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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

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

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

An improved interval model updating method via adaptive Kriging models

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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

Endomorphism Algebras of Support τ-Tilting Modules

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Algebra Colloquium 2024年第2期31卷 333-340页

作者： Yonggang hu Panyue Zhou Nanqing ding Department of International Economics China Foreign Affairs University Beijing 100037China School of Mathematics and Statistics Changsha University of Science and Technology Changsha 410114China 不详

Let A be a finite dimensional k-algebra and T be a supportτ-tilting right *** this note,we give lower and upper bounds for the global dimension of the endomorphism algebra End_(A)(T)under some mild ***,we give some e... 详细信息

关键词： supportτ-tilting module τ-tilting module tilting module global dimension

A new mixed type crack propagation criterion in shale reservoirs

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Petroleum 2024年第1期10卷 85-92页

作者： Muru ding Zhirong Jin Yanjun Zhang Jinghong hu Beijing Key Laboratory of Unconventional Natural Gas Geology Evaluation and Development Engineering China University of GeosciencesBeijingChina Sinopec Jiangsu Oil Field Branch YangzhouChina Oil&Gas Technology Research Institute Changqing Oilefiled CompanyPetroChinaXi'anChina

Hydraulic fracturing is a mainstream technology for unconventional oil and gas reservoirs development all over the *** to use this technology to achieve high-level oil and gas resource extraction and how to form complex fracture networks as hydrocarbon transportation channels in tight reservoirs,which depends to a large extent on the interaction between hydraulic and pre-existing *** hydraulic fracturing of fractured reservoirs,the impact of natural fractures,perforation direction,stress disturbances,faults and other influencing factors will produce a mixed I&II mode hydraulic *** forecast whether hydraulic fractures cross pre-existing fractures,according to elastic mechanics and fracture mechanics,a stress state of cracks under the combination of tensile(I)and shear(II)is presented.A simple mixed-mode I&II hydraulic fracture's crossing judgment criterion is established,and the propagation of hydraulic fractures after encountering natural fractures is *** results show that for a given approaching angle there exists a certain range of stress ratio when crossing *** high approaching angle and large stress ratio,it is likely that hydraulic cracks will go directly through pre-existing *** reinitiated angle is always controlled within the range of approximately 30among the main direction of penetration.

关键词： Crack propagation criterion Stress ratio Approaching angle Reinitiated angle Mechanical model

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

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

A human-sensitive frequency band vibration isolator for heavy-duty truck seats

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Applied Mathematics and Mechanics(English Edition) 2024年第10期45卷 1733-1748页

作者： Qingqing LIU Shenlong WANG Ge YAN hu.ding Haihua WANG Qiang SHI Xiaohong ding huijie YU School of Mechanical Engineering University of Shanghai for Science and TechnologyShanghai 200093China State Key Laboratory of Mechanical System and Vibration School of Mechanical EngineeringShanghai Jiao Tong UniversityShanghai 200240China 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 State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body College of Mechanical and Vehicle EngineeringHunan UniversityChangsha 410082China Yanfeng Adient Seating Co. Ltd.Shanghai 201315China College of Mechanical and Electrical Engineering Jiaxing Nanhu UniversityJiaxing 314001Zhejiang ProvinceChina

In this study,a human-sensitive frequency band vibration isolator(HFBVI)with quasi-zero stiffness(QZS)characteristics for heavy-duty truck seats is designed to improve the comfort of heavy-duty truck drivers on uneven ***,the analytical expressions for the force and displacement of the HFBVI are derived with the Lagrange equation and d'Alembert's principle,and are validated through the prototype restoring force ***,the harmonic balance method(HBM)is used to obtain the dynamic responses under harmonic excitation,and further the influence of pre-stretching on the dynamic characteristics and transmissibility is ***,the experimental prototype of the HFBVI is fabricated,and vibration experiments are conducted under harmonic excitation to verify the vibration isolation performance(VIP)of the proposed vibration *** experimental results indicate that the HFBVI can effectively suppress the frequency band(4-8 Hz)to which the human body is sensitive to vertical *** addition,under real random road spectrum excitation,the HFBVI can achieve low-frequency vibration isolation close to 2 Hz,providing new prospects for ensuring the health of heavy-duty truck drivers.

关键词： human-sensitive frequency band quasi-zero stiffness(QZS) heavy-duty truck seat real random road spectrum low-frequency vibration isolation