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 de...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.展开更多
In this paper,the nonlinear forced vibrations and stability of an axially moving large deflection plate immersed in fluid are investigated.Based on von Karman's large deflec・tion plate theory and taking into consi...In this paper,the nonlinear forced vibrations and stability of an axially moving large deflection plate immersed in fluid are investigated.Based on von Karman's large deflec・tion plate theory and taking into consideration the influence of fluid-strueture interaction,axial moving and axial tension,nonlinear dynamic equations are obtained by applying D'Alembert's principle.These dynamic equations are further discretized into ordinary differential equations via the Galerkin method.The frequency-response curves of system are obtained and examined.Then numerical method is used to analyze the bifurcation behaviors of immersed plate.Results show that as the parameters vary,the system displays periodic,multi-periodic,quasi-periodic and even chaotic motion.Through the analysis on global dynamic characteristics of fluid-strueture interaction system,rich and varied nonlinear dynamic characteristics are obtained,and various ways that lead to chaotic motion of the system are further revealed.展开更多
The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches....The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.展开更多
Based on the energy flow theory of nonlinear dynamical system,the stabilities,bifurcations,possible periodical/chaotic motions of nonlinear water-lubricated bearing-shaft coupled systems are investigated in this paper...Based on the energy flow theory of nonlinear dynamical system,the stabilities,bifurcations,possible periodical/chaotic motions of nonlinear water-lubricated bearing-shaft coupled systems are investigated in this paper.It is revealed that the energy flow characteristics around the equlibrium point of system behaving in the three types with different friction-para-mters.(a)Energy flow matrix has two negative and one positive energy flow factors,constructing an attractive local zero-energy flow surface,in which free vibrations by initial disturbances show damped modulated oscillations with the system tending its equlibrium state,while forced vibrations by external forces show stable oscillations,(b)Energy flow matrix has one negative and two positive energy flow factors,spaning a divergence local zero-energy flow surface,so that the both free and forced vibrations are divergence oscillations with the system being unstable,(c)Energy flow matrix has a zero-energy flow factor and two opposite factors,which constructes a local zero-energy flow surface dividing the local phase space into stable,unstable and central subspace,and the simulation shows friction self-induced unstable vibrations for both free and forced cases.For a set of friction parameters,the system behaves a periodical oscillation,where the bearing motion tends zero and the shaft motion reaches a stable limit circle in phase space with the instant energy flow tending a constant and the time averaged one tending zero.Numerical simulations have not found any possible chaotic motions of the system.It is discovered that the damping matrices of cases(a),(b)and(c)respectively have positive,negative and zero diagonal elements,resulting in the different dynamic behavour of system,which gives a giderline to design the water-lubricated bearing unit with expected performance by adjusting the friction parameters for applications.展开更多
The influence of weights is usually ignored in the study of nonlinear vibrations of plates.In this paper,the effect of structure weights on the nonlinear vibration of a composite circular plate with a rigid body is pr...The influence of weights is usually ignored in the study of nonlinear vibrations of plates.In this paper,the effect of structure weights on the nonlinear vibration of a composite circular plate with a rigid body is presented.The nonlinear governing equations are derived from the generalized Hamilton's principle and the von Kármán plate theory.The equilibrium configurations due to weights are determined and validated by the finite element method(FEM).A nonlinear model for the vibration around the equilibrium configuration is established.Moreover,the natural frequencies and amplitude-frequency responses of harmonically forced vibrations are calculated.The study shows that the structure weights introduce additional linear and quadratic nonlinear terms into the dynamical model.This leads to interesting phenomena.For example,considering weights increases the natural frequency.Furthermore,when the influence of weights is considered,the vibration response of the plate becomes asymmetrical.展开更多
This paper investigates the effect of porosity on active damping of geometrically nonlinear vibrations(GNLV)of the magneto-electro-elastic(MEE)functionally graded(FG)plates incorporated with active treatment constrict...This paper investigates the effect of porosity on active damping of geometrically nonlinear vibrations(GNLV)of the magneto-electro-elastic(MEE)functionally graded(FG)plates incorporated with active treatment constricted layer damping(ATCLD)patches.The perpendicularly/slanted reinforced 1-3 piezoelectric composite(1-3 PZC)constricting layer.The constricted viscoelastic layer of the ATCLD is modeled in the time-domain using Golla-Hughes-Mc Tavish(GHM)technique.Different types of porosity distribution in the porous magneto-electro-elastic functionally graded PMEE-FG plate graded in the thickness direction.Considering the coupling effects among elasticity,electrical,and magnetic fields,a three-dimensional finite element(FE)model for the smart PMEE-FG plate is obtained by incorporating the theory of layer-wise shear deformation.The geometric nonlinearity adopts the von K arm an principle.The study presents the effects of a variant of a power-law index,porosity index,the material gradation,three types of porosity distribution,boundary conditions,and the piezoelectric fiber’s orientation angle on the control of GNLV of the PMEE-FG plates.The results reveal that the FG substrate layers’porosity significantly impacts the nonlinear behavior and damping performance of the PMEE-FG plates.展开更多
In this study, a slightly curved Euler Bernoulli beam carrying a concentrated mass was handled. The beam was resting on an elastic foundation and simply supported at both ends. Effects of the concentrated mass on nonl...In this study, a slightly curved Euler Bernoulli beam carrying a concentrated mass was handled. The beam was resting on an elastic foundation and simply supported at both ends. Effects of the concentrated mass on nonlin- ear vibrations were investigated. Sinusoidal and parabolic type functions were used as curvature functions. Equations of motion have cubic nonlinearities because of elongations during vibrations. Damping and harmonic excitation terms were added to the equations of motion. Method of mul- tiple scales, a perturbation technique, was used for solving integro-differential equation analytically. Natural frequen- cies were calculated exactly for different mass ratios, mass locations, curvature functions, and linear elastic foundation coefficients. Amplitude-phase modulation equations were found by considering primary resonance case. Effects of nonlinear terms on natural frequencies were calculated. Frequency-amplitude and frequency-response graphs were plotted. Finally effects of concentrated mass and chosen curvature function on nonlinear vibrations were investigated.展开更多
We analyze the transverse nonlinear vibrations of a rotating flexible disk subjected to a rotating point force with a periodically varying rotating speed. Based on Hamilton’s principle, the nonlinear governing equati...We analyze the transverse nonlinear vibrations of a rotating flexible disk subjected to a rotating point force with a periodically varying rotating speed. Based on Hamilton’s principle, the nonlinear governing equations of motion (coupled equations among the radial, tangential and transverse displacements) are derived for the rotating flexible disk. When the in-plane inertia is ignored and a stress function is introduced, the three nonlinearly coupled partial differential equations are reduced to two nonlinearly coupled partial differential equations. According to Galerkin’s approach, a four-degree-of-freedom nonlinear system governing the weakly split resonant modes is derived. The resonant case considered here is 1:1:2:2 internal resonance and a critical speed resonance. The primary parametric resonance for the first-order sin and cos modes and the fundamental parametric resonance for the second-order sin and cos modes are also considered. The method of multiple scales is used to obtain a set of eight-dimensional nonlinear averaged equations. Based on the averaged equations, using numerical simulations, the influence of different parameters on the nonlinear vibrations of the spinning disk is detected. It is concluded that there exist complicated nonlinear behaviors including the periodic, period-n and multi-pulse type chaotic motions for the spinning disk with a varying rotating speed. It is also found that among all parameters, the damping and excitation have great influence on the nonlinear responses of the spinning disk with a varying rotating speed.展开更多
This paper is concerned with the effects of boundary conditions on the large-amplitude free vi-brations of Timoshenko beams. The effects of nonlinear terms on the frequency of Timoshenko beams with simply supported en...This paper is concerned with the effects of boundary conditions on the large-amplitude free vi-brations of Timoshenko beams. The effects of nonlinear terms on the frequency of Timoshenko beams with simply supported ends (supported-supported, SS), clamped ends (clamped-clamped, CC) and one end simply supported and the other end clamped (clamped-supported, CS) are discussed in detail. Given a spe-cific vibration amplitude, the change of nonlinear frequency according to the effects of boundary conditions is always in the following descending order: SS, CS, and CC. It is found that the slenderness ratio has a significant influence on the nonlinear frequency. For slender beams, the nonlinear effects of bending curva-ture and shear strain are negligible regardless of the boundary conditions. For short beams and especially for those of large amplitude vibrations, however, the nonlinear effects of bending curvature and shear strain become noticeable in the following ascending order: SS, CS, and CC.展开更多
Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes(CNTs)are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems.Therefo...Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes(CNTs)are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems.Therefore,the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscousfluid and supported on a nonlinear elastic foundation.The proposed model is based on nonlocal Euler–Bernoulli beam theory.The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation,respectively.A detailed parametric study is reported into how the nonlocal parameter,foundation coefficients,fluid viscosity,and amplitude and frequency of the external force influence the nonlinear dynamics of the system.Subharmonic,quasi-periodic,and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories,frequency-response curves,bifurcation diagrams,phase portraits,power spectra,and Poincarémaps.Also,the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters.展开更多
The nonlinear transverse vibrations of ordered and disordered twodimensional(2D)two-span composite laminated plates are studied.Based on the von Karman’s large deformation theory,the equations of motion of each-span ...The nonlinear transverse vibrations of ordered and disordered twodimensional(2D)two-span composite laminated plates are studied.Based on the von Karman’s large deformation theory,the equations of motion of each-span composite laminated plate are formulated using Hamilton’s principle,and the partial differential equations are discretized into nonlinear ordinary ones through the Galerkin’s method.The primary resonance and 1/3 sub-harmonic resonance are investigated by using the method of multiple scales.The amplitude-frequency relations of the steady-state responses and their stability analyses in each kind of resonance are carried out.The effects of the disorder ratio and ply angle on the two different resonances are analyzed.From the numerical results,it can be concluded that disorder in the length of the two-span 2D composite laminated plate will cause the nonlinear vibration localization phenomenon,and with the increase of the disorder ratio,the vibration localization phenomenon will become more obvious.Moreover,the amplitude-frequency curves for both primary resonance and 1/3 sub-harmonic resonance obtained by the present analytical method are compared with those by the numerical integration,and satisfactory precision can be obtained for engineering applications and the results certify the correctness of the present approximately analytical solutions.展开更多
Unbalanced force produced by the unbalanced mass will affect vibrations of rotor systems,which probably results in the components failures of rotating machinery.To study the effects of unbalanced mass on the vibration...Unbalanced force produced by the unbalanced mass will affect vibrations of rotor systems,which probably results in the components failures of rotating machinery.To study the effects of unbalanced mass on the vibration characteristics of rotor systems,a flexible rotor system model considering the unbalanced mass is proposed.The time-varying bearing force is considered.The developed model is verified by the experimental and theoretical frequency spectrums.The displacements and axis orbits of flexible and rigid rotor systems are compared.The results show that the unbalanced mass will affect the vibration characteristics of rotor system.This model can be more suitable and effective to calculate vibration characteristics of rotor system with the flexible deformation and unbalanced mass.This paper provides a new reference and research method for predicting the vibrations of flexible rotor system considering the unbalanced mass.展开更多
Molecular dynamics(MD)is a powerful method widely used in materials science and solid-state physics.The accuracy of MD simulations depends on the quality of the interatomic potentials.In this work,a special class of e...Molecular dynamics(MD)is a powerful method widely used in materials science and solid-state physics.The accuracy of MD simulations depends on the quality of the interatomic potentials.In this work,a special class of exact solutions to the equations of motion of atoms in a body-centered cubic(bcc)lattice is analyzed.These solutions take the form of delocalized nonlinear vibrational modes(DNVMs)and can serve as an excellent test of the accuracy of the interatomic potentials used in MD modeling for bcc crystals.The accuracy of the potentials can be checked by comparing the frequency response of DNVMs calculated using this or that interatomic potential with that calculated using the more accurate ab initio approach.DNVMs can also be used to train new,more accurate machine learning potentials for bcc metals.To address the above issues,it is important to analyze the properties of DNVMs,which is the main goal of this work.Considering only the point symmetry groups of the bcc lattice,34 DNVMs are found.Since interatomic potentials are not used in finding DNVMs,they are exact solutions for any type of potential.Here,the simplest interatomic potentials with cubic anharmonicity are used to simplify the analysis and to obtain some analytical results.For example,the dispersion relations for small-amplitude phonon modes are derived,taking into account interactions between up to the fourth nearest neighbor.The frequency response of the DNVMs is calculated numerically,and for some DNVMs examples of analytical analysis are given.The energy stored by the interatomic bonds of different lengths is calculated,which is important for testing interatomic potentials.The pros and cons of using DNVMs to test and improve interatomic potentials for metals are discussed.Since DNVMs are the natural vibrational modes of bcc crystals,any reliable interatomic potential must reproduce their properties with reasonable accuracy.展开更多
This paper analyzes the nonlinear dynamic characteristics and stability of Aero-Engine Dual-Rotor(AEDR)systems under high-frequency excitation,based on the Adaptive Harmonic Balance with the Asymptotic Harmonic Select...This paper analyzes the nonlinear dynamic characteristics and stability of Aero-Engine Dual-Rotor(AEDR)systems under high-frequency excitation,based on the Adaptive Harmonic Balance with the Asymptotic Harmonic Selection(AHB-AHS)method.A finite element dynamic equation for the AEDR system is introduced,considering complex nonlinearities of the intershaft bearing,unbalanced excitations,and high-frequency excitation.A solving strategy combining the AHB-AHS method and improved arclength continuation method is proposed to solve highdimensional dynamic equations containing complex nonlinearities and to track periodic solutions with parameter variations.The Floquet theory is used to analyze the types of bifurcation points in the system and the stability of periodic motions.The results indicate that high-frequency excitation can couple high-order and low-order modes,especially when the system undergoes superharmonic resonance.High-frequency excitation leads to more combination frequency harmonics,among which N_(f)ω_(1)-2ω_(2)dominates.Furthermore,changing the parameters(amplitude and frequency)of high-frequency excitation widens or shifts the unstable regions of the system.These findings contribute to understanding the mechanism of high-frequency excitation on aero-engines and demonstrate that the proposed AHB-AHS method is a powerful tool for analyzing highdimensional complex nonlinear dynamic systems under multi-frequency excitation.展开更多
Fatigue failure caused by vibration is the most common type of pipeline failure.The core of this research is to obtain the nonlinear dynamic stress of a pipeline system accurately and efficiently,a topic that needs to...Fatigue failure caused by vibration is the most common type of pipeline failure.The core of this research is to obtain the nonlinear dynamic stress of a pipeline system accurately and efficiently,a topic that needs to be explored in the existing literature.The shell theory can better simulate the circumferential stress distribution,and thus the Mindlin-Reissner shell theory is used to model the pipeline.In this paper,the continuous pipeline system is combined with clamps through modal expansion for the first time,which realizes the coupling problem between a shell and a clamp.While the Bouc-Wen model is used to simulate the nonlinear external force generated by a clamp,the nonlinear coupling characteristics of the system are effectively captured.Then,the dynamic equation of the clamp-pipeline system is established according to the Lagrange energy equation.Based on the resonance frequency and stress amplitude obtained from the experiment,the nonlinear parameters of the clamp are identified with the semi-analytical method(SAM)and particle swarm optimization(PSO)algorithm.This study provides a theoretical basis for the clamp-pipeline system and an efficient and universal solution for stress prediction and analysis of pipelines in engineering.展开更多
The nonlinear traveling wave vibration of rotating ferromagnetic functionally graded(FG)cylindrical shells under multi-physics fields is investigated.Grounded in the Kirchhoff-Love thin shell theory,the geometric nonl...The nonlinear traveling wave vibration of rotating ferromagnetic functionally graded(FG)cylindrical shells under multi-physics fields is investigated.Grounded in the Kirchhoff-Love thin shell theory,the geometric nonlinearity is incorporated into the model,and the constitutive equations are derived.The physical parameters of functionally graded materials(FGMs),which exhibit continuous variation across the thickness gradient,are of particular interest.The nonlinear magneto-thermoelastic governing equations are derived in accord with Hamilton's principle.The nonlinear partial differential equations are discretized with the Galerkin method,and the analytical expression of traveling wave frequencies is derived with an approximate method.The accuracy of the proposed method is validated through the comparison with the results from the literature and numerical solutions.Finally,the visualization analyses are conducted to examine the effects of key parameters on the traveling wave frequencies.The results show that the factors including the power-law index,temperature,magnetic field intensity,and rotating speed have the coupling effects with respect to the nonlinear vibration behavior.展开更多
The nonlinear vibrations of viscoelastic Euler-Bernoulli nanobeams are studied using the fractional calculus and the Gurtin-Murdoch theory. Employing Hamilton＇s principle, the governing equation considering surface e...The nonlinear vibrations of viscoelastic Euler-Bernoulli nanobeams are studied using the fractional calculus and the Gurtin-Murdoch theory. Employing Hamilton＇s principle, the governing equation considering surface effects is derived. The fractional integro-partial differential governing equation is first converted into a fractional-ordinary differential equation in the time domain using the Galerkin scheme. Thereafter, the set of nonlinear fractional time-dependent equations expressed in a state-space form is solved using the predictorcorrector method. Finally, the effects of initial displacement, fractional derivative order, viscoelasticity coefficient, surface parameters and thickness-to-length ratio on the nonlinear time response of simply-supported and clamped-free silicon viscoelastic nanobeams are investigated.展开更多
An electromechanical nonlinear model of rotor system of electric machine is built.Respondance curves in parameter excited nonlinear vibration of this system caused by electromagnetic forces are investigated.Further mo...An electromechanical nonlinear model of rotor system of electric machine is built.Respondance curves in parameter excited nonlinear vibration of this system caused by electromagnetic forces are investigated.Further more,the analysis reveals the effects of various electromagnetic and mechanical parameters on resonances, and some valuable results are obtained.The analytical result of this paper provides electric machine with the condition of 1/2 subharmonic resonance under the electromechanical electromagnetic forces.Electromagnetic forces apparently affect the stability zone, and both linear term and nonlinear term can excite parametric resonance.The revealed dynamic phenomena provide some new theories and active methods for the fault recognition of electric machine and the defination of stability range,and the theoretical bases for qualitatively controlling the stable operating state of rotors.展开更多
There exists a lot of research on the nonlinear vibration of the pipeline system with different boundary conditions.To the best of our knowledge,little research on the actual constraint of the clamp has been performed...There exists a lot of research on the nonlinear vibration of the pipeline system with different boundary conditions.To the best of our knowledge,little research on the actual constraint of the clamp has been performed.In this paper,according to hysteresis loops of the clamp obtained from experimental test,the simplified bilinear stiffness and damping model is proposed.Then the Finite Element(FE)model of L-type pipeline system with clamps is established using Timoshenko beam theory in combination with aforementioned stiffness-damping model.Both hammering and shaker tests verify the FE model via the comparisons of natural frequencies and vibration responses.The results show that the maximum errors of natural frequencies and vibration responses are about 8.31%and 17.6%,respectively.The proposed model can simulate the dynamic characteristics of the L-type pipeline system with clamps well,which is helpful to provide some guidance for the early design stage of pipeline in aero-engine.展开更多
Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts.The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonli...Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts.The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonlinear friction force is investigated.On the basis of the generalized dissipation Lagrange's equation,the dynamics equation of nonlinear torsional vibration system is deduced.The bifurcation and chaotic motion in the system subjected to an external harmonic excitation is studied by theoretical analysis and numerical simulation.The stability of unperturbed system is analyzed by using the stability theory of equilibrium positions of Hamiltonian systems.The criterion of existence of chaos phenomena under a periodic perturbation is given by means of Melnikov's method.It is shown that the existence of homoclinic and heteroclinic orbits in the unperturbed system implies chaos arising from breaking of homoclinic or heteroclinic orbits under perturbation.The validity of the result is checked numerically.Periodic doubling bifurcation route to chaos,quasi-periodic route to chaos,intermittency route to chaos are found to occur due to the amplitude varying in some range.The evolution of system dynamic responses is demonstrated in detail by Poincare maps and bifurcation diagrams when the system undergoes a sequence of periodic doubling or quasi-periodic bifurcations to chaos.The conclusion can provide reference for deeply researching the dynamic behavior of mechanical drive systems.展开更多
基金The authors are grateful to the National Natural Science Foundation of China(Grants 51679167,51979193,and 51608059)for financial support.
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.11502050 and 11672072).
文摘In this paper,the nonlinear forced vibrations and stability of an axially moving large deflection plate immersed in fluid are investigated.Based on von Karman's large deflec・tion plate theory and taking into consideration the influence of fluid-strueture interaction,axial moving and axial tension,nonlinear dynamic equations are obtained by applying D'Alembert's principle.These dynamic equations are further discretized into ordinary differential equations via the Galerkin method.The frequency-response curves of system are obtained and examined.Then numerical method is used to analyze the bifurcation behaviors of immersed plate.Results show that as the parameters vary,the system displays periodic,multi-periodic,quasi-periodic and even chaotic motion.Through the analysis on global dynamic characteristics of fluid-strueture interaction system,rich and varied nonlinear dynamic characteristics are obtained,and various ways that lead to chaotic motion of the system are further revealed.
基金Project supported by the National Natural Science Foundation of China(Nos.11832002 and 12072201)。
文摘The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.
基金We gratefully acknowledge NSFC(51509194)CSC for providing finacial support eanabling Li Qin and Hongling Qin to visit the University of Southampton to engage the related research.
文摘Based on the energy flow theory of nonlinear dynamical system,the stabilities,bifurcations,possible periodical/chaotic motions of nonlinear water-lubricated bearing-shaft coupled systems are investigated in this paper.It is revealed that the energy flow characteristics around the equlibrium point of system behaving in the three types with different friction-para-mters.(a)Energy flow matrix has two negative and one positive energy flow factors,constructing an attractive local zero-energy flow surface,in which free vibrations by initial disturbances show damped modulated oscillations with the system tending its equlibrium state,while forced vibrations by external forces show stable oscillations,(b)Energy flow matrix has one negative and two positive energy flow factors,spaning a divergence local zero-energy flow surface,so that the both free and forced vibrations are divergence oscillations with the system being unstable,(c)Energy flow matrix has a zero-energy flow factor and two opposite factors,which constructes a local zero-energy flow surface dividing the local phase space into stable,unstable and central subspace,and the simulation shows friction self-induced unstable vibrations for both free and forced cases.For a set of friction parameters,the system behaves a periodical oscillation,where the bearing motion tends zero and the shaft motion reaches a stable limit circle in phase space with the instant energy flow tending a constant and the time averaged one tending zero.Numerical simulations have not found any possible chaotic motions of the system.It is discovered that the damping matrices of cases(a),(b)and(c)respectively have positive,negative and zero diagonal elements,resulting in the different dynamic behavour of system,which gives a giderline to design the water-lubricated bearing unit with expected performance by adjusting the friction parameters for applications.
基金Project supported by the National Natural Science Foundation of China(No.12002195)the National Science Fund for Distinguished Young Scholars of China(No.12025204)the Program of Shanghai Municipal Education Commission of China(No.2019-01-07-00-09-E00018)。
文摘The influence of weights is usually ignored in the study of nonlinear vibrations of plates.In this paper,the effect of structure weights on the nonlinear vibration of a composite circular plate with a rigid body is presented.The nonlinear governing equations are derived from the generalized Hamilton's principle and the von Kármán plate theory.The equilibrium configurations due to weights are determined and validated by the finite element method(FEM).A nonlinear model for the vibration around the equilibrium configuration is established.Moreover,the natural frequencies and amplitude-frequency responses of harmonically forced vibrations are calculated.The study shows that the structure weights introduce additional linear and quadratic nonlinear terms into the dynamical model.This leads to interesting phenomena.For example,considering weights increases the natural frequency.Furthermore,when the influence of weights is considered,the vibration response of the plate becomes asymmetrical.
文摘This paper investigates the effect of porosity on active damping of geometrically nonlinear vibrations(GNLV)of the magneto-electro-elastic(MEE)functionally graded(FG)plates incorporated with active treatment constricted layer damping(ATCLD)patches.The perpendicularly/slanted reinforced 1-3 piezoelectric composite(1-3 PZC)constricting layer.The constricted viscoelastic layer of the ATCLD is modeled in the time-domain using Golla-Hughes-Mc Tavish(GHM)technique.Different types of porosity distribution in the porous magneto-electro-elastic functionally graded PMEE-FG plate graded in the thickness direction.Considering the coupling effects among elasticity,electrical,and magnetic fields,a three-dimensional finite element(FE)model for the smart PMEE-FG plate is obtained by incorporating the theory of layer-wise shear deformation.The geometric nonlinearity adopts the von K arm an principle.The study presents the effects of a variant of a power-law index,porosity index,the material gradation,three types of porosity distribution,boundary conditions,and the piezoelectric fiber’s orientation angle on the control of GNLV of the PMEE-FG plates.The results reveal that the FG substrate layers’porosity significantly impacts the nonlinear behavior and damping performance of the PMEE-FG plates.
文摘In this study, a slightly curved Euler Bernoulli beam carrying a concentrated mass was handled. The beam was resting on an elastic foundation and simply supported at both ends. Effects of the concentrated mass on nonlin- ear vibrations were investigated. Sinusoidal and parabolic type functions were used as curvature functions. Equations of motion have cubic nonlinearities because of elongations during vibrations. Damping and harmonic excitation terms were added to the equations of motion. Method of mul- tiple scales, a perturbation technique, was used for solving integro-differential equation analytically. Natural frequen- cies were calculated exactly for different mass ratios, mass locations, curvature functions, and linear elastic foundation coefficients. Amplitude-phase modulation equations were found by considering primary resonance case. Effects of nonlinear terms on natural frequencies were calculated. Frequency-amplitude and frequency-response graphs were plotted. Finally effects of concentrated mass and chosen curvature function on nonlinear vibrations were investigated.
基金support of the National Science Foundation for Distinguished Young Scholars of China (Grant No. 10425209)the National Natural Science Foundation of China (Grant No. 10732020)the Funding Project for Academic Human Resources Devel-opment in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality
文摘We analyze the transverse nonlinear vibrations of a rotating flexible disk subjected to a rotating point force with a periodically varying rotating speed. Based on Hamilton’s principle, the nonlinear governing equations of motion (coupled equations among the radial, tangential and transverse displacements) are derived for the rotating flexible disk. When the in-plane inertia is ignored and a stress function is introduced, the three nonlinearly coupled partial differential equations are reduced to two nonlinearly coupled partial differential equations. According to Galerkin’s approach, a four-degree-of-freedom nonlinear system governing the weakly split resonant modes is derived. The resonant case considered here is 1:1:2:2 internal resonance and a critical speed resonance. The primary parametric resonance for the first-order sin and cos modes and the fundamental parametric resonance for the second-order sin and cos modes are also considered. The method of multiple scales is used to obtain a set of eight-dimensional nonlinear averaged equations. Based on the averaged equations, using numerical simulations, the influence of different parameters on the nonlinear vibrations of the spinning disk is detected. It is concluded that there exist complicated nonlinear behaviors including the periodic, period-n and multi-pulse type chaotic motions for the spinning disk with a varying rotating speed. It is also found that among all parameters, the damping and excitation have great influence on the nonlinear responses of the spinning disk with a varying rotating speed.
基金Supported by Basic Research Foundation of Tsinghua University (No. JC2001003)
文摘This paper is concerned with the effects of boundary conditions on the large-amplitude free vi-brations of Timoshenko beams. The effects of nonlinear terms on the frequency of Timoshenko beams with simply supported ends (supported-supported, SS), clamped ends (clamped-clamped, CC) and one end simply supported and the other end clamped (clamped-supported, CS) are discussed in detail. Given a spe-cific vibration amplitude, the change of nonlinear frequency according to the effects of boundary conditions is always in the following descending order: SS, CS, and CC. It is found that the slenderness ratio has a significant influence on the nonlinear frequency. For slender beams, the nonlinear effects of bending curva-ture and shear strain are negligible regardless of the boundary conditions. For short beams and especially for those of large amplitude vibrations, however, the nonlinear effects of bending curvature and shear strain become noticeable in the following ascending order: SS, CS, and CC.
文摘Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes(CNTs)are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems.Therefore,the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscousfluid and supported on a nonlinear elastic foundation.The proposed model is based on nonlocal Euler–Bernoulli beam theory.The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation,respectively.A detailed parametric study is reported into how the nonlocal parameter,foundation coefficients,fluid viscosity,and amplitude and frequency of the external force influence the nonlinear dynamics of the system.Subharmonic,quasi-periodic,and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories,frequency-response curves,bifurcation diagrams,phase portraits,power spectra,and Poincarémaps.Also,the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters.
基金This research is supported by the National Natural Science Foundation of China(Nos.11572007 and 11172084).
文摘The nonlinear transverse vibrations of ordered and disordered twodimensional(2D)two-span composite laminated plates are studied.Based on the von Karman’s large deformation theory,the equations of motion of each-span composite laminated plate are formulated using Hamilton’s principle,and the partial differential equations are discretized into nonlinear ordinary ones through the Galerkin’s method.The primary resonance and 1/3 sub-harmonic resonance are investigated by using the method of multiple scales.The amplitude-frequency relations of the steady-state responses and their stability analyses in each kind of resonance are carried out.The effects of the disorder ratio and ply angle on the two different resonances are analyzed.From the numerical results,it can be concluded that disorder in the length of the two-span 2D composite laminated plate will cause the nonlinear vibration localization phenomenon,and with the increase of the disorder ratio,the vibration localization phenomenon will become more obvious.Moreover,the amplitude-frequency curves for both primary resonance and 1/3 sub-harmonic resonance obtained by the present analytical method are compared with those by the numerical integration,and satisfactory precision can be obtained for engineering applications and the results certify the correctness of the present approximately analytical solutions.
基金Support by Shanxi Provincial Key Research and Development Plan of China(Grant No.2024GH-ZDXM-29)National Natural Science Foundation of China(Grant No.52175120)Shaanxi Provincial Innovation Capability Support Program of China(Grant No.2024RS-CXTD-15)。
文摘Unbalanced force produced by the unbalanced mass will affect vibrations of rotor systems,which probably results in the components failures of rotating machinery.To study the effects of unbalanced mass on the vibration characteristics of rotor systems,a flexible rotor system model considering the unbalanced mass is proposed.The time-varying bearing force is considered.The developed model is verified by the experimental and theoretical frequency spectrums.The displacements and axis orbits of flexible and rigid rotor systems are compared.The results show that the unbalanced mass will affect the vibration characteristics of rotor system.This model can be more suitable and effective to calculate vibration characteristics of rotor system with the flexible deformation and unbalanced mass.This paper provides a new reference and research method for predicting the vibrations of flexible rotor system considering the unbalanced mass.
基金support of the RSF Grant No.24-11-00139(analytics,numerical results,manuscript writing)Daxing Xiong acknowledges the support of the NNSF Grant No.12275116,the NSF Grant No.2021J02051,and the startup fund Grant No.MJY21035For Aleksey A.Kudreyko,this work was supported by the Bashkir StateMedicalUniversity StrategicAcademic Leadership Program(PRIORITY-2030)(analytics).
文摘Molecular dynamics(MD)is a powerful method widely used in materials science and solid-state physics.The accuracy of MD simulations depends on the quality of the interatomic potentials.In this work,a special class of exact solutions to the equations of motion of atoms in a body-centered cubic(bcc)lattice is analyzed.These solutions take the form of delocalized nonlinear vibrational modes(DNVMs)and can serve as an excellent test of the accuracy of the interatomic potentials used in MD modeling for bcc crystals.The accuracy of the potentials can be checked by comparing the frequency response of DNVMs calculated using this or that interatomic potential with that calculated using the more accurate ab initio approach.DNVMs can also be used to train new,more accurate machine learning potentials for bcc metals.To address the above issues,it is important to analyze the properties of DNVMs,which is the main goal of this work.Considering only the point symmetry groups of the bcc lattice,34 DNVMs are found.Since interatomic potentials are not used in finding DNVMs,they are exact solutions for any type of potential.Here,the simplest interatomic potentials with cubic anharmonicity are used to simplify the analysis and to obtain some analytical results.For example,the dispersion relations for small-amplitude phonon modes are derived,taking into account interactions between up to the fourth nearest neighbor.The frequency response of the DNVMs is calculated numerically,and for some DNVMs examples of analytical analysis are given.The energy stored by the interatomic bonds of different lengths is calculated,which is important for testing interatomic potentials.The pros and cons of using DNVMs to test and improve interatomic potentials for metals are discussed.Since DNVMs are the natural vibrational modes of bcc crystals,any reliable interatomic potential must reproduce their properties with reasonable accuracy.
基金the financial support from the National Key R&D Program of China(No.2023YFE0125900)National Natural Science Foundation of China(Nos.12372008 and 12102234)+1 种基金Natural Science Foundation of Heilongjiang Province,China(No.YQ2022A008)Taif University,Saudi Arabia,for supporting this work through Project number(TU-DSPP-2024-73).
文摘This paper analyzes the nonlinear dynamic characteristics and stability of Aero-Engine Dual-Rotor(AEDR)systems under high-frequency excitation,based on the Adaptive Harmonic Balance with the Asymptotic Harmonic Selection(AHB-AHS)method.A finite element dynamic equation for the AEDR system is introduced,considering complex nonlinearities of the intershaft bearing,unbalanced excitations,and high-frequency excitation.A solving strategy combining the AHB-AHS method and improved arclength continuation method is proposed to solve highdimensional dynamic equations containing complex nonlinearities and to track periodic solutions with parameter variations.The Floquet theory is used to analyze the types of bifurcation points in the system and the stability of periodic motions.The results indicate that high-frequency excitation can couple high-order and low-order modes,especially when the system undergoes superharmonic resonance.High-frequency excitation leads to more combination frequency harmonics,among which N_(f)ω_(1)-2ω_(2)dominates.Furthermore,changing the parameters(amplitude and frequency)of high-frequency excitation widens or shifts the unstable regions of the system.These findings contribute to understanding the mechanism of high-frequency excitation on aero-engines and demonstrate that the proposed AHB-AHS method is a powerful tool for analyzing highdimensional complex nonlinear dynamic systems under multi-frequency excitation.
基金Project supported by the National Science and Technology Major Project(No.J2019-I-0008-0008)the National Natural Science Foundation of China(No.52305096)the Chinese Postdoctoral Science Foundation(No.GZB20230117)。
文摘Fatigue failure caused by vibration is the most common type of pipeline failure.The core of this research is to obtain the nonlinear dynamic stress of a pipeline system accurately and efficiently,a topic that needs to be explored in the existing literature.The shell theory can better simulate the circumferential stress distribution,and thus the Mindlin-Reissner shell theory is used to model the pipeline.In this paper,the continuous pipeline system is combined with clamps through modal expansion for the first time,which realizes the coupling problem between a shell and a clamp.While the Bouc-Wen model is used to simulate the nonlinear external force generated by a clamp,the nonlinear coupling characteristics of the system are effectively captured.Then,the dynamic equation of the clamp-pipeline system is established according to the Lagrange energy equation.Based on the resonance frequency and stress amplitude obtained from the experiment,the nonlinear parameters of the clamp are identified with the semi-analytical method(SAM)and particle swarm optimization(PSO)algorithm.This study provides a theoretical basis for the clamp-pipeline system and an efficient and universal solution for stress prediction and analysis of pipelines in engineering.
基金supported by the National Natural Science Foundation of China(No.12172321)。
文摘The nonlinear traveling wave vibration of rotating ferromagnetic functionally graded(FG)cylindrical shells under multi-physics fields is investigated.Grounded in the Kirchhoff-Love thin shell theory,the geometric nonlinearity is incorporated into the model,and the constitutive equations are derived.The physical parameters of functionally graded materials(FGMs),which exhibit continuous variation across the thickness gradient,are of particular interest.The nonlinear magneto-thermoelastic governing equations are derived in accord with Hamilton's principle.The nonlinear partial differential equations are discretized with the Galerkin method,and the analytical expression of traveling wave frequencies is derived with an approximate method.The accuracy of the proposed method is validated through the comparison with the results from the literature and numerical solutions.Finally,the visualization analyses are conducted to examine the effects of key parameters on the traveling wave frequencies.The results show that the factors including the power-law index,temperature,magnetic field intensity,and rotating speed have the coupling effects with respect to the nonlinear vibration behavior.
文摘The nonlinear vibrations of viscoelastic Euler-Bernoulli nanobeams are studied using the fractional calculus and the Gurtin-Murdoch theory. Employing Hamilton＇s principle, the governing equation considering surface effects is derived. The fractional integro-partial differential governing equation is first converted into a fractional-ordinary differential equation in the time domain using the Galerkin scheme. Thereafter, the set of nonlinear fractional time-dependent equations expressed in a state-space form is solved using the predictorcorrector method. Finally, the effects of initial displacement, fractional derivative order, viscoelasticity coefficient, surface parameters and thickness-to-length ratio on the nonlinear time response of simply-supported and clamped-free silicon viscoelastic nanobeams are investigated.
文摘An electromechanical nonlinear model of rotor system of electric machine is built.Respondance curves in parameter excited nonlinear vibration of this system caused by electromagnetic forces are investigated.Further more,the analysis reveals the effects of various electromagnetic and mechanical parameters on resonances, and some valuable results are obtained.The analytical result of this paper provides electric machine with the condition of 1/2 subharmonic resonance under the electromechanical electromagnetic forces.Electromagnetic forces apparently affect the stability zone, and both linear term and nonlinear term can excite parametric resonance.The revealed dynamic phenomena provide some new theories and active methods for the fault recognition of electric machine and the defination of stability range,and the theoretical bases for qualitatively controlling the stable operating state of rotors.
基金supported by National Natural Science Foundation of China(No.11772089)Fundamental Research Funds for the Central Universities(Nos.N170308028,N170306004 and N180708009)Program for the Innovative Talents of Higher Learning Institutions of Liaoning(LR2017035)。
文摘There exists a lot of research on the nonlinear vibration of the pipeline system with different boundary conditions.To the best of our knowledge,little research on the actual constraint of the clamp has been performed.In this paper,according to hysteresis loops of the clamp obtained from experimental test,the simplified bilinear stiffness and damping model is proposed.Then the Finite Element(FE)model of L-type pipeline system with clamps is established using Timoshenko beam theory in combination with aforementioned stiffness-damping model.Both hammering and shaker tests verify the FE model via the comparisons of natural frequencies and vibration responses.The results show that the maximum errors of natural frequencies and vibration responses are about 8.31%and 17.6%,respectively.The proposed model can simulate the dynamic characteristics of the L-type pipeline system with clamps well,which is helpful to provide some guidance for the early design stage of pipeline in aero-engine.
基金supported by National Key Technologies R&D Program of the 10th Five-year Plan of China(Grant No.ZZ02-13B-02-03-1)Hebei Provincial Natural Science Foundation of China(Grant No.F2008000882)Hebei Provincial Education Office Scientific Research Projects of China(Grant No.ZH2007102,2007496)
文摘Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts.The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonlinear friction force is investigated.On the basis of the generalized dissipation Lagrange's equation,the dynamics equation of nonlinear torsional vibration system is deduced.The bifurcation and chaotic motion in the system subjected to an external harmonic excitation is studied by theoretical analysis and numerical simulation.The stability of unperturbed system is analyzed by using the stability theory of equilibrium positions of Hamiltonian systems.The criterion of existence of chaos phenomena under a periodic perturbation is given by means of Melnikov's method.It is shown that the existence of homoclinic and heteroclinic orbits in the unperturbed system implies chaos arising from breaking of homoclinic or heteroclinic orbits under perturbation.The validity of the result is checked numerically.Periodic doubling bifurcation route to chaos,quasi-periodic route to chaos,intermittency route to chaos are found to occur due to the amplitude varying in some range.The evolution of system dynamic responses is demonstrated in detail by Poincare maps and bifurcation diagrams when the system undergoes a sequence of periodic doubling or quasi-periodic bifurcations to chaos.The conclusion can provide reference for deeply researching the dynamic behavior of mechanical drive systems.
