International Journal of Mechanical Sciences最新文献_第7页

A continuous-discontinuous coupling computational method for multi-material mixtures 多材料混合物的连续-非连续耦合计算方法

IF 7.1 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2024-09-29 DOI: 10.1016/j.ijmecsci.2024.109760

Changhong Zhou , Qing Zhong , Mu Chen , Tao Wen , Xionghua Wu , Weitong Meng , Miaomiao Zhang

Considering the important role of particle-reinforced composites (PRCs), and to accurately assess the mechanical properties of PRC with arbitrarily complex internal structures, this paper proposes a new continuous-discontinuous coupled computational method, i.e., the multi-material integrated analysis (MIA) method, by combining the advantages of the discontinuous deformation analysis (DDA) method, the numerical manifold method (NMM), and the meshless method, for the continuous-discontinuous dual state of this kind of materials when they are subjected to forces. The core idea of this method is by establishing a single physical cover (PC) on each particle and defining a unified and piecewise approximation function over it to achieve displacement coordination between the particles and the matrix. In this model, the particles can maintain the contact and separation characteristics like the blocks, while the matrix is able to achieve the bonding function by overlapping different covers. Two numerical integration schemes, namely single-point Gaussian integration and Monte Carlo integration, are proposed to address the integration issues in stiffness matrix calculations. Meanwhile by considering the similarity between NMM and meshless method interpolation function construction, this paper combines circular coverage and 0th-order moving least squares to construct the interpolation function to form the displacement approximation function for the whole solution space. Moreover, the method of lattice retrieval (also Nearest Neighbor Search, NNS) is invoked for particle contact determination to improve the efficiency of contact and coverage relationship determination. The validity of the model is verified by taking asphalt mixture, a typical PRC, as a demonstrative case study. The results show that the MIA method solves the one-sided problem that the existing algorithms usually only consider the continuous or discontinuous properties of PRC, and provides a new method for comprehensively analyzing the micromechanical response of PRC and solving its large deformation problem.

考虑到颗粒增强复合材料（PRC）的重要作用，并为了准确评估具有任意复杂内部结构的PRC的力学性能，本文提出了一种新的连续-非连续耦合计算方法，即多材料综合分析（MIA）方法、本文结合非连续变形分析（DDA）方法、数值流形方法（NMM）和无网格方法的优点，提出了一种新的连续-非连续耦合计算方法，即多材料综合分析（MIA）方法，用于研究这类材料受力时的连续-非连续双重状态。该方法的核心思想是在每个粒子上建立一个单一的物理覆盖（PC），并在其上定义一个统一的分片近似函数，以实现粒子与基体之间的位移协调。在这个模型中，粒子可以像块体一样保持接触和分离特性，而基体则可以通过重叠不同的覆盖层来实现结合功能。针对刚度矩阵计算中的积分问题，提出了两种数值积分方案，即单点高斯积分和蒙特卡罗积分。同时，考虑到 NMM 与无网格法插值函数构造的相似性，本文结合圆形覆盖和 0 次移动最小二乘法构造插值函数，形成整个求解空间的位移近似函数。此外，本文还引用了网格检索法（也称近邻搜索法，NNS）进行粒子接触确定，以提高接触和覆盖关系确定的效率。以典型的沥青混合料为例，验证了该模型的有效性。结果表明，MIA 方法解决了现有算法通常只考虑沥青混合料连续或不连续特性的片面问题，为全面分析沥青混合料的微观力学响应和解决其大变形问题提供了一种新方法。

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引用次数: 0

Experiment-in-the-Loop system for fast and effective tuning of active vibration controllers 用于快速有效调整主动振动控制器的环中实验系统

IF 7.1 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2024-09-28 DOI: 10.1016/j.ijmecsci.2024.109753

Tarcisio M.P. Silva , Prabakaran Balasubramanian , Giulio Franchini , Abdulaziz Buabdulla , Marco Amabili

Tuning active controllers is one of the main challenges in the field of active vibration control (AVC). To address this challenge, this study introduces a novel approach called Experiment in the Loop (EITL). The EITL method, unlike traditional techniques, automates the tuning process through an algorithm based on Particle Swarm Optimization (PSO). This algorithm carries out numerous experimental tests on a structure and, at each test, tries a new configuration of the controller, evaluates its performance, and iteratively improves the control parameters. The EITL's innovation lies in its ability to achieve fast and efficient tuning without any numerical model, making it a significant advancement in AVC technology. The EITL approach is validated by tuning five Multiple-Input Multiple-Output (MIMO) Positive Position Feedback (PPF) active vibration controllers on a composite beam equipped with three piezoelectric sensors and three piezoelectric actuators. Experimental results show that the ‖H‖_∞ norm of the composite beam is reduced up to 96.1% on certain modes, and an average reduction of 74.7% is achieved in a frequency range from 0 to 200 Hz with minimal spillover effects. The developed EITL opens the avenue to a fast and effective tuning of AVC without numerical models.

调整主动控制器是主动振动控制（AVC）领域的主要挑战之一。为应对这一挑战，本研究引入了一种名为 "环中实验（EITL）"的新方法。与传统技术不同，EITL 方法通过基于粒子群优化（PSO）的算法实现了调谐过程的自动化。该算法对结构进行多次实验测试，每次测试都会尝试新的控制器配置，评估其性能，并迭代改进控制参数。EITL 的创新之处在于无需任何数值模型即可实现快速高效的调整，这使其成为 AVC 技术的一大进步。通过在装有三个压电传感器和三个压电致动器的复合梁上调整五个多输入多输出（MIMO）正位置反馈（PPF）主动振动控制器，对 EITL 方法进行了验证。实验结果表明，复合梁的 "H"∞规范在某些模式下降低了 96.1%，在 0 到 200 Hz 的频率范围内平均降低了 74.7%，溢出效应最小。所开发的 EITL 为无需数值模型就能快速有效地调整 AVC 开辟了途径。

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引用次数: 0

Nonlinear dynamics of dielectric actuator: Exploring electrode mechanics 电介质致动器的非线性动力学：探索电极力学

IF 7.1 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2024-09-28 DOI: 10.1016/j.ijmecsci.2024.109755

Rashi Aditi Ranjan , Somnath Sarangi , Ranjan Bhattacharyya

Dielectric elastomer (DE) is a smart material with various biomedical, soft robotics, and vibration control applications. Modeling of the DE actuator is essential for its practical applicability by virtue of its nonlinear characteristic. Many existing models neglect the effect of the electrode despite substantial experimental work demonstrating the electrode’s influence. This work presents the model and nonlinear analysis of the equi-biaxial motion of a planar dielectric membrane incorporating the effect of the electrode. The uniqueness of the paper is due to the inclusion of terms related to inertia, stiffness and damping of the electrode in the governing equation. The elastomer and the electrode are both assumed to be hyperelastic materials having different physical properties, and the governing equation is derived by considering the mechanical aspects of both the elastomer and electrode materials. The behavior of the system for both constant and time-varying voltages is analyzed. Static response and its dependence are explored by presenting the equilibrium stretch plot, potential energy characteristics, and the basin of attraction. The analysis is further expanded for the time-varying voltage, and the impact of the electrode material on the system’s stretch range is also demonstrated. Backward and forward frequency sweeps are used to obtain the amplitude–frequency response and show its dependence on the electrode. Furthermore, time response, phase plot, Poincare map, and Lyapunov exponent are utilized to demonstrate the impact of the mechanical characteristic of the elastomer and electrode on the overall dynamics. The proposed model is validated with the experiment for different voltage conditions. A comparison is also presented between the experiment and system behavior with and without the electrode effect. The findings indicate that the electrode influences the static and dynamic response of the actuator. This work gives a more realistic model of the DE actuator and guides more accurate design of the actuator for various applications.

介电弹性体（DE）是一种智能材料，在生物医学、软机器人和振动控制等领域有着广泛的应用。由于其非线性特性，电介质致动器的建模对其实际应用至关重要。尽管大量实验证明了电极的影响，但许多现有模型都忽略了电极的影响。本文介绍了包含电极效应的平面介电膜等轴向运动模型和非线性分析。本文的独特之处在于将与电极的惯性、刚度和阻尼有关的项纳入了控制方程。假设弹性体和电极都是具有不同物理性质的超弹性材料，并通过考虑弹性体和电极材料的机械特性推导出控制方程。分析了恒定电压和时变电压下的系统行为。通过展示平衡拉伸图、势能特征和吸引力盆地，探讨了静态响应及其依赖性。针对时变电压的分析得到了进一步扩展，同时还展示了电极材料对系统拉伸范围的影响。利用后向和前向频率扫描获得幅频响应，并显示其与电极的关系。此外，还利用时间响应、相位图、Poincare 地图和 Lyapunov 指数来证明弹性体和电极的机械特性对整体动力学的影响。提出的模型与不同电压条件下的实验进行了验证。此外，还对实验结果和有无电极效应的系统行为进行了比较。研究结果表明，电极会影响致动器的静态和动态响应。这项研究为 DE 激励器提供了一个更真实的模型，并为各种应用提供了更精确的激励器设计指导。

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引用次数: 0

Phase-field model of hydraulic fracturing in thermoelastic–plastic media 热塑性介质中的水力压裂相场模型

IF 7.1 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2024-09-27 DOI: 10.1016/j.ijmecsci.2024.109750

Duo Yi , Zhaozhong Yang , Liangping Yi , Jianping Liu , Changxin Yang , Liangjie Gou , Nanxin Zheng , Xiaogang Li , Dongrui Fu , Zhangyao Huang

In this study, we present a thermodynamically consistent thermo-fluid–solid–elastic–plastic phase-field model to accurately capture the propagation process of hydraulic fracture in deep shale. The developed model takes into account the degradation of the thermoelastic–plastic parameters, strain hardening, mixed-mode fracture, and thermal convection. The model incorporates an uncorrelated Drucker–Prager constitutive model with a nonlinear saturated strain function to capture the deformation behavior of shale. The driving force of the fracture integrates the effects of elastic, plastic dissipative, fluid, and thermal energies of the rock. The model is constructed in a numerical computation iteration format using finite element discretization and Newton–Raphson iteration. To solve the coupled problem more efficiently, a staggered iteration algorithm is adopted to solve the displacement, pressure, temperature, and phase fields. Several numerical results are extracted and compared with the analytical solution results and experimental test data to demonstrate the accuracy and validity of the proposed model. In addition, the propagation behavior of hydraulic fractures in thermoelastic–plastic reservoirs with homogeneous, natural fractures or layering is investigated, and the results show that the model can capture complex fracture propagation patterns.

在本研究中，我们提出了一种热力学上一致的热流体-固体-弹塑性相场模型，以准确捕捉深层页岩中水力压裂的传播过程。所建立的模型考虑了热弹塑参数的退化、应变硬化、混合模式压裂和热对流。该模型采用了非相关德鲁克-普拉格构成模型和非线性饱和应变函数，以捕捉页岩的变形行为。断裂驱动力综合了岩石的弹性能、塑性耗散能、流体能和热能的影响。该模型采用有限元离散化和牛顿-拉斐森迭代的数值计算迭代格式。为了更有效地解决耦合问题，采用了交错迭代算法来求解位移、压力、温度和相场。提取了若干数值结果，并与分析求解结果和实验测试数据进行了比较，以证明所提模型的准确性和有效性。此外，还研究了具有均质天然裂缝或分层的热弹塑性储层中水力裂缝的传播行为，结果表明该模型能够捕捉复杂的裂缝传播模式。

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引用次数: 0

A pneumatic soft acoustic metamaterial through modular design 模块化设计的气动软声超材料

IF 7.1 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2024-09-27 DOI: 10.1016/j.ijmecsci.2024.109752

Kun Zhang , Ning Chen , Wenqing Zhu , Jian Liu

Tunable acoustic metamaterials have excellent sound waves control and manipulation properties because of their deformations under different stimuli. Pneumatic actuation has recently attracted the attention due to its low-cost, fast in response and easy to integrate. However, due to the difficulty in fabricating soft enough scatterers and ensuring their airtightness, the experimental realization of pneumatic soft acoustic metamaterials remains a great challenge. In this paper, a pneumatic soft acoustic metamaterial is designed and its tunable band gap has been experimentally demonstrated. The designed pneumatic soft acoustic metamaterial comprises an array of soft inflatable rubber cavities in the background of air. And the scatterer in the soft acoustic metamaterials can deform by adjusting the air pressure, which can switch on or off the band gaps. The effects of scatterer shapes and orientations on the adjustable band gap are studied using numerical simulation methods. Furthermore, the modular design is introduced to ensure the flexibility of the designed soft acoustic metamaterials. And we fabricate modularized pneumatic soft acoustic metamaterials with square scatterers through the casting molding approach. The acoustic experiment results are agreement with the simulation results, which demonstrates that the band gap can be efficiently tuned when applying the air pressure. Additionally, the average transmission drops by about 20.2 dB in the maximum band gap of 3209.7–4639.7 Hz. This study provides a guide for designing and fabricating a pneumatic soft acoustic metamaterial, and confirms the feasibility and application potential of the design of acoustic devices by harnessing pneumatic actuation.

可调谐声学超材料在不同刺激下会发生形变，因此具有出色的声波控制和操纵特性。最近，气动驱动因其成本低、响应快和易于集成而备受关注。然而，由于难以制造足够柔软的散射体并确保其气密性，气动软声超材料的实验实现仍然是一个巨大的挑战。本文设计了一种气动软声超材料，并通过实验证明了它的可调带隙。所设计的气动软声超材料由空气背景中的软充气橡胶空腔阵列组成。通过调节气压，软声超材料中的散射体可以变形，从而打开或关闭带隙。利用数值模拟方法研究了散射体形状和方向对可调带隙的影响。此外，我们还引入了模块化设计，以确保所设计的软声超材料的灵活性。我们还通过铸造成型方法制造了模块化的方形散射体气动软声超材料。声学实验结果与仿真结果一致，表明在施加气压时可以有效地调整带隙。此外，在 3209.7-4639.7 Hz 的最大带隙内，平均传输率下降了约 20.2 dB。这项研究为设计和制造气动软声超材料提供了指导，并证实了利用气动致动设计声学器件的可行性和应用潜力。

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引用次数: 0

Better than linear strength scaling of multifunctional ceramic truss lattice materials 多功能陶瓷桁架晶格材料的强度比例优于线性比例

IF 7.1 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2024-09-26 DOI: 10.1016/j.ijmecsci.2024.109725

Fakhreddin Emami, Andrew J. Gross

Driven by the goal of creating exceptionally strong and lightweight thermal insulators to enable the operation of a vacuum airship on Venus, conditions where ceramic truss lattice materials provide better than linear scaling of strength with respect to variations in relative density have been found. This enhanced scaling relationship is a consequence of the pressure sensitive shear strength of ceramic materials. A new Gibson-Ashby type scaling relationship is developed between strength and relative density. Elementary analysis is used to formulate theoretical limits for the compressive strength, minimum density, and minimum thermal conductivity for truss lattice materials subjected to hydrostatic pressure loads. Shape optimization using the covariance matrix adopted evolutionary strategy (CMA-ES) and highly resolved finite element models is conducted on silicon carbide Kelvin cells with variable cross-section axisymmetric struts considering three failure modes: buckling, tensile rupture, and shear failure. The optimized designs closely adhere to and validate the newly developed analytical scaling relationship with better than linear strength scaling. These optimized designs are found to withstand the extreme loading conditions on Venus while providing up to 43

\frac{kg}{m^{3}}

of buoyancy. The thermal conductivity of the optimized designs are computed and found to be less than 0.5

\frac{W}{m K}

, with one design outperforming silica aerogels at elevated temperature.

为了实现在金星上运行真空飞艇的目标，人们发现陶瓷桁架晶格材料的强度随相对密度变化的比例关系优于线性比例关系。这种增强的比例关系是陶瓷材料对压力敏感的剪切强度的结果。在强度和相对密度之间建立了一种新的 Gibson-Ashby 型比例关系。通过基本分析，为承受静水压力载荷的桁架晶格材料制定了抗压强度、最小密度和最小导热系数的理论极限。采用协方差矩阵进化策略（CMA-ES）和高分辨率有限元模型，对具有可变截面轴对称支柱的碳化硅开尔文电池进行了形状优化，考虑了三种失效模式：屈曲、拉伸断裂和剪切失效。优化设计与新开发的分析缩放关系密切相关，并验证了其优于线性强度缩放关系。这些优化设计能够承受金星上的极端载荷条件，同时提供高达 43 kgm3 的浮力。通过计算发现，优化设计的导热系数小于 0.5 WmK，其中一种设计在高温下的性能优于二氧化硅气凝胶。

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引用次数: 0

Effect of meshing-induced deformation on lubrication for journal planet gear bearings 啮合引起的变形对轴颈行星齿轮轴承润滑的影响

IF 7.1 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2024-09-25 DOI: 10.1016/j.ijmecsci.2024.109747

Jiayu Gong , Kun Liu , Fanming Meng , Hongxia Wang , Haoxun Xu

To increase the power density and reliability of wind turbine gearboxes (WTGs), journal planet gear bearings (JPGBs) are increasingly employed in their low-speed planet stages. Except for the pressure- and temperature-induced deformations, the JPGB is also structurally deformed by the gear pair meshing in this application, complicating the lubrication and deformation characteristics. Considering the above meshing-induced deformation, a thermo-elasto-hydrodynamic (TEHD) model is proposed for the JPGB, whose deformation is predicted using a self-programmed procedure based on the finite element method (FEM). Besides, this model is verified through a lubrication experiment of the JPGB in the WTG. It is found that the appropriate meshing-induced deformation, varying periodically in the meshing process, can improve the TEHD and misalignment behaviors of the JPGB due to the load-carrying region expansion or twice hydrodynamic action. This phenomenon becomes increasingly obvious with increasing the WTG's input power and the planet's inner radius.

为了提高风力涡轮机齿轮箱（WTG）的功率密度和可靠性，越来越多的低速行星级采用了轴颈行星齿轮轴承（JPGB）。在这种应用中，除了压力和温度引起的变形外，JPGB 还会因齿轮对啮合而产生结构变形，从而使润滑和变形特性变得复杂。考虑到上述啮合引起的变形，提出了 JPGB 的热-弹性-流体动力学（TEHD）模型，并使用基于有限元法（FEM）的自编程程序对其变形进行了预测。此外，还通过风电机组中 JPGB 的润滑实验对该模型进行了验证。研究发现，适当的网格诱导变形在网格划分过程中周期性变化，可以改善 JPGB 因承载区域膨胀或两次流体动力作用而产生的 TEHD 和错位行为。这种现象随着风电机组输入功率和行星内半径的增加而变得越来越明显。

引用次数: 0

Flexural wave compression behaviors of programmable graded piezoelectric meta-beams 可编程分级压电元梁的挠曲波压缩行为

IF 7.1 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2024-09-24 DOI: 10.1016/j.ijmecsci.2024.109743

Shoubo Dai, Hao Gao, Jiawei Mao, Penglin Gao, Yegao Qu

Active electromechanical metamaterials have drawn significant attention due to their remarkable tunability and adaptability in vibration and wave control. Exploiting the electromechanical coupling effect via controlled biased fields enables precise manipulation of the structural vibrations and wave transmissions. In this research, we have developed a programmable graded piezoelectric meta-beam that successfully imitates the wave compression behavior of an acoustic black hole without modifying the structural geometries. The effective parameters of the meta-beam are reshaped into a gradient distribution by tuning the electrical impedances of the digital shunting circuits. With such graded effective parameters, it becomes feasible to tailor the local wavenumber distribution of the meta-beam and hence achieve the desired wave compression. Numerical results validated our proposed paradigm of the programmable black hole in both straight and curved beams. In contrast to the straight beam, curvature of the curved beam reduces the tunable range of the local wavenumber. A comprehensive parametric study was conducted to investigate the influences of the gradient profile, electric damping, and curvature on the wave control function. For a given desired frequency, programmable control of wave compression location and amplified output of electrical signals are achieved.

有源机电超材料因其在振动和波控制方面显著的可调性和适应性而备受关注。通过可控偏置场利用机电耦合效应，可以精确控制结构振动和波的传输。在这项研究中，我们开发了一种可编程的分级压电元梁，在不改变结构几何形状的情况下成功地模仿了声学黑洞的波压缩行为。通过调整数字分流电路的电阻抗，元光束的有效参数被重塑为梯度分布。有了这种梯度有效参数，就可以定制元光束的局部波数分布，从而实现所需的波压缩。数值结果验证了我们提出的可编程黑洞范例在直波束和曲波束中的应用。与直光束相比，弯曲光束的曲率减小了局部波长的可调范围。为了研究梯度轮廓、电阻尼和曲率对波控制函数的影响，我们进行了全面的参数研究。对于给定的所需频率，可实现对波压缩位置和电信号放大输出的可编程控制。

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引用次数: 0

Multiscale modelling strategy for predicting fatigue performance of welded joints 预测焊接接头疲劳性能的多尺度建模策略

IF 7.1 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2024-09-24 DOI: 10.1016/j.ijmecsci.2024.109751

Hongchang Zhou , Masao Kinefuchi , Yasuhito Takashima , Kazuki Shibanuma

This study predicts the fatigue performance of welded joints through a multiscale modelling strategy accounting for material and structural inhomogeneities. An S-N curve and detailed fracture surfaces with distinct beach marks were first derived by uniaxial fatigue tests utilising the designed cruciform welded joints. Considering the intrinsic features of welded joints, a multiscale modelling strategy was proposed to integrate multiple factors, including microstructural variations, strength distributions within the heat-affected zone (HAZ), and the diversity of three-dimensional weld toe shapes. Significantly, a modelling strategy was presented for the first time to simulate the simultaneous initiation, growth, and coalescence of multiple cracks, and was validated against experimental evidence. The results indicate that the proposed strategy can accurately predict both the fatigue strength and the overall crack growth process. Additionally, comparative assessments of single-crack and multiple-crack modelling strategies revealed notably shorter predicted fatigue lives when considering crack coalescence. Overall, this work establishes a multiscale framework for assessing the fatigue performance of welded joints considering both microscopic and macroscopic factors, offering substantial practical implications for engineering applications.

本研究通过考虑材料和结构不均匀性的多尺度建模策略来预测焊接接头的疲劳性能。首先利用设计的十字形焊接接头进行单轴疲劳试验，得出 S-N 曲线和带有明显海滩痕迹的详细断裂面。考虑到焊接接头的内在特征，提出了一种多尺度建模策略，以综合多种因素，包括微观结构变化、热影响区（HAZ）内的强度分布以及三维焊趾形状的多样性。重要的是，首次提出了模拟多条裂纹同时产生、生长和凝聚的建模策略，并根据实验证据进行了验证。结果表明，所提出的策略可以准确预测疲劳强度和整个裂纹生长过程。此外，对单裂纹和多裂纹建模策略的比较评估显示，在考虑裂纹凝聚的情况下，预测的疲劳寿命明显更短。总之，这项工作建立了一个考虑微观和宏观因素的多尺度框架，用于评估焊接接头的疲劳性能，为工程应用提供了重要的实际意义。

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引用次数: 0

Mechanical interactions modeling of inertial wave energy converters 惯性波能转换器的机械相互作用建模

IF 7.1 1区工程技术 Q1 ENGINEERING, MECHANICAL

International Journal of Mechanical Sciences

Pub Date : 2024-09-24 DOI: 10.1016/j.ijmecsci.2024.109731

Fabio Carapellese, Nicolás Faedo

Numerous technological solutions for wave energy converters (WECs), referred as inertial reaction mass (IRM) systems, incorporate a reacting mass within the floater, coupled with a power take-off (PTO) system, to shelter all electronic components from the hostile sea environment. While the overall complexity of the system increases, the current modeling procedures persist in considering only a limited number of modes of motion, neglecting relevant dynamical effects. In this context, this paper proposes a systematic procedure for defining the kinematic characteristics and overall analytical model for the dynamics of IRM WECs. The significance of the proposed procedure lies in the statement of the reaction mass-related dynamic equation, considering the floater’s parametric excitation in six degrees of freedom (DoF). Additionally, it introduces the procedure for defining the reaction forces that the inertial mass exerts on the floater, which are often neglected in the literature for the full simulation of such systems. Furthermore, the proposed analytical modeling procedure allows the definition of approximated models in more simplified nonlinear forms for dynamic analysis and ultimately in fully linear approximations. This enables the application of methodologies and techniques commonly used in the literature for linear systems. The development of the framework is kept generic, in order to introduce a versatile mathematical procedure, that can be easily adjusted, with minor modifications, to accurately capture and represent the mechanical interaction for a wide family of IRM WEC devices. Subsequently, a case study on a vertical-hinged pendulum WEC is analyzed, to showcase the effectiveness of the proposed methodology. Moreover, to test the reliability of the analytical framework, a comparison with the output of a commercial software is conducted.

波浪能转换器（WECs）的许多技术解决方案被称为惯性反力质量（IRM）系统，在浮筒内加入一个反力质量，再加上一个动力输出（PTO）系统，以保护所有电子元件免受恶劣海洋环境的影响。虽然系统的整体复杂性有所增加，但目前的建模程序始终只考虑有限的运动模式，忽略了相关的动态效应。在这种情况下，本文提出了一种系统程序，用于定义 IRM 水力发电装置的运动特性和整体动力学分析模型。考虑到浮筒在六个自由度（DoF）中的参数激励，所提出程序的意义在于陈述与反作用质量相关的动态方程。此外，它还介绍了定义惯性质量对浮筒施加的反作用力的程序，而在文献中，对此类系统进行全面模拟时往往忽略了这些反作用力。此外，所提出的分析建模程序允许以更简化的非线性形式定义近似模型，用于动态分析，并最终定义为完全线性近似模型。这使得文献中常用于线性系统的方法和技术得以应用。该框架的开发保持了通用性，目的是引入一种通用的数学程序，只需稍加修改即可轻松调整，以准确捕捉和表示各种 IRM 水力发电装置的机械相互作用。随后，对垂直铰链摆式风力发电设备进行了案例分析，以展示所提方法的有效性。此外，为了测试分析框架的可靠性，还与商业软件的输出结果进行了比较。

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