0

Mathematical analytical model for interaction between tunnel viscoelastic-plastic surrounding rock and circumferential yielding lining considering stress path effect 考虑应力路径效应的隧道粘弹塑性围岩与周向屈服衬砌相互作用的数学分析模型

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-07-01 Epub Date: 2026-01-15 DOI: 10.1016/j.apm.2026.116765

Nannan Zhao , Jiacheng Luo , Su Qin , Zhushan Shao , Kui Wu

The application of circumferential yielding lining proposes a good solution to the problem of overstress and failure of preliminary support in squeezing large deformation tunnels. Establishing a practical theoretical model to predict the mechanical response of tunnels using circumferential yielding lining can provide meaningful guidance for the initial design of support. This study suggests that the surrounding rock exhibits viscoelastic-plastic behaviour, and also shows plastic softening and residual characteristics after reaching a plastic state; the deformation process of circumferential yielding lining is divided into elastic, yielding and compaction stages, according to the mechanical properties of special elements. A simplified two-dimensional mechanical model is established to capture the interaction between the surrounding rock and circumferential yielding lining, taking into account the effects of tunnel face advancement and stress path. Based on the engineering reality (stress state of the surrounding rock at the time of lining installation), the interaction between the surrounding rock and lining is discussed in various cases; corresponding analytical solutions for the tunnel displacement and support pressure are proposed for each case. Furthermore, a numerical simulation is conducted using an actual tunnel, and a comprehensive comparison is performed between the theoretical prediction results, numerical simulation data, and monitored tunnel displacement. Finally, parametric sensitivity analysis is completed based on the proposed theoretical model, and the impacts of geological parameters and support parameters are discussed. By using this theoretical model, the design rationality of the circumferential yielding lining can be quickly evaluated and some design recommendations can be easily obtained.

周向屈服衬砌的应用，很好地解决了挤压大变形隧道初支护的超应力破坏问题。建立一个实用的理论模型来预测周向屈服衬砌隧道的力学响应，对支护的初始设计具有指导意义。研究表明，围岩表现出粘弹塑性特性，同时也表现出塑性软化和塑性状态后的残余特性；根据特殊构件的力学性能，将周向屈服衬砌的变形过程分为弹性、屈服和压实三个阶段。考虑巷道工作面推进和应力路径的影响，建立了围岩与周向屈服衬砌相互作用的简化二维力学模型。根据工程实际（衬砌安装时围岩的应力状态），讨论了各种情况下围岩与衬砌的相互作用；针对每种情况，提出了相应的巷道位移和支护压力解析解。并利用某实际隧道进行了数值模拟，将理论预测结果、数值模拟数据与隧道位移监测结果进行了全面对比。最后，根据提出的理论模型进行了参数敏感性分析，讨论了地质参数和支护参数的影响。利用该理论模型，可以快速评价周向屈服衬砌的设计合理性，并给出设计建议。

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引用次数: 0

Applicability of Shear Horizontal guided waves in non-classical continuum theory and calibration of higher-order mode scale parameters 剪切水平导波在非经典连续介质理论中的适用性及高阶模态尺度参数的标定

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2026-07-01 Epub Date: 2026-01-14 DOI: 10.1016/j.apm.2026.116763

Chuang Yang, Jiangong Yu, Zhi Li, Xiaoming Zhang

As core theories of non-classical continuum theory, the nonlocal, nonlocal strain gradient theory, and Gurtin-Murdoch surface elasticity theories have yet to resolve how to determine the high-order modal scale parameters and applicability in wave propagation. In this study, molecular dynamics simulations combined with a GA-BP neural network were used to calibrate the scale parameters of higher-order Shear Horizontal (SH) modes and investigate the applicability of these theories. The results show the nonlocal and nonlocal strain gradient theories exhibit good applicability, whereas the Gurtin-Murdoch surface elasticity theory alone is inapplicable to higher-order modes. However, when combined with the nonlocal theory, it can accurately describe them. Moreover, the scale parameters exhibit clear differences between higher- and lower-order modes, with the scale parameters of higher-order modes being smaller than those of lower-order modes. Theoretical predictions based on the calibrated parameters agree well with MD simulations, with errors below 2%. These findings provide a basis for evaluating the applicability of non-classical continuum theories and guiding the design of sensitive nanodevices.

作为非经典连续介质理论的核心理论，非局部应变梯度理论、非局部应变梯度理论和Gurtin-Murdoch表面弹性理论如何确定高阶模态尺度参数及其在波传播中的适用性还有待解决。本研究采用分子动力学模拟与GA-BP神经网络相结合的方法，对高阶剪切水平（SH）模态的尺度参数进行了标定，并探讨了这些理论的适用性。结果表明，非局部应变梯度理论和非局部应变梯度理论具有较好的适用性，而单独的Gurtin-Murdoch表面弹性理论不适用于高阶模态。然而，当与非定域理论相结合时，它可以准确地描述它们。高阶模态和低阶模态的尺度参数差异明显，高阶模态的尺度参数小于低阶模态的尺度参数。基于校准参数的理论预测与MD模拟吻合良好，误差低于2%。这些发现为评价非经典连续介质理论的适用性和指导敏感纳米器件的设计提供了依据。

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引用次数: 0