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几何非线性 2

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Numerical analysis of strongly nonlinear oscillation systems using He’s max-min method

H. BABAZADEH, G. DOMAIRRY, A. BARARI, R. AZAMI, A. G. DAVODI

《机械工程前沿（英文）》 2011年第6卷第4期页码 435-441 doi: 10.1007/s11465-011-0243-x

摘要：

Nonlinear functions are crucial points and terms in engineering problems. Actual and physical problems can be solved by solving and processing such functions. Thus, most scientists and engineers focus on solving these equations. This paper presents a novel method called the max-min method for presenting an accurate approximate analytical solution to strong nonlinear oscillators. It can solve many linear or nonlinear differential equations without the tangible restriction of sensitivity to the degree of the nonlinear term. It is also quite convenient due to the reduction in the size of calculations. The algorithm suggests a promising approach and is systematically illustrated step by step.

关键词： min-max method nonlinear oscillation duffing equation mathematical pendulum He’s energy balance method

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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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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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电力系统低频振荡中的非线性奇异现象

马景兰,王伟,万京生,张永丽

《中国工程科学》 2009年第11卷第8期页码 93-96

摘要：

低频振荡是影响电力系统稳定运行的一个重要方面。阐述了低频振荡产生的机理和分析方法，利用Hopf分歧理论，针对一个四阶模型的单机无穷大系统，分析了在临界点附近时可能出现的非线性奇异现象。研究表明：由于分歧的存在，导致系统稳定性在临界点附近出现奇异，从而影响了电力系统的稳定域。

关键词：低频振荡分歧理论非线性奇异

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Evaluation of the influence of El Niño–Southern Oscillation on air quality in southern China from long-term

《环境科学与工程前沿（英文）》 2022年第16卷第2期 doi: 10.1007/s11783-021-1460-0

摘要：

•Strong ENSO influence on AOD is found in southern China region.

关键词： El Niño–Southern Oscillation Aerosol concentration Aerosol particle size Contribution separation Decadal trend Southern China

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New nonlinear stiffness actuator with predefined torque‒deflection profile

《机械工程前沿（英文）》 2023年第18卷第1期 doi: 10.1007/s11465-022-0721-3

摘要： A nonlinear stiffness actuator (NSA) could achieve high torque/force resolution in low stiffness range and high bandwidth in high stiffness range, both of which are beneficial for physical interaction between a robot and the environment. Currently, most of NSAs are complex and hardly used for engineering. In this paper, oriented to engineering applications, a new simple NSA was proposed, mainly including leaf springs and especially designed cams, which could perform a predefined relationship between torque and deflection. The new NSA has a compact structure, and it is lightweight, both of which are also beneficial for its practical application. An analytical methodology that maps the predefined relationship between torque and deflection to the profile of the cam was developed. The optimal parameters of the structure were given by analyzing the weight of the NSA and the mechanic characteristic of the leaf spring. Though sliding friction force is inevitable because no rollers were used in the cam-based mechanism, the sliding displacement between the cam and the leaf spring is very small, and consumption of sliding friction force is very low. Simulations of different torque‒deflection profiles were carried out to verify the accuracy and applicability of performing predefined torque‒deflection profiles. Three kinds of prototype experiments, including verification experiment of the predefined torque‒deflection profile, torque tracking experiment, and position tracking experiment under different loads, were conducted. The results prove the accuracy of performing the predefined torque‒deflection profile, the tracking performance, and the interactive performance of the new NSA.

关键词： compliant actuator nonlinear stiffness actuator nonlinear spring predefined torque−deflection profile

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Mean wind load induced incompatibility in nonlinear aeroelastic simulations of bridge spans

Zhitian ZHANG

《结构与土木工程前沿（英文）》 2019年第13卷第3期页码 605-617 doi: 10.1007/s11709-018-0499-x

摘要： Mean wind response induced incompatibility and nonlinearity in bridge aerodynamics is discussed, where the mean wind and aeroelastic loads are applied simultaneously in time domain. A kind of incompatibility is found during the simultaneous simulation of the mean wind and aeroelastic loads, which leads to incorrect mean wind structural responses. It is found that the mathematic expectations (or limiting characteristics) of the aeroelastic models are fundamental to this kind of incompatibility. In this paper, two aeroelastic models are presented and discussed, one of indicial-function-denoted (IF-denoted) and another of rational-function-denoted (RF-denoted). It is shown that, in cases of low wind speeds, the IF-denoted model reflects correctly the mean wind load properties, and results in correct mean structural responses; in contrast, the RF-denoted model leads to incorrect mean responses due to its nonphysical mean properties. At very high wind speeds, however, even the IF-denoted model can lead to significant deviation from the correct response due to steady aerodynamic nonlinearity. To solve the incompatibility at high wind speeds, a methodology of subtraction of pseudo-steady effects from the aeroelastic model is put forward in this work. Finally, with the method presented, aeroelastic nonlinearity resulted from the mean wind response is investigated at both moderate and high wind speeds.

关键词： bridge aerodynamics nonlinear aeroelastic model Pseudo-steady mean wind loads

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General expression for linear and nonlinear time series models

Ren HUANG, Feiyun XU, Ruwen CHEN

《机械工程前沿（英文）》 2009年第4卷第1期页码 15-24 doi: 10.1007/s11465-009-0015-z

摘要： The typical time series models such as ARMA, AR, and MA are founded on the normality and stationarity of a system and expressed by a linear difference equation; therefore, they are strictly limited to the linear system. However, some nonlinear factors are within the practical system; thus, it is difficult to fit the model for real systems with the above models. This paper proposes a general expression for linear and nonlinear auto-regressive time series models (GNAR). With the gradient optimization method and modified AIC information criteria integrated with the prediction error, the parameter estimation and order determination are achieved. The model simulation and experiments show that the GNAR model can accurately approximate to the dynamic characteristics of the most nonlinear models applied in academics and engineering. The modeling and prediction accuracy of the GNAR model is superior to the classical time series models. The proposed GNAR model is flexible and effective.

关键词： linear and nonlinear autoregressive model system identification time series analysis

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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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Numerical analysis of nonlinear dynamic behavior of earth dams

Babak EBRAHIMIAN

《结构与土木工程前沿（英文）》 2011年第5卷第1期页码 24-40 doi: 10.1007/s11709-010-0082-6

摘要： A numerical study is conducted to investigate the dynamic behavior of earth dams. The numerical investigation employs a fully nonlinear dynamic finite difference analysis incorporating a simple elastic perfectly plastic constitutive model to describe the stress-strain response of the soil and the Rayleigh damping to increase the level of hysteretic damping. The extended Masing rules are implemented into the constitutive model to explain more accurately the soil response under general cyclic loading. The soil stiffness and hysteretic damping change with loading history. The procedures for calibrating the constructed numerical model with centrifuge test data and also a real case history are explained. For the latter, the Long Valley (LV) earth dam subjected to the 1980 Mammoth Lake earthquake as a real case-history is analyzed and the obtained numerical results are compared with the real measurements at the site in both the time and frequency domains. Relatively good agreement is observed between computed and measured quantities. It seems that the Masing rules combined with a simple elasto-plastic model gives reasonable numerical predictions. Afterwards, a comprehensive parametric study is carried out to identify the effects of dam height, input motion characteristics, soil behavior, strength of the shell materials and dam reservoir condition on the dynamic response of earth dams. Three real earthquake records with different levels and peak acceleration values (PGAs) are used as input motions. The results show that the crest acceleration decreases when the dam height increases and no amplification is observed. Further, more inelastic behavior and more earthquake energy absorption are observed in higher dams.

关键词： earth dam numerical nonlinear response dynamic analysis earthquake dam height

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Depth of cut models for multipass abrasive waterjet cutting of alumina ceramics with nozzle oscillation

Jun WANG

《机械工程前沿（英文）》 2010年第5卷第1期页码 19-32 doi: 10.1007/s11465-009-0082-1

摘要： An experimental study of the depth of cut in multipass abrasive waterjet (AWJ) cutting of alumina ceramics with controlled nozzle oscillation is presented. It is found that this cutting technique can significantly increase the depth of cut by an average of 50.8% as compared to single pass cutting without nozzle oscillation under the corresponding cutting conditions and within the same cutting time. Predictive models for the depth of cut are then developed. The modelling process starts with single pass cutting using a dimensional analysis technique and the particle erosion theories applied to alumina ceramics, before progressing to the development of the models for multipass cutting. The models are finally assessed both qualitatively and quantitatively with experimental data. It is shown that the model predictions are in good agreement with the experimental data with the average deviations of about 1%.

关键词： abrasive waterjet engineering ceramics depth of cut cutting performance nozzle oscillation machining

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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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Analytical approach to robust design of nonlinear mechanical systems

Jian ZHANG, Nengsheng BAO, Guojun ZHANG, Peihua GU

《机械工程前沿（英文）》 2009年第4卷第2期页码 203-214 doi: 10.1007/s11465-009-0022-0

摘要： The robustness of mechanical systems is influenced by various factors. Their effects must be understood for designing robust systems. This paper proposes a model for describing the relationships among functional requirements, structural characteristics, design parameters and uncontrollable variables of nonlinear systems. With this model, the sensitivity of systems was analyzed to formulate a system sensitivity index and robust sensitivity matrix to determine the importance of the factors in relation to the robustness of systems. Based on the robust design principle, an optimization model was developed. Combining this optimization model and the Taguchi method for robust design, an analysis was carried out to reveal the characteristics of the systems. For a nonlinear mechanical system, relationships among structural characteristics of the system, design parameters, and uncontrollable variables can be formulated as a mathematical function. The characteristics of the system determine how design parameters affect the functional requirements of the system. Consequently, they affect the distribution of system performance functions. Nonlinearity of the system can facilitate the selection of design parameters to achieve the required functional requirements.

关键词： robust design nonlinear

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Iterative finite element model of nonlinear viscoplastic analyses for blended granular porous media

WU Yuching, ZHU Cimian

《结构与土木工程前沿（英文）》 2007年第1卷第4期页码 464-473 doi: 10.1007/s11709-007-0063-6

摘要： The iterative finite element model, in which an element is used to represent a single particle, is generated to analyze the global behavior of multiple-material aggregates of materially nonlinear viscoplastic particles. The genera

关键词： nonlinear viscoplastic iterative behavior multiple-material

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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