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Design, Analysis, and Experimental Validation of a Variable-Gap Magnetorheological Damper for Seat Suspension 座椅悬架变间隙磁流变阻尼器的设计、分析和实验验证
IF 3.6 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-10-08 Epub Date: 2026-06-21 DOI: 10.1002/msd2.70077
Min Wei, Yuchen He, Xiaoting Rui, Yixin Liu, Lilin Gu

To address the dual challenges of routine driving vibration and impact loads in vehicle seat suspensions, a novel variable-gap magnetorheological damper (VGMRD) is proposed. By combining a tapered piston with a conformal variable-diameter cylinder, stroke-dependent, dual-mode damping characteristics are achieved without the need for complex control valves. A theoretical model incorporating the stroke-dependent gap flow dynamics is established, and a finite element analysis of the internal magnetic field distribution is conducted. Numerical results indicate that the magnetic flux lines are concentrated by the converging geometry of the buffer zone, increasing the magnetic flux density by 17.4% without additional power input. Experimental validations utilizing a servo-hydraulic testing system are performed, and the experimental results show good agreement with the theoretical predictions. Specifically, the damping force remains stable within the damping zone. As the piston enters the buffer zone, the damping force increases significantly with displacement. Through the passive self-reinforcement mechanism, the peak damping force is effectively elevated from 2240 N in the damping zone to a maximum of 4296 N. These findings demonstrate the reliability of the proposed VGMRD in preventing mechanical “bottoming-out” while maintaining routine ride comfort.

针对汽车座椅悬架中日常行驶振动和冲击载荷的双重挑战,提出了一种新型变间隙磁流变阻尼器(VGMRD)。通过将锥形活塞与保形变直径气缸相结合,无需复杂的控制阀即可实现与冲程相关的双模阻尼特性。建立了含冲程相关间隙流动动力学的理论模型,并对内部磁场分布进行了有限元分析。数值计算结果表明,在不增加功率输入的情况下,通过缓冲带的会聚几何形状使磁通量线集中,磁通量密度提高了17.4%。利用伺服液压测试系统进行了实验验证,实验结果与理论预测吻合较好。具体来说,阻尼力在阻尼区内保持稳定。当活塞进入缓冲区时,阻尼力随位移显著增大。通过被动自增强机制,有效地将阻尼区的峰值阻尼力从2240 N提升到最大4296 N。这些发现证明了所提出的VGMRD在保持常规乘坐舒适性的同时防止机械“触底”的可靠性。
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引用次数: 0
Cover Image, Volume 6, Number 2, June 2026 封面图片,第6卷第2期,2026年6月
IF 3.6 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-06-26 DOI: 10.1002/msd2.70084

This cover highlights a multistage control framework for solar-powered wheeled mobile robots, enabling accurate bidirectional trajectory tracking under varying operating conditions. The proposed strategy integrates input–output linearization with differential flatness–based control of the actuator-driver and power-stage subsystems, including an H-bridge and a Buck converter. By explicitly modeling and controlling the actuator-driver dynamics for the first time in this context, the approach achieves robust real-time performance despite parameter uncertainties and voltage disturbances. The experimental validation on a real differential-drive robot prototype, when an emulated photovoltaic source is used, confirms the effectiveness of the integrated control architecture.

本封面重点介绍了太阳能轮式移动机器人的多级控制框架,可在不同的操作条件下实现精确的双向轨迹跟踪。所提出的策略将输入输出线性化与基于差分平坦度的执行器-驱动器和功率级子系统(包括h桥和Buck转换器)的控制相结合。在这种情况下,通过首次显式建模和控制致动器-驱动器动力学,该方法在参数不确定性和电压干扰的情况下实现了鲁棒的实时性能。在一个实际的差动驱动机器人样机上进行了实验验证,并使用了仿真光伏电源,验证了集成控制体系结构的有效性。
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引用次数: 0
Nonlinear Dynamics of a Passive Walker: Bifurcation and Stability Insights With Spring and Damper Mechanics 被动步行器的非线性动力学:分岔和稳定性与弹簧和阻尼力学的见解
IF 3.6 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-06-26 Epub Date: 2026-04-16 DOI: 10.1002/msd2.70057
Zhongqu Xie, Xue Gong, Qidi Fu, Pierluigi Arpenti, Shichao Zhou, Anhua You, Xiaolong Yang, Lingkun Chen, Yulin Wang

This study explores the nonlinear dynamics associated with a passive dynamic walker (PDW), focusing on the bifurcation and stability insights derived from spring and damper mechanics. PDWs, which rely on gravity for stable locomotion without active control, exhibit a rich spectrum of behaviors, from periodic to chaotic motion. The study examines the effects of key system parameters, such as the hip mass ratio, the leg center of mass (CoM) location, spring stiffness, and damper coefficient, on the stability and gait performance of the walker. Through a combination of theoretical analysis and numerical simulations, the paper identifies bifurcation points where periodic orbits transition into chaotic dynamics, shedding light on the critical conditions for stable walking. The results reveal that increased hip mass, spring stiffness, and leg CoM location ratio contribute to faster walking speeds. All of these physical parameters show a non-monotonic effect on stability. Stability first improves and then deteriorates as the parameter values increase. In contrast, the influence of damping on passive walking is relatively minor, and increasing damping does not significantly improve stability, even sometimes leading to the inability to find a stable solution. Moreover, the results also suggest that the addition of the spring can mitigate the bifurcations of the system. This research provides a deeper understanding of the stability transitions in PDWs, with implications for the design of more efficient and robust legged robots.

本研究探讨了与被动动态行走器(PDW)相关的非线性动力学,重点关注来自弹簧和阻尼器力学的分岔和稳定性见解。pdw依靠重力稳定运动,没有主动控制,表现出丰富的行为谱,从周期运动到混沌运动。该研究考察了关键系统参数,如髋关节质量比、腿部质量中心(CoM)位置、弹簧刚度和阻尼系数,对助行器的稳定性和步态性能的影响。通过理论分析和数值模拟相结合,确定了周期轨道过渡到混沌动力学的分岔点,揭示了稳定行走的临界条件。结果表明,髋部质量、弹簧刚度和腿部CoM位置比的增加有助于加快步行速度。所有这些物理参数对稳定性都表现出非单调的影响。随着参数值的增加,稳定性先提高后降低。相比之下,阻尼对被动行走的影响相对较小,增加阻尼并不能明显提高稳定性,甚至有时会导致无法找到稳定的解决方案。此外,结果还表明,弹簧的加入可以减轻系统的分岔。这项研究为pdw的稳定性转变提供了更深入的理解,对设计更高效、更健壮的有腿机器人具有指导意义。
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引用次数: 0
Experimental Modal Analysis-Driven Gaussian Process Regression Modeling of Rectangular Steel Beams With Various Hole Geometries 不同孔几何矩形钢梁的实验模态分析驱动高斯过程回归模型
IF 3.6 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-06-26 Epub Date: 2025-10-01 DOI: 10.1002/msd2.70049
Amir Hossein Rabiee, Majid Rajaei, Mohammad Hossein Mahdavi Nasab, Parsa Shafiei

Understanding the dynamic behavior of structural components is crucial for optimizing performance and ensuring structural integrity. This study presents a new method that combines a systematic experimental investigation of four distinct hole geometries (circular, square, compact rectangular, and long rectangular) with varying hole counts, all designed to maintain equal material removal, and the application of Gaussian Process Regression to model and predict natural frequencies from experimental modal analysis. Experimental modal testing was conducted on 36 beam specimens to evaluate changes in vibrational properties. The results demonstrate a clear relationship between hole geometry and the attenuation of natural frequencies: circular holes resulted in minimal reductions due to uniform stress distribution, whereas square and rectangular holes caused greater stiffness loss, with the most substantial attenuation observed in beams with long rectangular holes where the first natural frequency decreased by up to 44%. The proposed Gaussian Process Regression model achieved high predictive accuracy on the test set, with coefficients of determination (R2) of approximately 0.98 for the first natural frequency, 0.93 for the second, and 0.92 for the third. Sensitivity analysis identified the number of holes as the most influential parameter, contributing 67.8% to variations in the first natural frequency. These findings provide practical guidelines for structural design by identifying optimal hole geometries and counts to achieve weight reduction while maintaining stiffness, and demonstrate the utility of Gaussian Process Regression for reliable modeling of vibrational behavior in perforated beams.

了解结构部件的动态行为对于优化性能和确保结构完整性至关重要。本研究提出了一种新方法,该方法结合了四种不同孔洞几何形状(圆形、方形、紧致矩形和长矩形)的系统实验研究,这些孔洞的设计都是为了保持相同的材料去除,并应用高斯过程回归从实验模态分析中建模和预测固有频率。对36根梁试件进行了模态试验,以评估其振动特性的变化。结果表明,孔的几何形状与固有频率的衰减之间存在明确的关系:由于均匀的应力分布,圆孔导致的衰减最小,而正方形和矩形孔导致的刚度损失更大,在长矩形孔的梁中观察到的衰减最显著,其中第一固有频率下降高达44%。所提出的高斯过程回归模型在测试集上取得了较高的预测精度,第一个固有频率的决定系数(R2)约为0.98,第二个固有频率为0.93,第三个固有频率为0.92。灵敏度分析发现,孔数是影响最大的参数,对第一固有频率的变化贡献了67.8%。这些发现为结构设计提供了实用的指导,通过确定最佳孔洞几何形状和数量,在保持刚度的同时实现减重,并证明了高斯过程回归在穿孔梁振动行为可靠建模中的实用性。
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引用次数: 0
A Passive Low-Frequency, High-Sensitivity Diamagnetic Levitation Accelerometer 无源低频、高灵敏度抗磁悬浮加速度计
IF 3.6 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-06-26 Epub Date: 2026-04-13 DOI: 10.1002/msd2.70066
Yuanping Xu, Yang Wang, Lu Yang, Jin Zhou, Zhiqiang Zhang, Yanxiao Lei

Despite the great potential of diamagnetic levitation accelerometers in detecting low-frequency and weak motion, there is still a demand to further enhance their sensitivity for geophysical and microgravity applications. In this study, a straightforward structural modulating approach is presented to enhance the sensitivity of diamagnetic levitation accelerometer from both theoretical and experimental aspects. It is demonstrated that by regulating the structural parameters of sensing element and permanent magnets, one can refine the magnetic field, diamagnetic forces, and eddy current effect, making it feasible to improve the sensitivity. With the optimized structural parameters, a remarkable sensitivity of 7.32 mm/g, accompanied by ultra-low frequency detection capability (0–1.8 Hz), fine resolution (32 μg), and low noise (6.256 μg/Hz1/2), can be achieved, highlighting the viability of structural design in developing a high-sensitivity accelerometer.

尽管反磁悬浮加速度计在检测低频和弱运动方面具有巨大的潜力,但在地球物理和微重力应用方面仍需要进一步提高其灵敏度。本文提出了一种简单的结构调制方法,从理论和实验两方面提高了反磁悬浮加速度计的灵敏度。结果表明,通过调节传感元件和永磁体的结构参数,可以细化磁场、反磁力和涡流效应,从而提高灵敏度。优化后的结构参数可实现7.32 mm/g的灵敏度、0 ~ 1.8 Hz的超低频率检测能力、32 μg的高分辨率分辨率和6.256 μg/Hz1/2的低噪声,显示了高灵敏度加速度计结构设计的可行性。
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引用次数: 0
Introduction to the State Key Laboratory of Complex Multibody System Dynamics 复杂多体系统动力学国家重点实验室简介
IF 3.6 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-06-26 Epub Date: 2026-04-29 DOI: 10.1002/msd2.70071
Xiaoting Rui, Hailong Yu
<p>The State Key Laboratory of Complex Multibody System Dynamics is dedicated to addressing critical demands for enhancing the scientific, technological, and industrial research and development capabilities with the goal of improving equipment performance. The laboratory tackles major scientific and technological challenges in the multibody system modeling of equipment. These challenges include poor design and performance, low manufacturing quality, high testing and evaluation costs, and operational safety risks, which have long constrained equipment development.</p><p>The Laboratory has assumed leadership in more than 100 major ongoing and completed engineering and research projects, with research results that had impact on more than 150 major engineering applications and 40 different equipment types, significantly improving performance, reducing testing costs, and ensuring operational safety. Several scientific breakthroughs have been achieved, including the Multibody System Transfer Matrix Method, internationally renowned as the Rui method, which represents a milestone in the history of scientific and technological development. The Laboratory has received eight National Science and Technology Progress Awards and National Technological Invention Awards. It serves as the host or affiliated institution for three international entities: the International Society for Mechanical System Dynamics, the International Journal of Mechanical System Dynamics, and the International Conference on Mechanical System Dynamics.</p><p>The Laboratory has made significant contributions to solving serious and challenging problems that restricted equipment development, including enhancing computational efficiency to meet the requirements of system dynamics modeling and simulation. To this end, the theoretical and technical framework of the Rui method was established and used as the basis for developing a high-performance, large-scale industrial software for equipment virtual analysis and design, achieving the fastest computational speed to meet the urgent need for rapid and cost-effective virtual prototyping.</p><p>The software encompasses a wide range of multibody dynamics modules for various equipment, features advanced launch-dynamics functions, and is supported by a state-of-the-art database of equipment system dynamics. Its computational speed surpasses that of similar software. Moreover, the software supports cross-platform operation on Windows and Linux. It features automated equation derivation, automated post-processing visualization of, and standard output for evaluation of system performance, enabling effective modeling and simulation of complex multibody dynamics of equipment. The software has been successfully used in the dynamics analysis and performance evaluation of large-scale industry equipment such as weapons, ships, astronautics, and aeronaoutics. The software contributes to enhancing design capabilities, manufacturing, testing, evaluation, and uti
复杂多体系统动力学国家重点实验室致力于解决提高科学、技术和工业研发能力的关键需求,目标是提高设备性能。该实验室解决了设备多体系统建模中的重大科学和技术挑战。这些挑战包括设计和性能差、制造质量低、测试和评估成本高以及操作安全风险,长期以来一直制约着设备的发展。实验室主导了100多个正在进行和已完成的重大工程和研究项目,研究成果影响了150多个重大工程应用和40种不同的设备类型,显著提高了性能,降低了测试成本,确保了运行安全。取得了多项科学突破,包括国际知名的多体系统传递矩阵法,这是科技发展史上的一个里程碑。实验室先后八次获得国家科学技术进步奖和国家技术发明奖。它是三个国际实体的主办机构或附属机构:国际机械系统动力学学会,国际机械系统动力学杂志和国际机械系统动力学会议。该实验室在解决制约设备发展的严重和具有挑战性的问题方面做出了重大贡献,包括提高计算效率以满足系统动力学建模和仿真的要求。为此,建立了Rui方法的理论和技术框架,并以此为基础开发了高性能、大规模的工业软件,用于设备虚拟分析与设计,实现了最快的计算速度,以满足快速、高性价比的虚拟样机的迫切需求。该软件包含广泛的多体动力学模块,适用于各种设备,具有先进的发射动力学功能,并由最先进的设备系统动力学数据库支持。它的计算速度超过了同类软件。此外,该软件支持Windows和Linux的跨平台操作。它具有自动方程推导,自动后处理可视化和系统性能评估的标准输出,能够有效地建模和模拟设备的复杂多体动力学。该软件已成功应用于武器、舰船、航天、航空等大型工业装备的动力学分析和性能评价。该软件有助于提高设备系统的设计能力、制造、测试、评估和利用,包括车辆、机器、飞机、高速列车、机器人、工程机械、专用车辆和制造生产线。该实验室还在磁流变液、磁流变阻尼装置和磁流变控制系统方面做出了重要的研究贡献。纳米增强磁流变液;具有工作温度范围宽、屈服应力高、稳定性好、动态性能好、响应快的可变刚度和阻尼;被开发。这些贡献促成了为磁共振材料、器件和设备振动控制建立了一个全面的技术框架。该技术成果已在六种设备中得到验证或应用,典型设备的振动降低了30%至80%。MR阻尼系统的减振效果是被动阻尼系统的几倍,同时在功耗、响应速度、成本和可靠性方面明显优于主动阻尼系统。该技术可应用于各种设备的振动控制,包括车辆、飞机、高速列车、机器人、机床、工程机械和专用车辆。具体应用包括悬挂系统、座椅、发动机、驾驶室和惯性测量单元。
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引用次数: 0
Nonlinear Vibration Characteristic Analysis of Electric Vehicle–Road Coupling System 电动汽车-道路耦合系统非线性振动特性分析
IF 3.6 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-06-26 Epub Date: 2026-03-18 DOI: 10.1002/msd2.70064
Guizhen Feng, Shaohua Li, Xuewei Wang

In-wheel motor drive is the developing direction of automobile electrification and intelligence. However, the increased unsprung mass in in-wheel motor-driven electric vehicles (IWMEVs) leads to higher dynamic tire loads, thereby intensifying vehicle–road coupling interactions. To address this problem, an 11-degree-of-freedom nonlinear dynamic model of a vehicle–motor–road coupled system is developed, incorporating nonlinear suspension, tire stiffness, and road foundation. Using the Galerkin method and trigonometric product formulas, an analytical expression for the sandwich plate road model on a nonlinear viscoelastic foundation is obtained. The vehicle–motor–road coupled model is solved with a validated fixed-step Runge–Kuta method to investigate the coupled effects of electromagnetic excitation, road irregularity, and road vibration. Results reveal that the amplitude–frequency characteristics of electromagnetic excitation are closely related to vehicle–road coupled vibrations. Multiple excitations adversely affect the IWMEV ride comfort. Furthermore, comparative analysis of linear and nonlinear models demonstrates the importance of the developed nonlinear vehicle–motor–road coupling model.

轮毂电机驱动是汽车电气化、智能化的发展方向。然而,轮毂电机驱动电动汽车(iwmev)的非簧载质量增加导致了更高的动态轮胎载荷,从而加剧了车路耦合相互作用。为了解决这一问题,建立了考虑非线性悬架、轮胎刚度和道路基础的11自由度车辆-电机-道路耦合系统的非线性动力学模型。利用伽辽金法和三角积公式,得到了非线性粘弹性地基夹层板道路模型的解析表达式。采用经过验证的定步龙格-库塔法求解车-机-路耦合模型,研究了电磁激励、道路不平整度和道路振动的耦合效应。结果表明,电磁激励的幅频特性与车辆-道路耦合振动密切相关。多重激励对IWMEV的平顺性有不利影响。通过对线性模型和非线性模型的对比分析,证明了所建立的非线性车-机-路耦合模型的重要性。
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引用次数: 0
Interaction Between Vortex-Induced Vibrations and Base Vibrations in Piezoelectric Harvesters 压电收割机中涡激振动与基座振动的相互作用
IF 3.6 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-06-26 Epub Date: 2025-11-23 DOI: 10.1002/msd2.70054
Michele Tonan, Ilaria Palomba, Alberto Pasetto, Alberto Doria

In the present era, powering sensors using green energy is a significant challenge. One promising solution for the power supply of small sensors relies on piezoelectric energy harvesters excited by vortex-induced vibrations (VIVs) generated by wind. In these devices, the harvester typically features a cylindrical bluff body that generates the vortex shedding and also tunes the natural frequency of the cantilever according to the frequency of the excitation. However, in many practical applications, the harvester is not mounted on a perfectly rigid base. The compliance of the base can significantly influence the behavior of the system. Furthermore, harvesters are often installed on moving structures or machines, where base vibrations introduce additional complexities. Therefore, understanding the impact of both harmonic and random base excitations on VIV is essential for harvester design. This paper investigates these phenomena in a comprehensive way. It presents a multiphysics mathematical model of a piezoelectric energy harvester mounted on a moving base, numerical results, and a wide series of experimental tests. The model reliably predicts the harvester behavior under various conditions and enables to extend the experimental investigation. Experimental and numerical results show that base vibrations and VIV can generate voltage in a synergistic way. Nevertheless, for large base vibrations, nonlinear effects take place that affect the maximum amplitude of the generated voltage in the lock-in region. The study shows that these phenomena happen with both harmonic and random base excitation.

在当今时代,使用绿色能源为传感器供电是一项重大挑战。小型传感器供电的一个很有前途的解决方案是依靠由风产生的涡激振动(VIVs)激发的压电能量收集器。在这些装置中,收割机通常具有产生涡流脱落的圆柱形钝体,并且还根据激励的频率调整悬臂的固有频率。然而,在许多实际应用中,收割机并没有安装在一个完全刚性的基础上。地基的柔度对系统的性能有很大的影响。此外,收割机通常安装在移动的结构或机器上,基座振动会带来额外的复杂性。因此,了解谐波和随机基激励对激振的影响对收割机的设计至关重要。本文对这些现象进行了较为全面的研究。提出了一种移动基座上压电能量采集器的多物理场数学模型、数值结果和一系列广泛的实验测试。该模型可靠地预测了收割机在各种条件下的性能,为进一步的实验研究奠定了基础。实验和数值结果表明,基振和涡激振动可以协同产生电压。然而,对于大的基底振动,会发生非线性效应,影响锁定区域产生电压的最大振幅。研究表明,这些现象在谐波和随机基激励下都会发生。
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引用次数: 0
Numerical Insights Into the Resistance Reduction Mechanisms of Forward Tapered Transoms in High-Speed Catamaran: A Computational Fluid Dynamics-Based Study 高速双体船前锥形横梁减阻机理的数值研究:基于计算流体动力学的研究
IF 3.6 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-06-26 Epub Date: 2025-12-13 DOI: 10.1002/msd2.70055
Chalermkiat Nuchturee, Chairat Napasaksri, Ramil Kesvarakul, Sarawuth Srinakaew

This study investigates the hydrodynamic influence of forward transom tapering on a displacement catamaran hull using computational fluid dynamics (CFD) simulations. Five taper configurations ranging from a vertical transom base design to a fully tapered stern (1.00B) were evaluated over a wide Froude number range (Fr = .3 to 1.0). The simulations were performed using a RANS-based solver coupled with the volume of fluid (VOF) method to accurately capture free-surface effects. Turbulence was modeled using the SST k–ω approach to account for boundary layer evolution and wake separation. The analysis focused on resistance components, free-surface wave elevation mapping, transom pressure distribution, and wake streamline to assess hydrodynamic performance. Results indicate that forward tapering significantly affects pressure resistance while frictional resistance is slightly altered. The 0.75B taper configuration consistently demonstrated optimal performance, reducing the total resistance coefficient (CT) by up to 6.39% and enhancing stern pressure recovery without introducing flow instabilities at higher speeds. Wave elevation analysis revealed a marked reduction in stern hollows and improved surface coherence with longer tapers. Transom pressure mapping showed attenuation of suction zones, while streamline visualizations illustrated wake narrowing and recirculation suppression in tapered configurations. The novelty of this study lies in its focus on geometric forward transom tapering. These findings not only advance the understanding of transom hydrodynamics but also establish the 0.75B forward taper configuration as a practical and efficient design recommendation for resistance reduction in high-speed displacement catamarans.

利用计算流体动力学(CFD)模拟研究了前尾梁变细对排水量双体船船体的水动力影响。在较宽的弗劳德数范围内(Fr =)评估了从垂直尾梁基础设计到全锥形尾梁(1.00B)的五种锥形配置。3 ~ 1.0)。模拟使用基于ranss的求解器和流体体积(VOF)方法进行,以准确捕获自由表面效应。湍流采用海温k -ω方法模拟,以考虑边界层演化和尾流分离。分析的重点是阻力分量、自由面波高程映射、尾板压力分布和尾流流线,以评估水动力性能。结果表明,前向锥度对摩擦阻力的影响较小,而对压力阻力的影响较大。0.75B锥形配置始终表现出最佳性能,可将总阻力系数(CT)降低6.39%,并在不引入高速流动不稳定性的情况下提高尾压恢复。波浪高程分析显示,尾部凹陷明显减少,较长的锥度改善了表面相干性。尾板压力图显示了吸力区域的衰减,而流线图显示了锥形配置下尾流变窄和再循环抑制。这项研究的新颖之处在于它的重点是几何前横梁逐渐变细。这些发现不仅促进了对尾梁流体力学的理解,而且还确立了0.75B前锥结构作为高速排水量双体船减阻实用高效的设计建议。
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引用次数: 0
Robust Linearization and Eigenvalue Analysis of General Complex Constrained Multibody Systems 一般复杂约束多体系统的鲁棒线性化及特征值分析
IF 3.6 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-06-26 Epub Date: 2026-04-13 DOI: 10.1002/msd2.70067
Zhiwen Xiao, Gexue Ren

The derivation of linearized equations and subsequent eigenvalue analysis is the basis for tasks such as frequency-domain response analysis, control design, and stability assessment for mechanical systems. However, for general multibody systems with redundant or nonholonomic constraints, practical challenges persist in achieving numerically stable linearization and reliable eigenvalue analysis. This study provides numerically reliable linearization and eigenvalue analysis algorithms of Lagrange's equations of the first kind for general multibody systems, and forms a systematic computational framework. First, a robust linearization methodology is developed to automatically generate linearized state-space equations. Coordinate partitioning is employed not only to eliminate redundant constraints and dependent coordinates, but also to significantly simplify the calculations. Second, a direct eigenvalue analysis on Redundant Coordinate Set Jacobians is performed instead of decomposing the state matrix, for its better numerical conditioning and sparsity. The equivalence of the eigenvalue problems is strictly proven theoretically. The methodology is validated by various benchmark problems and practical cases. The proposed approach has been implemented and released with a general-purpose rigid-flexible coupled multibody dynamics software INTESIM-FMBD (v7.0), and provides a reliable numerical tool for linearizing general mechanical systems.

线性化方程的推导和随后的特征值分析是诸如频域响应分析、控制设计和机械系统稳定性评估等任务的基础。然而,对于具有冗余或非完整约束的一般多体系统,实现数值稳定的线性化和可靠的特征值分析仍然存在实际挑战。本研究为一般多体系统提供了数值可靠的第一类拉格朗日方程线性化和特征值分析算法,形成了系统的计算框架。首先,开发了一种鲁棒线性化方法来自动生成线性化的状态空间方程。采用坐标划分不仅消除了冗余约束和依赖坐标,而且大大简化了计算。其次,利用冗余坐标集雅可比矩阵的直接特征值分析代替分解状态矩阵,使其具有更好的数值条件和稀疏性;从理论上严格证明了特征值问题的等价性。通过各种基准问题和实际案例验证了该方法的有效性。该方法已在通用刚柔耦合多体动力学软件INTESIM-FMBD (v7.0)上实现并发布,为一般机械系统的线性化提供了可靠的数值工具。
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国际机械系统动力学学报(英文)
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