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Steady-state responses of a belt-drive dynamical system under dual excitations

Acta Mechanica Sinica 2016年第1期32卷 156-169页

作者： hu ding Shanghai Institute of Applied Mathematics and Mechanics Shanghai Key Laboratory of Mechanics in Energy EngineeringShanghai UniversityShanghai 200072China

The stable steady-state periodic responses of a belt-drive system with a one-way clutch are studied. For the first time, the dynamical system is investigated under dual excitations. The system is simultaneously excited by the firing pulsations of the engine and the harmonic motion of the foundation. Nonlinear discrete-continuous equations are derived for coupling the transverse vibration of the belt spans and the rotations of the driving and driven pulleys and the accessory pulley. The nonlinear dynamics is studied under equal and multiple relations between the frequency of the fir- ing pulsations and the frequency of the foundation motion. Furthermore, translating belt spans are modeled as axially moving strings. A set of nonlinear piecewise ordinary differ- ential equations is achieved by using the Galerkin truncation. Under various relations between the excitation frequencies, the time histories of the dynamical system are numerically simulated based on the time discretization method. Further- more, the stable steady-state periodic response curves are calculated based on the frequency sweep. Moreover, the convergence of the Galerkin truncation is examined. Numer- ical results demonstrate that the one-way clutch reduces the resonance amplitude of the rotations of the driven pul- ley and the accessory pulley. On the other hand, numerical examples prove that the resonance areas of the belt spans are decreased by eliminating the torque-transmitting in the opposite direction. With the increasing amplitude of the foun- dation excitation, the damping effect of the one-way clutch will be reduced. Furthermore, as the amplitude of the firing pulsations of the engine increases, the jumping phenomena in steady-state response curves of the belt-drive system with or without a one-way clutch both occur.

关键词： Nonlinear vibration One-way clutch Dynamical system Steady-state responses Galerkinmethod

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NES cell

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Applied Mathematics and Mechanics(English Edition) 2022年第12期43卷 1793-1804页

作者： hu ding Yufei SHAO Shanghai Key Laboratory of Mechanics in Energy Engineering School of Mechanics and Engineering ScienceShanghai UniversityShanghai200072China

A broadband adaptive vibration control strategy with high reliability and flexible versatility is *** high vibration damping performance of nonlinear energy sink(NES)has attracted ***,targeted energy transfer may cause severe vibration of ***,it is difficult to realize pure nonlinear stiffness without the linear *** a result,the reliability of NES is not *** low reliability of NES has hindered its application in *** addition,the performance of NES depends on its mass ratio of the primary system,and NES lacks versatility for different vibration ***,this paper proposes the concept of NES *** advantages of the adaptive vibration control of NES are applied to cellular *** applying a large number of NES cells in parallel,the reliability of NES and its versatility to complex vibration structures are *** elastic beam is used as the primary vibration structure,and a limited NES is used as the *** relationship between the vibration suppression effect of NES cells and the number of NES cell is *** addition,the effect of the distribution of NES cells on the multi-mode resonance suppression of the beam is also *** summary,the mode of the primary structure can be efficiently controlled by a large number of lightweight NES ***,the lightweight NES cell is flexible for vibration control of complex *** addition,it improves the reliability of NES ***,the distributed application of NES cells proposed in this paper is a valuable vibration suppression strategy.

关键词： vibration nonlinear energy sink(NES) NES cell vibration control clamped beam harmonic balance method(HBM)

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A vertical track nonlinear energy sink

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Applied Mathematics and Mechanics(English Edition) 2024年第6期45卷 931-946页

作者： Meng LI hu ding Shanghai Key Laboratory of Mechanics in Energy Engineering School of Mechanics and Engineering ScienceShanghai Frontier Science Center of MechanoinformaticsShanghai UniversityShanghai 200444China

Eliminating the effects of gravity and designing nonlinear energy sinks(NESs)that suppress vibration in the vertical direction is a challenging task with numerous damping *** this paper,the dynamic design of a vertical track nonlinear energy sink(VTNES)with zero linear stiffness in the vertical direction is proposed and realized for the first *** motion differential equations of the VTNES coupled with a linear oscillator(LO)are *** the strong nonlinearity considered of the VTNES,the steady-state response of the system is analyzed with the harmonic balance method(HBM),and the accuracy of the HBM is verified *** this basis,the VTNES prototype is manufactured,and its nonlinear stiffness is *** damping effect and dynamic characteristics of the VTNES are studied theoretically and *** results show that the VTNES has better damping effects when strong modulation responses(SMRs)***,even for small-amplitude vibration,the VTNES also has a good vibration suppression *** sum up,in order to suppress the vertical vibration,an NES is designed and developed,which can suppress the vertical vibration within certain ranges of the resonance frequency and the vibration intensity.

关键词： track nonlinear energy sink(TNES) vertical direction gravity nonlinear stiffness harmonic balance method(HBM) vibration control

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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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Approximate and numerical analysis of nonlinear forced vibration of axially moving viscoelastic beams

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Acta Mechanica Sinica 2011年第3期27卷 426-437页

作者： hu ding Li-Qun Chen Shanghai Institute of Applied Mathematics and Mechanics Shanghai University 200072 Shanghai China Department of Mechanics Shanghai University 200436 Shanghai China

Steady-state periodical response is investigated for an axially moving viscoelastic beam with hybrid supports via approximate analysis with numerical confirmation. It is assumed that the excitation is spatially uniform and temporally harmonic. The transverse motion of axially moving beams is governed by a nonlinear partial-differential equation and a nonlinear integro-partial-differential equation. The material time derivative is used in the viscoelastic constitutive relation. The method of multiple scales is applied to the governing equations to investigate primary resonances under general boundary conditions. It is demonstrated that the mode uninvolved in the resonance has no effect on the steady-state response. Numerical examples are presented to demonstrate the effects of the boundary constraint stiffness on the amplitude and the stability of the steady-state response. The results derived for two governing equations are qualitatively the same,but quantitatively different. The differential quadrature schemes are developed to verify those results via the method of multiple scales.

关键词： Axially moving beam. Nonlinearity . Mate-rial time derivative . Method of multiple scales. Differentialquadrature method

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Vibration control of fluid-conveying pipes: a state-of-the-art review

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Applied Mathematics and Mechanics(English Edition) 2023年第9期44卷 1423-1456页

作者： hu ding J.C.JI Shanghai Key Laboratory of Mechanics in Energy Engineering School of Mechanics and Engineering ScienceShanghai UniversityShanghai 200072China Shaoxing Institute of Technology Shanghai UniversityShaoxing 312074Zhejiang ProvinceChina Shanghai Institute of Aircraft Mechanics and Control Shanghai 200092China School of Mechanical and Mechatronic Engineering University of Technology SydneyNew South Wales 2007Australia

Fluid-conveying pipes are widely used to transfer bulk fluids from one point to another in many engineering *** are subject to various excitations from the conveying fluids,the supporting structures,and the working environment,and thus are prone to vibrations such as flow-induced vibrations and acoustic-induced *** can generate variable dynamic stress and large deformation on fluid-conveying pipes,leading to vibration-induced fatigue and damage on the pipes,or even leading to failure of the entire piping system and catastrophic ***,the vibration control of fluid-conveying pipes is essential to ensure the integrity and safety of pipeline systems,and has attracted considerable attention from both researchers and *** present paper aims to provide an extensive review of the state-of-the-art research on the vibration control of fluid-conveying *** vibration analysis of fluid-conveying pipes is briefly discussed to show some key issues involved in the vibration ***,the research progress on the vibration control of fluid-conveying pipes is reviewed from four aspects in terms of passive control,active vibration control,semi-active vibration control,and structural optimization design for vibration ***,the main results of existing research on the vibration control of fluid-conveying pipes are summarized,and future promising research directions are recommended to address the current research *** paper contributes to the understanding of vibration control of fluid-conveying pipes,and will help the research work on the vibration control of fluidconveying pipes attract more attention.

关键词： fuid-conveying pipe vibration passive control nonlinear energy sink(NES) active control semi-active control

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Bending vibration control of pipes conveying fluids by nonlinear torsional absorbers at the boundary

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Science China(Technological Sciences) 2021年第8期64卷 1690-1704页

作者： MAO XiaoYe ding hu CHEN LiQun Shanghai Institute of Applied Mathematics and Mechanics Shanghai UniversityShanghai200072China Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai UniversityShanghai200072China School of Mechanics and Engineering Science Shanghai UniversityShanghai200444China

A nonlinear torsional absorber,which can overcome the influence of the fluid velocity on the natural frequency,is employed at the boundary to restrain the bending vibration of a pipe for the first *** using the rotating angle at the end of the pipe,the bending vibration energy is pumped to the boundary *** nonlinearly coupled pipe-absorber governing equations are obtained by the generalized Hamilton’s ***-state responses subjected to a basement excitation are discussed by the *** to this method,the boundaries of the pipe are treated as the generalized governing *** this way,those nonlinearities and time-dependent terms in the boundary are involved in the response completely.A direct simulation method,called the differential quadrature element method(DQEM),is used to verify these analytical *** investigation indicates that the nonlinear boundary absorber owns two outstanding *** first one is that the natural characters remain the same and the absorber can capture the resonance of the pipe *** second one is that the absorber works at all natural ***,by using the nonlinear damping,the absorber will not worsen the weak vibration in the non-resonance *** parameters of the absorber are investigated to optimize the efficiency in *** result finds that good efficiency can be achieved with a tiny ***,the efficiency becomes better as the damping *** the help of these investigations,the work provides a new strategy to protect pipes conveying fluids from being destroyed by the vibration.

关键词： pipes conveying fluid boundary control nonlinear torsional absorber boundary nonlinear energy sink nonlinear damping

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NONLINEAR DYNAMICS OF AXIALLY ACCELERATING VISCOELASTIC BEAMS BASED ON DIFFERENTIAL QUADRATURE

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Acta Mechanica Solida Sinica 2009年第3期22卷 267-275页

作者： hu ding Liqun Chen Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China Department of Mechanics Shanghai University Shanghai 200444 China

This paper investigates nonlinear dynamical behaviors in transverse motion of an axially accelerating viscoelastic beam via the differential quadrature method. The governing equation, a nonlinear partial-differential equation, is derived from the viscoelastic constitution relation using the material derivative. The differential quadrature scheme is developed to solve numerically the governing equation. Based on the numerical solutions, the nonlinear dynamical behaviors are identified by use of the Poincare map and the phase portrait. The bifurcation diagrams are presented in the case that the mean axial speed and the amplitude of the speed fluctuation are respectively varied while other parameters are fixed. The Lyapunov exponent and the initial value sensitivity of the different points of the beam, calculated from the time series based on the numerical solutions, are used to indicate periodic motions or chaotic motions occurring in the transverse motion of the axially accelerating viscoelastic beam.

关键词： nonlinear partial-differential equation numerical solution chaos bifurcation differential quadrature

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Nonlinear dynamics of axially moving viscoelastic Timoshenko beam under parametric and external excitations

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Applied Mathematics and Mechanics(English Edition) 2015年第8期36卷 971-984页

作者： Qiaoyun YAN hu ding Liqun CHEN Shanghai Institute of Applied Mathematics and Mechanics Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University Department of Mechanics Shanghai University

This investigation focuses on the nonlinear dynamic behaviors in the trans- verse vibration of an axiMly accelerating viscoelastic Timoshenko beam with the external harmonic excitation. The parametric excitation is caused by the harmonic fluctuations of the axial moving speed. An integro-partial-differential equation governing the transverse vibration of the Timoshenko beam is established. Many factors are considered, such as viscoelasticity, the finite axial support rigidity, and the longitudinally varying tension due to the axial acceleration. With the Galerkin truncation method, a set of nonlinear ordinary differential equations are derived by discretizing the governing equation. Based on the numerical solutions, the bifurcation diagrams are presented to study the effect of the external transverse excitation. Moreover, the frequencies of the two excitations are assumed to be multiple. Further, five different tools, including the time history, the Poincaré map, and the sensitivity to initial conditions, are used to identify the motion form of the nonlinear vibration. Numerical results also show the characteristics of the quasiperiodic motion of the translating Timoshenko beam under an incommensurable re- lationship between the dual-frequency excitations.

关键词： axially accelerating Timoshenko beam viscoelasticity nonlinear dynamics,parametric excitation external excitation

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Dynamic stiffness method for free vibration of an axially moving beam with generalized boundary conditions

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Applied Mathematics and Mechanics(English Edition) 2019年第7期40卷 911-924页

作者： hu ding Minhui Zhu Liqun CHEN Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai University Shanghai 200072 China Department of Mechanics Shanghai University Shanghai 200444 China

Axially moving beams are often discussed with several classic boundary conditions, such as simply-supported ends, fixed ends, and free ends. Here, axially moving beams with generalized boundary conditions are discussed for the first time. The beam is supported by torsional springs and vertical springs at both ends. By modifying the stiffness of the springs, generalized boundaries can replace those classical boundaries. Dynamic stiffness matrices are, respectively, established for axially moving Timoshenko beams and Euler-Bernoulli (EB) beams with generalized boundaries. In order to verify the applicability of the EB model, the natural frequencies of the axially moving Timoshenko beam and EB beam are compared. Furthermore, the effects of constrained spring stiffness on the vibration frequencies of the axially moving beam are studied. Interestingly, it can be found that the critical speed of the axially moving beam does not change with the vertical spring stiffness. In addition, both the moving speed and elastic boundaries make the Timoshenko beam theory more needed. The validity of the dynamic stiffness method is demonstrated by using numerical simulation.

关键词： axially moving beam natural frequency Timoshenko beam model dynamic stiffness matrix generalized boundary condition

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