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振动 6

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Lipschitz非线性系统；动态输出反馈控制；事件触发控制；全局渐近稳定 1

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Evaluation of transmissibility for a class of nonlinear passive vibration isolators

Z. K. PENG, Z. Q. LANG, G. MENG

《机械工程前沿（英文）》 2012年第7卷第4期页码 401-409 doi: 10.1007/s11465-012-0349-9

摘要：

In this study, the concept of Output Frequency Response Functions (OFRFs) is applied to represent the transmissibility of nonlinear isolators in frequency domain. With the OFRFs estimated from numerical simulation responses, an explicit analytical relationship between the transmissibility and the nonlinear characteristic parameters is derived for a wide class of nonlinear isolators that have nonlinear anti-symmetric damping characteristics and a comprehensive pattern about how the nonlinear damping characteristic parameters might affect the force and displacement transmissibility is built for the vibration isolators. The results reveal that it is reasonable to analyze the force and displacement transmissibility of the nonlinear isolators by simply investigating the fundamental harmonic components of the force and displacement outputs of the nonlinear isolators, and the introduction of a nonlinear anti-symmetric damping into vibration isolators can significantly suppress both the force and displacement transmissibility over the resonant frequency region, but has almost no effect on the transmissibility at non-resonant regions. These conclusions are of significant importance in the analysis and design of the nonlinear vibration isolators with nonlinear anti-symmetric damping.

关键词： nonlinear vibration volterra series Output Frequency Response Functions (OFRFs) nonlinear damping vibration isolator

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Velocity gradient elasticity for nonlinear vibration of carbon nanotube resonators

Hamid M. SEDIGHI, Hassen M. OUAKAD

《结构与土木工程前沿（英文）》 2020年第14卷第6期页码 1520-1530 doi: 10.1007/s11709-020-0672-x

摘要： In this study, for the first time, we investigate the nonlocality superimposed to the size effects on the nonlinear dynamics of an electrically actuated single-walled carbon-nanotube-based resonator. We undertake two models to capture the nanostructure nonlocal size effects: the strain and the velocity gradient theories. We use a reduced-order model based on the differential quadrature method (DQM) to discretize the governing nonlinear equation of motion and acquire a discretized-parameter nonlinear model of the system. The structural nonlinear behavior of the system assuming both strain and velocity gradient theories is investigated using the discretized model. The results suggest that nonlocal and size effects should not be neglected because they improve the prediction of corresponding dynamic amplitudes and, most importantly, the critical resonant frequencies of such nanoresonators. Neglecting these effects may impose a considerable source of error, which can be amended using more accurate modeling techniques.

关键词： velocity gradient elasticity theory nanotube resonators differential-quadrature method nonlinear vibration

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Vibration suppression of speed-controlled robots with nonlinear control

Paolo BOSCARIOL,Alessandro GASPARETTO

《机械工程前沿（英文）》 2016年第11卷第2期页码 204-212 doi: 10.1007/s11465-016-0380-3

摘要：

In this paper, a simple nonlinear control strategy for the simultaneous position tracking and vibration damping of robots is presented. The control is developed for devices actuated by speed-controlled servo drives. The conditions for the asymptotic stability of the closed-loop system are derived by ensuring its passivity. The capability of achieving improved trajectory tracking and vibration suppression is shown through experimental tests conducted on a three-axis Cartesian robot. The control is aimed to be compatible with most industrial applications given the simplicity of implementation, the reduced computational requirements, and the use of joint position as the only measured signal.

关键词： industrial robot nonlinear control vibration damping model-free control motion control

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Numerical analysis of vehicle-bridge coupling vibration concerning nonlinear stress-dependent damping

Pengfei LI; Jinquan ZHANG; Shengqi MEI; Zhenhua DONG; Yan MAO

《结构与土木工程前沿（英文）》 2022年第16卷第2期页码 239-249 doi: 10.1007/s11709-021-0804-y

摘要： Damping is known to have a considerable influence on the dynamic behavior of bridges. The fixed damping ratios recommended in design codes do not necessarily represent the complicated damping characteristics of bridge structures. This study investigated the application of stress-dependent damping associated with vehicle-bridge coupling vibration and based on that investigation proposed the stress-dependent damping ratio. The results of the investigation show that the stress-dependent damping ratio is significantly different from the constant damping ratio (5%) defined in the standard specification. When vehicles travel at speeds of 30, 60, and 90, the damping ratios of the bridge model are 3.656%, 3.658%, and 3.671%, respectively. The peak accelerations using the regular damping ratio are 18.9%, 21.3%, and 14.5% of the stress-dependent damping ratio, respectively. When the vehicle load on the bridge is doubled, the peak acceleration of the mid-span node increases by 5.4 times, and the stress-related damping ratio increases by 2.1%. A corrugated steel-web bridge is being used as a case study, and the vibration response of the bridge is compared with the measured results. The acceleration response of the bridge which was calculated using the stress-dependent damping ratio is significantly closer to the measured acceleration response than that using the regular damping ratio.

关键词： vehicle-bridge vibration system dynamic analysis stress-dependent damping energy dissipation

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Parametric oscillation of cables and aerodynamic effect

Yong XIA, Jing ZHANG, Youlin XU, Yozo FUJINO,

《结构与土木工程前沿（英文）》 2010年第4卷第3期页码 321-325 doi: 10.1007/s11709-010-0028-z

摘要： This paper addresses the aerodynamic effect on the nonlinear oscillation, particularly parametric vibration of cables in cable-stayed bridges. A simplified 2-DOF model, including a beam and a stayed cable, is formulated first. Response of the cable under global harmonic excitation which is associated with wind speed is obtained using the multiple scales method. Via numerical analysis, the stability condition of the cable in terms of wind speed is derived. The method is applied to a numerical example and a long-span bridge to analyze its all stay cables. It is demonstrated that very large vibration at one of the longest cables in the middle span of the bridge can be parametrically excited when the wind speed is over around 210 km/h (58.5 m/s).

关键词： parametric vibration cables cable-stayed bridge nonlinear vibration

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Nonlinear dynamic behavior of rotating blade with breathing crack

Laihao YANG, Zhu MAO, Shuming WU, Xuefeng CHEN, Ruqiang YAN

《机械工程前沿（英文）》 2021年第16卷第1期页码 196-220 doi: 10.1007/s11465-020-0609-z

摘要： This study aims at investigating the nonlinear dynamic behavior of rotating blade with transverse crack. A novel nonlinear rotating cracked blade model (NRCBM), which contains the spinning softening, centrifugal stiffening, Coriolis force, and crack closing effects, is developed based on continuous beam theory and strain energy release rate method. The rotating blade is considered as a cantilever beam fixed on the rigid hub with high rotating speed, and the crack is deemed to be open and close continuously in a trigonometric function way with the blade vibration. It is verified by the comparison with a finite element-based contact crack model and bilinear model that the proposed NRCBM can well capture the dynamic characteristics of the rotating blade with breathing crack. The dynamic behavior of rotating cracked blade is then investigated with NRCBM, and the nonlinear damage indicator (NDI) is introduced to characterize the nonlinearity caused by blade crack. The results show that NDI is a distinguishable indicator for the severity level estimation of the crack in rotating blade. It is found that severe crack (i.e., a closer crack position to blade root as well as larger crack depth) is expected to heavily reduce the stiffness of rotating blade and apparently result in a lower resonant frequency. Meanwhile, the super-harmonic resonances are verified to be distinguishable indicators for diagnosing the crack existence, and the third-order super-harmonic resonances can serve as an indicator for the presence of severe crack since it only distinctly appears when the crack is severe.

关键词： rotating blade breathing crack nonlinear vibration nonlinear damage indicator

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Nonlinear dynamic analysis of functionally graded carbon nanotube-reinforced composite plates using MISQ20

《结构与土木工程前沿（英文）》页码 1072-1085 doi: 10.1007/s11709-023-0951-4

摘要： The main objective of this study is to further extend the mixed integration smoothed quadrilateral element with 20 unknowns of displacement (MISQ20) to investigate the nonlinear dynamic responses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates with four types of carbon nanotube distributions. The smooth finite element method is used to enhance the accuracy of the Q4 element and avoid shear locking without using any shear correction factors. This method yields accurate results even if the element exhibits a concave quadrilateral shape and reduces the error when the element meshing is rough. Additionally, the element stiffness matrix is established by integrating the boundary of the smoothing domains. The motion equation of the FG-CNTRC plates is solved by adapting the Newmark method combined with the Newton–Raphson algorithm. Subsequently, the calculation program is coded in the MATLAB software and verified by comparing it with other published solutions. Finally, the effects of the input parameters on the nonlinear vibration of the plates are investigated.

关键词： carbon nanotube MISQ20 FG-CNTRC plate nonlinear vibration nonlinear dynamic analysis SFEM

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Computation and investigation of mode characteristics in nonlinear system with tuned/mistuned contact

Houxin SHE, Chaofeng LI, Qiansheng TANG, Hui MA, Bangchun WEN

《机械工程前沿（英文）》 2020年第15卷第1期页码 133-150 doi: 10.1007/s11465-019-0557-7

摘要： This study derived a novel computation algorithm for a mechanical system with multiple friction contact interfaces that is well-suited to the investigation of nonlinear mode characteristic of a coupling system. The procedure uses the incremental harmonic balance method to obtain the nonlinear parameters of the contact interface. Thereafter, the computed nonlinear parameters are applied to rebuild the matrices of the coupling system, which can be easily solved to calculate the nonlinear mode characteristics by standard iterative solvers. Lastly, the derived method is applied to a cycle symmetry system, which represents a shaft–disk–blade system subjected to dry friction. Moreover, this study analyzed the effects of the tuned and mistuned contact features on the nonlinear mode characteristics. Numerical results prove that the proposed method is particularly suitable for the study of nonlinear characteristics in such nonlinear systems.

关键词： coupling vibration nonlinear mode original algorithm contact interface

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混沌工程学

龙运佳

《中国工程科学》 2001年第3卷第2期页码 10-15

摘要：

世界是非线性的，线性只是其近似描述，混沌的发现表明：某些确定性非线性系统具有内在的随机行为。事实上，以往20年，无所不在的混沌现象几乎在每个学科都有所报道，如数学、物理学、化学，甚至社会科学。但理论研究学者的主要兴趣在于探究混沌的本质。与此同时，混沌的实际利用在许多工程领域受到重视，如信息工程、系统工程、医药工程、农业工程、电气工程、生物工程、机械工程、土木工程等。混沌工程学是一门新的研究混沌实际利用及其基本理论的非线性工程科学。文章对现代混沌工程学的定义、对象、概念、方法、理论与应用加以总结，并介绍其近来的进展及作者的工作。混沌工程学在国民经济与国防建设中研究的热点是：混沌分析技术，混沌控制技术与混沌生成技术。

关键词：非线性混沌振荡振动波

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板壳分析与应用

刘人怀

《中国工程科学》 2000年第2卷第11期页码 60-67

摘要：

板壳分析是现代固体力学的一个重要分支。这门学科几乎与一切工程设计都有关联，对航天、航空、航海、机械、石化、建筑、水利、动力、仪表、交通等工程设计，尤其具有指导意义。现今，经典的薄板壳线性理论已较成熟，并在各种工程设计中起着指导作用。然而，在薄板壳非线性领域和厚板壳线性领域，还有许多问题未被解决。文章在介绍这门学科发展历史的基础上，概述了作者近四十年结合工程实际对波纹板壳、单层板壳、双层金属旋转扁壳、网格扁壳、夹层板壳和复合材料层合板壳等六类薄板壳的非线性弯曲、稳定和振动问题以及厚、薄板壳弯曲问题进行理论探索的情况。

关键词：薄板壳厚板壳非线性线性弯曲稳定振动

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用于预测涡振稳态振幅的箱梁竖向涡激力简化非线性模型

朱乐东, 孟晓亮, 杜林清, 丁明畅

《工程（英文）》 2017年第3卷第6期页码 854-862 doi: 10.1016/j.eng.2017.06.001

摘要：

采用同步测力测振大比例节段模型风洞试验方法，研究了作用在全封闭、半封闭和中央开槽三种典型箱梁上竖向涡激力的非线性特性，通过分析竖向涡激力不同成分的能量演化规律和对涡振响应的贡献，探索了竖向涡激共振的起振、发展和自限幅的机理。结果显示：不同类型箱梁的竖向涡激力的非线性成分通常会有所不同，但控制竖向涡激振动稳态响应幅值的最重要涡激力成分都是速度一次线性和三次非线性气动阻尼力成分。前者向振动系统提供了一个恒定的负气动阻尼比，因而是驱动涡振振幅发展的根本动力，而后者则向系统提供了一个与涡振速度平方成正比的正气动阻尼比，从而实质上成为导致涡振自限幅现象的内在因素。有鉴于此，本文提出了一个能高精度预测大跨度桥梁涡振稳态振幅的箱梁断面竖向涡激力通用简化非线性数学模型，并进行了验证。

关键词：箱形桥梁竖向涡激振动竖向涡激力简化非线性模型风洞试验大比例节段模型同步测力测振

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Vibration characteristics and machining performance of a novel perforated ultrasonic vibration platform

《机械工程前沿（英文）》 2023年第18卷第1期 doi: 10.1007/s11465-022-0730-2

摘要： Ultrasonic vibration-assisted grinding (UVAG) is an advanced hybrid process for the precision machining of difficult-to-cut materials. The resonator is a critical part of the UVAG system. Its performance considerably influences the vibration amplitude and resonant frequency. In this work, a novel perforated ultrasonic vibration platform resonator was developed for UVAG. The holes were evenly arranged at the top and side surfaces of the vibration platform to improve the vibration characteristics. A modified apparent elasticity method (AEM) was proposed to reveal the influence of holes on the vibration mode. The performance of the vibration platform was evaluated by the vibration tests and UVAG experiments of particulate-reinforced titanium matrix composites. Results indicate that the reasonable distribution of holes helps improve the resonant frequency and vibration mode. The modified AEM, the finite element method, and the vibration tests show a high degree of consistency for developing the perforated ultrasonic vibration platform with a maximum frequency error of 3%. The employment of ultrasonic vibration reduces the grinding force by 36% at most, thereby decreasing the machined surface defects, such as voids, cracks, and burnout.

关键词： ultrasonic vibration-assisted grinding perforated ultrasonic vibration platform vibration characteristics apparent elasticity method grinding force surface integrity

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Recent development of vibration utilization engineering

WEN Bangchun

《机械工程前沿（英文）》 2008年第3卷第1期页码 1-9 doi: 10.1007/s11465-008-0017-2

摘要： The utilization of vibration and wave, which was developed during the latter half of the 20th century, is one of the most valueable technology applications and has been rapidly developing recently . Because the technique is closely associated with industry and agriculture, it can create huge social and economical benefits and provide excellent services for society. Thus, due to its necessity in industry and daily life, extensive research has been devoted to vibration utillization engineering. In this paper, vibration utilization is classified into linear or non-linear vibrations, waves, and electric-magnetic oscillations. Their phenomena, patterns, and applications in nature and society are introduced. Some research results about vibration utilization engineering are described.

关键词： utilization engineering non-linear vibration vibration utillization utillization engineering

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Application of python-based Abaqus preprocess and postprocess technique in analysis of gearbox vibration

Guilian YI, Yunkang SUI, Jiazheng DU

《机械工程前沿（英文）》 2011年第6卷第2期页码 229-234 doi: 10.1007/s11465-011-0128-z

摘要：

To reduce vibration and noise, a damping layer and constraint layer are usually pasted on the inner surface of a gearbox thin shell, and their thicknesses are the main parameters in the vibration and noise reduction design. The normal acceleration of the point on the gearbox surface is the main index that can reflect the vibration and noise of that point, and the normal accelerations of different points can reflect the degree of the vibration and noise of the whole structure. The K-S function is adopted to process many points’ normal accelerations as the comprehensive index of the vibration characteristics of the whole structure, and the vibration acceleration level is adopted to measure the degree of the vibration and noise. Secondary development of the Abaqus preprocess and postprocess on the basis of the Python scripting programming automatically modifies the model parameters, submits the job, and restarts the analysis totally, which avoids the tedious work of returning to the Abaqus/CAE for modifying and resubmitting and improves the speed of the preprocess and postprocess and the computational efficiency.

关键词： Abaqus secondary development Python language vibration and noise reduction K-S function vibration acceleration level

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Similitude design for the vibration problems of plates and shells: A review

Yunpeng ZHU, You WANG, Zhong LUO, Qingkai HAN, Deyou WANG

《机械工程前沿（英文）》 2017年第12卷第2期页码 253-264 doi: 10.1007/s11465-017-0418-1

摘要：

Similitude design plays a vital role in the analysis of vibration and shock problems encountered in large engineering equipment. Similitude design, including dimensional analysis and governing equation method, is founded on the dynamic similitude theory. This study reviews the application of similitude design methods in engineering practice and summarizes the major achievements of the dynamic similitude theory in structural vibration and shock problems in different fields, including marine structures, civil engineering structures, and large power equipment. This study also reviews the dynamic similitude design methods for thin-walled and composite material plates and shells, including the most recent work published by the authors. Structure sensitivity analysis is used to evaluate the scaling factors to attain accurate distorted scaling laws. Finally, this study discusses the existing problems and the potential of the dynamic similitude theory for the analysis of vibration and shock problems of structures.

关键词： review dynamic similitude vibration model test