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An improved interval model updating method via adaptive Kriging models

Applied Mathematics and Mechanics(English Edition) 2024年第3期45卷 497-514页

作者： Sha WEI Yifeng chen Hu DING liqun chen Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai Frontier Science Center of MechanoinformaticsShanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200072China Shanghai Institute of Aircraft Mechanics and Control Shanghai 200092China

Interval model updating(IMU)methods have been widely used in uncertain model updating due to their low requirements for sample ***,the surrogate model in IMU methods mostly adopts the one-time construction *** makes the accuracy of the surrogate model highly dependent on the experience of users and affects the accuracy of IMU ***,an improved IMU method via the adaptive Kriging models is *** method transforms the objective function of the IMU problem into two deterministic global optimization problems about the upper bound and the interval diameter through universal grey *** optimization problems are addressed through the adaptive Kriging models and the particle swarm optimization(PSO)method to quantify the uncertain parameters,and the IMU is *** the construction of these adaptive Kriging models,the sample space is gridded according to sensitivity *** sampling is then performed in key subspaces based on the maximum mean square error(MMSE)*** interval division coefficient and random sampling coefficient are adaptively adjusted without human interference until the model meets accuracy *** effectiveness of the proposed method is demonstrated by a numerical example of a three-degree-of-freedom mass-spring system and an experimental example of a butted cylindrical *** results show that the updated results of the interval model are in good agreement with the experimental results.

关键词： interval model updating(IMU) non-probabilistic uncertainty adaptive Kriging model surrogate model grey number

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Parametric resonance of axially functionally graded pipes conveying pulsating fluid

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Applied Mathematics and Mechanics(English Edition) 2024年第2期45卷 239-260页

作者： Jie JING Xiaoye MAO Hu DING liqun chen Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai Frontier Science Center of MechanoinformaticsShanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200444China Shanghai Institute of Aircraft Mechanics and Control Shanghai 200092China

Based on the generalized Hamilton's principle,the nonlinear governing equation of an axially functionally graded(AFG)pipe is *** non-trivial equilibrium configuration is superposed by the modal functions of a simply supported *** the direct multi-scale method,the response and stability boundary to the pulsating fluid velocity are solved analytically and verified by the differential quadrature element method(DQEM).The influence of Young's modulus gradient on the parametric resonance is investigated in the subcritical and supercritical *** general,the pipe in the supercritical region is more sensitive to the pulsating *** nonlinearity changes from hard to soft,and the non-trivial equilibrium configuration introduces more frequency components to the ***,the increasing Young's modulus gradient improves the critical pulsating flow velocity of the parametric resonance,and further enhances the stability of the *** addition,when the temperature increases along the axial direction,reducing the gradient parameter can enhance the response *** work further complements the theoretical analysis of pipes conveying pulsating fluid.

关键词： pipe conveying fluid axially functionally graded supercritical resonance multi-scale method parametric resonance

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Natural vibration and critical velocity of translating Timoshenko beam with non-homogeneous boundaries

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Applied Mathematics and Mechanics(English Edition) 2024年第9期45卷 1523-1538页

作者： Yanan LI Jieyu DING Hu DING liqun chen Shanghai Institute of Applied Mathematics and Mechanics Shanghai Key Laboratory of Mechanics in Energy EngineeringShanghai Frontier Science Center of MechanoinformaticsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200072China School of Mathematics and Statistics Qingdao UniversityQingdao 266071Shandong ProvinceChina

In most practical engineering applications,the translating belt wraps around two fixed *** boundary conditions of the dynamic model are typically specified as simply supported or fixed *** this paper,non-homogeneous boundaries are introduced by the support *** the translating belt as the mechanical prototype,the vibration characteristics of translating Timoshenko beam models with nonhomogeneous boundaries are investigated for the first *** governing equations of Timoshenko beam are deduced by employing the generalized Hamilton's *** effects of parameters such as the radius of wheel and the length of belt on vibration characteristics including the equilibrium deformations,critical velocities,natural frequencies,and modes,are numerically calculated and *** numerical results indicate that the beam experiences deformation characterized by varying curvatures near the *** radii of the wheels play a pivotal role in determining the change in trend of the relative difference between two beam *** the results unearths that the relative difference in equilibrium deformations between the two beam models is more pronounced with smaller-sized *** the two wheels are of equal size,the critical velocities of both beam models reach their respective *** addition,the relative difference in natural frequencies between the two beam models exhibits nonlinear variation and can easily exceed 50%.Furthermore,as the axial velocities increase,the impact of non-homogeneous boundaries on modal shape of translating beam becomes more *** dealing with non-homogeneous boundaries is challenging,beam models with non-homogeneous boundaries are more sensitive to parameters,and the differences between the two types of beams undergo some interesting variations under the influence of non-homogeneous boundaries.

关键词： translating beam Timoshenko beam non-homogeneous boundary natural frequency critical velocity

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Dynamics and vibration reduction performance of asymmetric tristable nonlinear energy sink

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Applied Mathematics and Mechanics(English Edition) 2024年第3期45卷 389-406页

作者： Hongyan chen Youcheng ZENG Hu DING Siukai LAI liqun chen School of Mechanical Engineering University of Science and Technology BeijingBeijing 100083China Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai Frontier Science Center of MechanoinformaticsShanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200444China Department of Civil and Environmental Engineering The Hong Kong Polytechnic UniversityKowloonHong KongChina

With its complex nonlinear dynamic behavior,the tristable system has shown excellent performance in areas such as energy harvesting and vibration suppression,and has attracted a lot of *** this paper,an asymmetric tristable design is proposed to improve the vibration suppression efficiency of nonlinear energy sinks(NESs)for the first *** proposed asymmetric tristable NES(ATNES)is composed of a pair of oblique springs and a vertical ***,the three stable states,symmetric and asymmetric,can be achieved by the adjustment of the distance and stiffness asymmetry of the oblique *** governing equations of a linear oscillator(LO)coupled with the ATNES are *** approximate analytical solution to the coupled system is obtained by the harmonic balance method(HBM)and verified *** vibration suppression efficiency of three types of ATNES is *** results show that the asymmetric design can improve the efficiency of vibration reduction through comparing the chaotic motion of the NES oscillator between asymmetric steady *** addition,compared with the symmetrical tristable NES(TNES),the ATNES can effectively control smaller structural *** other words,the ATNES can effectively solve the threshold problem of TNES failure to weak ***,this paper reveals the vibration reduction mechanism of the ATNES,and provides a pathway to expand the effective excitation amplitude range of the NES.

关键词： asymmetric nonlinear energy sink(NES) tristable vibration control po-tential barrier

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Dynamic performance and parameter optimization of a half-vehicle system coupled with an inerter-based X-structure nonlinear energy sink

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Applied Mathematics and Mechanics(English Edition) 2024年第1期45卷 85-110页

作者： Yong WANG Peili WANG Haodong MENG liqun chen .Automotive Engineering Research Institute Jiangsu UniversityZhenjiang 212013Jiangsu ProvinceChina Guangxi Key Laboratory of Automobile Components and Vehicle Technology Guangxi University of Science and TechnologyLiuzhou 545006Guangxi Zhuang Autonomous RegionChina School of Automotive Engineering Changzhou Institute of TechnologyChangzhou 213032Jiangsu ProvinceChina Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai Frontier Science Center of MechanoinformaticsShanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200444China

Inspired by the demand of improving the riding comfort and meeting the lightweight design of the vehicle, an inerter-based X-structure nonlinear energy sink(IXNES) is proposed and applied in the half-vehicle system to enhance the dynamic performance. The X-structure is used as a mechanism to realize the nonlinear stiffness characteristic of the NES, which can realize the flexibility, adjustability, high efficiency, and easy operation of nonlinear stiffness, and is convenient to apply in the vehicle suspension, and the inerter is applied to replacing the mass of the NES based on the mass amplification characteristic. The dynamic model of the half-vehicle system coupled with the IX-NES is established with the Lagrange theory, and the harmonic balance method(HBM) and the pseudo-arc-length method(PALM) are used to obtain the dynamic response under road harmonic excitation. The corresponding dynamic performance under road harmonic and random excitation is evaluated by six performance indices, and compared with that of the original half-vehicle system to show the benefits of the IX-NES. Furthermore, the structural parameters of the IX-NES are optimized with the genetic algorithm. The results show that for road harmonic and random excitation, using the IX-NES can greatly reduce the resonance peaks and root mean square(RMS) values of the front and rear suspension deflections and the front and rear dynamic tire loads, while the resonance peaks and RMS values of the vehicle body vertical and pitching accelerations are slightly *** the structural parameters of the IX-NES are optimized, the vehicle body vertical and pitching accelerations of the half-vehicle system could reduce by 2.41% and 1.16%,respectively, and the other dynamic performance indices are within the reasonable ***, the IX-NES combines the advantages of the inerter, X-structure, and NES, which improves the dynamic performance of the half-vehicle system and provides an effective option for vibrati

关键词： inerter X-structure nonlinear energy sink(NES) half-vehicle system dynamic performance

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An active high-static-low-dynamic-stiffness vibration isolator with adjustable buckling beams:theory and experiment

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Applied Mathematics and Mechanics(English Edition) 2024年第3期45卷 425-440页

作者： Kefan XU Muqing NIU Yewei ZHANG liqun chen School of Science Harbin Institute of TechnologyShenzhen 518055Guangdong ProvinceChina College of Aerospace Engineering Shenyang Aerospace UniversityShenyang 110136China Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai Frontier Science Center of MechanoinformaticsShanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200444China Shanghai Institute of Aircraft Mechanics and Control Shanghai 200092China

High-static-low-dynamic-stiffness(HSLDS)vibration isolators with buckling beams have been widely used to isolate external *** active adjustable device composed of proportion integration(PI)active controllers and piezoelectric actuators is proposed for improving the negative stiffness stroke of buckling beams.A nonlinear output frequency response function is used to analyze the effect of the vibration *** prototype of the active HSLDS device is built,and the verification experiment is *** results show that compared with the traditional HSLDS vibration isolator,the active HSLDS device can broaden the isolation frequency bandwidth,and effectively reduce the resonant amplitude by adjusting the active control *** maximum vibration reduction rate of the active HSLDS vibration isolator can attain 89.9%,and the resonant frequency can be reduced from 31.08 Hz to 13.28 ***,this paper devotes to providing a new design scheme for enhanced HSLDS vibration isolators.

关键词： active control high-static-low-dynamic-stiffness(HSLDS) vibration isola-tor dynamic analysis

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A viscoelastic metamaterial beam for integrated vibration isolation and energy harvesting

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Applied Mathematics and Mechanics(English Edition) 2024年第7期45卷 1243-1260页

作者： Long ZHAO Zeqi LU Hu DING liqun chen Shanghai Institute of Applied Mathematics and Mechanics Shanghai Key Laboratory of Mechanics in Energy EngineeringShanghai Frontier Science Center of MechanoinformaticsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai200072China School of Microelectronics Shanghai UniversityShanghai201800China

Locally resonant metamaterials have low-frequency band gaps and the capability of converging vibratory energy in the band gaps at resonant *** has been demonstrated by several researchers that the dissipatioin of vibratory energy within the band gap can be improved by using viscoelastic *** paper designs an integrated viscoelastic metamaterial for energy harvesting and vibration *** viscoelastic metamaterial is achieved by a viscoelastic beam periodically arrayed with spatial ball-pendulum nonlinear energy *** nonlinear resonator with an energy harvesting function is achieved by placing a free-rolling magnetic ball in a spherical cavity with an additional induction *** dynamic equations of viscoelastic metamaterials under transverse excitation are established,and the energy harvesting and vibration isolation characteristics within the dispersion relation of viscoelastic metamaterials are *** results show that the vibrations of the main body of the viscoelastic metamaterial beam are significantly suppressed in the frequency range of the local resonance band *** the same time,the elastic waves are limited in the nonlinear resonator with an energy harvesting function,which improves the energy ***,an experimental platform of viscoelastic metamaterial vibration is established for validation purposes.

关键词： viscoelastic metamaterial nonlinear vibration vibration isolation energy harvesting

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Dirac method for nonlinear and non-homogenous boundary value problems of plates

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Applied Mathematics and Mechanics(English Edition) 2024年第1期45卷 15-38页

作者： Xiaoye MAO Jiabin WU Junning ZHANG Hu DING liqun chen Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai Frontier Science Center of MechanoinformaticsShanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200444China Shanghai Institute of Aircraft Mechanics and Control Shanghai 200092China

The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method(HBM) is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method(DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations;nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries.

关键词： rectangular plate Dirac operator nonlinear boundary time-dependent boundary boundary value problem

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Theoretical and experimental study of a bi-stable piezoelectric energy harvester under hybrid galloping and band-limited random excitations

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Applied Mathematics and Mechanics(English Edition) 2024年第3期45卷 461-478页

作者： Haitao LI Tianyu ZHENG Weiyang QIN Ruilan TIAN Hu DING J.C.JI liqun chen Department of Engineering Mechanics North University of ChinaTaiyuan 030051China Department of Engineering Mechanics Northwestern Polytechnical UniversityXi'an 710072China Department of Engineering Mechanics Shijiazhuang Tiedao UniversityShijiazhuang 050043China Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai Frontier Science Center of MechnoinformaticsShanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200072China School of Mechanical and Mechatronic Engineering University of Technology SydneyNew South Wales 2007Australia

In the practical environment,it is very common for the simultaneous occurrence of base excitation and *** the combined energy of vibration and wind with a single energy harvesting structure is *** this purpose,the effects of the wind speed and random excitation level are investigated with the stochastic averaging method(SAM)based on the energy *** results of the analytical prediction are verified with the Monte-Carlo method(MCM).The numerical simulation shows that the introduction of wind can reduce the critical excitation level for triggering an inter-well jump and make a bi-stable energy harvester(BEH)realize the performance enhancement for a weak base ***,as the strength of the wind increases to a particular level,the influence of the random base excitation on the dynamic responses is weakened,and the system exhibits a periodic galloping response.A comparison between a BEH and a linear energy harvester(LEH)indicates that the BEH demonstrates inferior performance for high-speed *** experiments are conducted to investigate the validity of the theoretical prediction and numerical *** experimental findings also show that strong random excitation is favorable for the BEH in the range of low wind ***,as the speed of the incoming wind is up to a particular level,the disadvantage of the BEH becomes clear and evident.

关键词： bi-stability inter-well response galloping band-limited random

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压电纤维复合材料对悬臂结构的作动行为研究

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力学学报 2024年第5期56卷 1439-1447页

作者：张博谢华珂丁虎陈立群长安大学理学院西安710064 上海大学力学与工程科学学院上海200444

压电纤维复合材料(macro fiber composite,MFC)是由美国NASA研发的综合性能优秀的新型压电材料,掌握MFC的力学行为有利于将其投入结构变形控制、减振降噪和健康监测等领域.目前对MFC宏观力学行为的研究中缺乏对作动力与驱动电压直接关... 详细信息

压电纤维复合材料(macro fiber composite,MFC)是由美国NASA研发的综合性能优秀的新型压电材料,掌握MFC的力学行为有利于将其投入结构变形控制、减振降噪和健康监测等领域.目前对MFC宏观力学行为的研究中缺乏对作动力与驱动电压直接关系的研究,现有的以MFC为作动器的应用中所使用力电关系的精度有限,不利于将MFC投入更精密的使用场景.针对此问题,文章采用经典板理论,考虑了MFC与受控结构的相对尺寸,推导了MFC对悬臂结构的作动力方程.为兼顾计算的准确性和便利性,建立了考虑MFC叉指电极真实电场的精细有限元模型开展压电静力仿真,给出将MFC叉指电极的弯曲电场简化为匀强电场的修正系数.搭建MFC-悬臂梁结构的实验装置,对有限元模型和作动力公式加以验证.精细模型与简化模型的仿真结果与实验进行对比,总体误差较小,验证了模型和修正系数的可靠性.理论计算与仿真结果对比,误差在1%以内,表明所得作动力预测公式在较大的宽度比范围内均具有较好精度.建立的MFC作动力模型对MFC应用于悬臂结构的变形控制和振动抑制有一定指导意义.

关键词：压电纤维复合材料作动方程叉指电极压电静力实验

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