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Nonlinear oscillations with parametric excitation solved by homotopy analysis method

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Acta Mechanica Sinica 2008年第3期24卷 325-329页

作者： Jianmin Wen Zhengcai Cao School of Shipbuilding Engineering Harbin Institute of Technology at WeihaiWeihai 264209 China CIMS Research Center Tongji University Shanghai 200092 China

An analytical technique, namely the homotopy analysis method （HAM）, is used to solve problems of nonlinear oscillations with parametric excitation. Unlike perturbation methods, HAM is not dependent on any small physical parameters at all, and thus valid for both weakly and strongly nonlinear problems. In addition, HAM is different from all other analytic techniques in providing a simple way to adjust and control convergence region of the series solution by means of an auxiliary parameter h. In the present paper, a periodic analytic approximations for nonlinear oscillations with parametric excitation are obtained by using HAM, and the results are validated by numerical simulations.

关键词： Nonlinear oscillation parametric excitation Series solutions Homotopy analysis method

Instability Assessment of Deep-Sea Risers Under parametric excitation

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China Ocean Engineering 2009年第4期23卷 603-612页

作者：杨和振李华军 State Key Laboratory of Ocean Engineering Shanghai Jiao Tong University College of Engineering Ocean University of China

This study deals with the nonlinear dynamic response of deep-sea risers subjected to parametric excitation at the top of a platform. As offshore oil and gas exploration is pushed into deep waters, difficulties encountered in deep-sea riser design may be attributed to the existence of parametric instability regarding platform heave motions. parametric resonance in risers can cause serious damage which might bring disastrous accidents such as environment pollution, property losses and even fatalities. Therefore, the paranletric instability analysis should attract more attention during the design process of deep-sea risers. In this work, an equation of motion for a deep-sea riser is derived firstly. The motion equation is analyzed by the Floquet theory which allows the determination of both system response and stability properties. The unstable regions in which parametric resonance easily occurs can be determined. The effects of damping on parametric instability are also investigated, and the stability maps are presented. The results demonstrate that the available damping is vital in suppressing the instability regions. The suggestions for reduction of instability regions are proposed in deep-sea riser design.

关键词： deep-sea riser parametric excitation instability vibration response

Nonlinear Dynamics of Torsional Vibration for Rolling Mill′s Main Drive System Under parametric excitation

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Journal of Iron and Steel Research(International) 2013年第1期20卷 7-12页

作者： SHI Pei-ming LI Ji-zhao JIANG Jin-shui LIU Bin HAN Dong-ying College of Electrical Engineering Yanshan University College of Vehicles and Energy Yanshan University

The jointed shaft in the drivelines of the rolling mill, with its angle continuously varying in the production, has obvious impact on the stability of the main drive system. Considering the effect caused by the joint angle and friction force of roller gap, the nonlinear vibration model of the main drive system which contains parametric excitation stiffness and nonlinear friction damping was established. The amplitude-frequency characteristic equation and bifurcation response equation were obtained by using the method of multiple scales. Depending on the bifurcation response equation, the transition set and the topology structure of bifurcation curve of the system were obtained by using the singularity theory. The transition set can separate the system into seven areas, which has different bifurcation forms respectively. By taking the 1 780 rolling mill of Chengde Steel Co for example, the simulation and analysis were performed. The amplitude-frequency curves under different joint angles, damping coefficients, and nonlinear stiffness were given. The variations of these parameters have strong influences on the stability of electromechanical resonances and the characteristic of the response curves. The best angle of the jointed shaft is 4.761 3° in this rolling mill.

关键词： rolling mill main drive system torsional vibration parametric excitation joint angle singularity

Non-Linear Response of Tethers Subjected to parametric excitation in Submerged Floating Tunnels

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China Ocean Engineering 2009年第1期23卷 167-174页

作者：孙胜男陈健云李静 State Key Laboratory of Coastal and Offshore Engineering Dalian University of Technology School of Civil and Hydraulic Engineering Dalian University of Technology

For the study of the non-linear response of inclined tethers subjected to parametric excitation in submerged floating tunnels, a theoretical model for coupled tube-tether vibration is developed. Upon the assumption that the static equilibri- um position of the tether is a quadratic parabola, the governing differential equations of the tether motion are derived by use of the Hamihon principle. An approximate numerical solution is obtained by use of Galerkin method and Runge-kutta method. The results show that, when the static equilibrium position of the tether is assumed to be. a quadratic parabola, the tether sag effect on its vibration may be reflected; the tether sag results in the asymmetry of tether vibration amplitude ; for the reduction of the tether amplitude, the buoyant unit weight of the tether should approach to zero as far as possible during the design.

关键词： submerged floating tunnel tether parametric excitation quadratic parabola sag

Theoretical Analysis of the Galloping Energy Harvesters under Bounded Random Parameter excitation

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Computer Modeling in Engineering & Sciences 2023年第11期137卷 1731-1747页

作者： Hang Deng Jimin Ye Wei Li Dongmei Huang School of Mathematics and Statistics Xidian UniversityXi’an710071China

In this paper,the response properties of galloping energy harvesters under bounded random parameter excitation are studied theoretically.The first-order approximate solution of the galloping energy harvester is derived by applying the multi-scales method.The expression for the largest Lyapunov exponent that determines the trivial solution is derived,and the corresponding simulation diagrams,including the largest Lyapunov exponent diagrams and time domain diagrams,verify our results.Then the steady-state response moments of the nontrivial solution are studied using the moment method,and the analytical expressions for the first-order and second-order moments of the voltage amplitude are obtained,respectively.The corresponding results show that wind speed enhances the steady-state response moments of the voltage amplitude.Meanwhile,the voltage output can be controlled by adjusting the cubic coefficient.To further verify the response characteristics of the galloping energy harvester,the stationary probability density functions of the displacement and velocity are obtained by the Monte-Carlo simulation method.The results show that the wind speed enhances the displacement of the bluff and the damping ratios should be reduced asmuch as possible to improve the performance.What’smore,the piezoelectric materials also impact the performance of the energy harvester.

关键词： Galloping energy harvester multi-scales method parametric excitation stability

Stability and nonlinear vibrations of a flexible pipe parametrically excited by an internal varying flow density

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Acta Mechanica Sinica 2020年第1期36卷 206-219页

作者： W.D.Xie X.F.Gao W.H.Xu State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin UniversityTianjin30072China

Pipes are often used to transport multiphase flows in many engineering applications.The total fluid flow density inside a pipe may vary with time and space.In this paper,a simply supported pipe conveying a variable density flow is modeled theoretically,and its stability and nonlinear vibrations are investigated in detail.The variation of the flow density is simulated using a mathematical function.The equation governing the vibration of the pipe is derived according to Euler-Bernoulli beam theory.When the internal flow density varies with time,the pipe is excited parametrically.The stability of the pipe is determined by Floquet theory.Some simple parametric and combination resonances are determined.For a higher mass ratio(mean flow mass/pipe structural mass),higher flow velocity,or smaller end axial tension,the pipe becomes unstable more easily due to wider parametric resonance regions.In the subcritical flow velocity regime,the vibrations of the pipe are periodic and quasiperiodic for simple and combination resonances,respectively.However,in the supercritical regime,the vibrations of the pipe exhibit much richer dynamics including periodic,multiperiodic,quasiperiodic,and chaotic behaviors.

关键词： Pipe Varying flow density parametric excitation Stability Nonlinear vibrations

Pseudo analytical solution to time periodic stiffness systems

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Chinese Physics B 2011年第4期20卷 97-102页

作者：王延忠周元子 School of Mechanical Engineering and Automation Beihang University

An analytical form of state transition matrix for a system of equations with time periodic stiffness is derived in order to solve the free response and also allow for the determination of system stability and bifurcation. A pseudoclosed form complete solution for parametrically excited systems subjected to inhomogeneous generalized forcing is developed, based on the Fourier expansion of periodic matrices and the substitution of matrix exponential terms via Lagrange-Sylvester theorem. A Mathieu type of equation with large amplitude is presented to demonstrate the method of formulating state transition matrix and Floquet multipliers. A two-degree-of-freedom system with irregular time periodic stiffness characterized by spiral bevel gear mesh vibration is presented to find forced response in stability and instability. The obtained results are presented and discussed.

关键词： parametric excitation time periodic stiffness stability response

Spin pumping by higher-order dipole-exchange spin-wave modes

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Chinese Physics B 2023年第3期32卷 531-536页

作者：王鹏 College of Mathematics and Physics Qingdao University of Science and TechnologyQingdao 266061China Advanced Optoelectronic Materials and Technologies Engineering Laboratory of Shandong Province Qingdao 266061China

Spin pumping(SP)and inverse spin Hall effect(ISHE)driven by parametrically-excited dipole-exchange spin waves in a yttrium iron garnet film have been systematically investigated.The measured voltage spectrum exhibits a feature of the field-induced transition from parallel pumping to perpendicular pumping because of the inhomogeneous excitation geometry.Thanks to the high precision of the SP-ISHE detection,two sets of fine structures in the voltage spectrum are observed,which can correspond well to two kinds of critical points in the multimode spin-wave spectrum for magnetic films.One is the q=0 point of each higher-order dispersion branch,and the other is the local minimum due to the interplay between the dipolar and exchange interactions.These fine structures on the voltage spectrum confirm the spin pumping by higher-order dipole-exchange spin-wave modes,and are helpful for probing the multimode spin-wave spectrum.

关键词： spin pumping parametric excitation spin-wave spectrum fine structures

Seismic Response of Submerged Floating Tunnel Tether

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China Ocean Engineering 2013年第1期27卷 43-50页

作者：苏志彬孙胜男 School of Architecture and Civil Engineering Liaocheng University

A mathematical equation for vibration of submerged floating tunnel tether under the effects of earthquake and parametric excitation is presented. Multi-step Galerkin method is used to simplify this equation and the fourth-order Runge-Kuta integration method is used for numerical analysis. Finally, vibration response of submerged floating tunnel tether subjected to earthquake and parametric excitation is analyzed in a few numerical examples. The results show that the vibration response of tether varies with the seismic wave type; the steady maximum mid-span displacement of tether subjected to seismic wave keeps constant when parametric resonance takes place; the transient maximum mid-span displacement of tether is related to the peak value of input seismic wave acceleration.

关键词： submerged floating tunnel seismic response Runge-Kuta integration method tether parametric excitation