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
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
Vibration isolation is one of the most efficient approaches to protecting host structures from harmful vibrations,especially in aerospace,mechanical,and architectural engineering,etc.Traditional linear vibration isola...Vibration isolation is one of the most efficient approaches to protecting host structures from harmful vibrations,especially in aerospace,mechanical,and architectural engineering,etc.Traditional linear vibration isolation is hard to meet the requirements of the loading capacity and isolation band simultaneously,which limits further engineering application,especially in the low-frequency range.In recent twenty years,the nonlinear vibration isolation technology has been widely investigated to broaden the vibration isolation band by exploiting beneficial nonlinearities.One of the most widely studied objects is the"three-spring"configured quasi-zero-stiffness(QZS)vibration isolator,which can realize the negative stiffness and high-static-low-dynamic stiffness(HSLDS)characteristics.The nonlinear vibration isolation with QZS can overcome the drawbacks of the linear one to achieve a better broadband vibration isolation performance.Due to the characteristics of fast response,strong stroke,nonlinearities,easy control,and low-cost,the nonlinear vibration with electromagnetic mechanisms has attracted attention.In this review,we focus on the basic theory,design methodology,nonlinear damping mechanism,and active control of electromagnetic QZS vibration isolators.Furthermore,we provide perspectives for further studies with electromagnetic devices to realize high-efficiency vibration isolation.展开更多
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
The primary resonance of a single-degree-of-freedom(SDOF)system subjected to a harmonic excitation is mitigated by the method of optimal time-delay feedback control.The stable regions of the time delays and feedback g...The primary resonance of a single-degree-of-freedom(SDOF)system subjected to a harmonic excitation is mitigated by the method of optimal time-delay feedback control.The stable regions of the time delays and feedback gains are obtained from the stable conditions of eigenvalue equation.Attenuation ratio is applied for evaluating the performance of the vibration control by taking aproportion of peak amplitude of primary resonance for the suspension system with or without controllers.Taking the attenuation ratio as the objective function and the stable regions of the time delays and feedback gains as constrains,the optimal feedback gains are determined by using minimum optimal method.Finally,simulation examples are also presented.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
Considering the dynamic influence of the roll vibration on the lubricant film thickness in the rolling deformation area,nonlinear dynamic rolling forces related to film thickness in the vertical and horizontal directi...Considering the dynamic influence of the roll vibration on the lubricant film thickness in the rolling deformation area,nonlinear dynamic rolling forces related to film thickness in the vertical and horizontal directions were obtained based on the Karman balance theory.Based on these dynamic rolling forces and the mechanical vibration of the rolling mill,a vertical-horizontal coupling nonlinear vibration dynamic model was established.The amplitude-frequency equation of the main resonance was derived by using the multiple-scale method.At last,the parameters of the 1780 rolling mill were used for numerical simulation,and the time-domain response curves of the system’s vibration displacement and lubricating film thickness under the steady and unsteady conditions were analyzed.The influences of parameters such as interface contact ratio,nonlinear parameters and external disturbances on the primary resonance frequency characteristics were obtained,which provided a theoretical reference for the suppression of rolling mill vibration.展开更多
The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condi- tion were established by von Karman plate theory, and then acc...The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condi- tion were established by von Karman plate theory, and then accordingly exact solution of static load and its numerical results were given. Based on time mode hypothesis and the variational method, the control equation of the space mode was derived, and then the amplitude frequency-load character relation of circular sandwich plate was obtained by the modified iteration method. Consequently the rule of the effect of the two kinds of load on the vibration character of the circular sandwich plate was investigated. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.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
In this paper nonlinear analysis of a thin rectangular functionally graded piate is formulated in terms of von-Karman＇s dynamic equations. Functionaily Graded Material （FGM） properties vary through the constant thi...In this paper nonlinear analysis of a thin rectangular functionally graded piate is formulated in terms of von-Karman＇s dynamic equations. Functionaily Graded Material （FGM） properties vary through the constant thickness of the plate at ambient temperature. By expansion of the solution as a series of mode functions, we reduce the governing equations of motion to a Duffing＇s equation. The homotopy perturbation solution of generated Duffing＇s equation is also obtained and compared with numerical solutions. The sufficient conditions for the existence of periodic oscillatory behavior of the plate are established by using Green＇s function and Schauder＇s fixed point theorem.展开更多
As a novel vibration absorber,Nitinol-steel wire rope(NiTi-ST)has rarely been studied on vibration suppression for lattice sandwich beams in supersonic airflow.In this paper,NiTi-ST with nonlinear stiffness and hyster...As a novel vibration absorber,Nitinol-steel wire rope(NiTi-ST)has rarely been studied on vibration suppression for lattice sandwich beams in supersonic airflow.In this paper,NiTi-ST with nonlinear stiffness and hysteretic damping is embedded in a lattice sandwich beam to control the beam's vibration.The nonlinear restoring and hysteretic damping force of NiTi-ST are treated as polynomials.The dynamic equation is established based on Hamilton's principle.The amplitude responses of the beam with different NiTi-ST configurations are calculated.The vibration-suppression effects and energy dissipation of lattice sandwich beam with different NiTi-ST configurations under different air velocities are also compared.The frequency-domain and time-domain methods are used to analyze the structural aeroelastic properties.Simulation results show that the use of NiTi-ST can significantly suppress excessive vibration of a lattice sandwich beam in supersonic airflow.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 optimal time-delay feedback control method is provided to mitigate the primary resonance of a single-walled carbon nanotube （SWCNT） subjected to a Lorentz force excited by a longitudinal magnetic field. The nonli...An optimal time-delay feedback control method is provided to mitigate the primary resonance of a single-walled carbon nanotube （SWCNT） subjected to a Lorentz force excited by a longitudinal magnetic field. The nonlinear governing equations of motion for the SWCNT under longitudinal magnetic field are derived and the modulation equations are obtained by using the method of multiple scales. The regions of the stable feedback gain are worked out by using the stability conditions of eigenvalue equation. Taking the attenuation ratio as the objective function and the stable vibration regions as constrained conditions, the optimal control parameters are worked out by using minimum optimal method. The optimal controllers are designed to control the dynamic behaviors of tile nonlinear vibration systems. It is found that the optimal feedback gain obtained by the optimal method can enhance the control performance of the primary resonance of SWCNT devices.展开更多
Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-para...Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-parameter foundation. Under the condition of free boundary, a set of trial functions satisfying all boundary conditions and crack＇s continuous conditions were proposed. By employing the Galerkin method and the harmonic balance method, the nonlinear vibration equations were solved and the nonlinear vibration behaviors of the plate were analyzed. In numerical computation, the effects of the different location and depth of crack, the different structural parameters of plates and the different physical parameters of foundation on the nonlinear amplitude frequency response curves of the plate were discussed.展开更多
Based on the nonlocal continuum theory, the nonlinear vibration of an embedded single-walled carbon nanotube （SWCNT） subjected to a harmonic load is in- vestigated. In the present study, the SWCNT is assumed to be a...Based on the nonlocal continuum theory, the nonlinear vibration of an embedded single-walled carbon nanotube （SWCNT） subjected to a harmonic load is in- vestigated. In the present study, the SWCNT is assumed to be a curved beam, which is unlike previous similar work. Firstly, the governing equations of motion are derived by the Hamilton principle, meanwhile, the Galerkin approach is carried out to convert the nonlinear integral-differential equation into a second-order nonlinear ordinary differ- ential equation. Then, the precise integration method based on the local linearzation is appropriately designed for solving the above dynamic equations. Besides, the numerical example is presented, the effects of the nonlocal parameters, the elastic medium constants, the waviness ratios, and the material lengths on the dynamic response are analyzed. The results show that the above mentioned effects have influences on the dynamic behavior of the SWCNT.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
Based on von Karman plate theory, the issue about nonlinear vibration for circular sandwich plates under circumjacent load with the loosely clamped boundary condition was researched. Nonlinear differential eigenvalue ...Based on von Karman plate theory, the issue about nonlinear vibration for circular sandwich plates under circumjacent load with the loosely clamped boundary condition was researched. Nonlinear differential eigenvalue equations and boundary conditions of the problem were formulated by variational method and then their exact static solution can be got. The solution was derived by modified iteration method, so the analytic relations between amplitude and nonlinear oscillating frequency for circular sandwich plates were obtained. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.展开更多
The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied. Based on the large deflection theories of von Krmn and the theor...The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied. Based on the large deflection theories of von Krmn and the theory of thermoelasticity, the whole governing equations and their simplified type are derived. The time-spatial variables are separated by Galerkin's technique, thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation. By means of regular perturbation method and multiple-scales method, the first-order approximate analytical solution for characteristic relation of frequency vs amplitude parameters along with the decay rate of amplitude are obtained, and the effects of different geometric parameters and coupling factors as well as boundary conditions on thermoelastically coupled nonlinear vibration behaviors are discussed.展开更多
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.
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the National Natural Science Foundation of China(No.52175125)。
文摘Vibration isolation is one of the most efficient approaches to protecting host structures from harmful vibrations,especially in aerospace,mechanical,and architectural engineering,etc.Traditional linear vibration isolation is hard to meet the requirements of the loading capacity and isolation band simultaneously,which limits further engineering application,especially in the low-frequency range.In recent twenty years,the nonlinear vibration isolation technology has been widely investigated to broaden the vibration isolation band by exploiting beneficial nonlinearities.One of the most widely studied objects is the"three-spring"configured quasi-zero-stiffness(QZS)vibration isolator,which can realize the negative stiffness and high-static-low-dynamic stiffness(HSLDS)characteristics.The nonlinear vibration isolation with QZS can overcome the drawbacks of the linear one to achieve a better broadband vibration isolation performance.Due to the characteristics of fast response,strong stroke,nonlinearities,easy control,and low-cost,the nonlinear vibration with electromagnetic mechanisms has attracted attention.In this review,we focus on the basic theory,design methodology,nonlinear damping mechanism,and active control of electromagnetic QZS vibration isolators.Furthermore,we provide perspectives for further studies with electromagnetic devices to realize high-efficiency vibration isolation.
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(51375228)the Aeronautical Science Fund(2013155202)+1 种基金the Fundamental Research Funds for the Central Universities(NJ20140012)the Priorty Academic Program Development of Jiangsu Higher Education Institutions
文摘The primary resonance of a single-degree-of-freedom(SDOF)system subjected to a harmonic excitation is mitigated by the method of optimal time-delay feedback control.The stable regions of the time delays and feedback gains are obtained from the stable conditions of eigenvalue equation.Attenuation ratio is applied for evaluating the performance of the vibration control by taking aproportion of peak amplitude of primary resonance for the suspension system with or without controllers.Taking the attenuation ratio as the objective function and the stable regions of the time delays and feedback gains as constrains,the optimal feedback gains are determined by using minimum optimal method.Finally,simulation examples are also presented.
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This research is supported by the National Natural Science Foundation of China(Grant Nos.61973262 and 51405068)the Natural Science Foundation of Hebei Province of China(Grant No.E2019203146).
文摘Considering the dynamic influence of the roll vibration on the lubricant film thickness in the rolling deformation area,nonlinear dynamic rolling forces related to film thickness in the vertical and horizontal directions were obtained based on the Karman balance theory.Based on these dynamic rolling forces and the mechanical vibration of the rolling mill,a vertical-horizontal coupling nonlinear vibration dynamic model was established.The amplitude-frequency equation of the main resonance was derived by using the multiple-scale method.At last,the parameters of the 1780 rolling mill were used for numerical simulation,and the time-domain response curves of the system’s vibration displacement and lubricating film thickness under the steady and unsteady conditions were analyzed.The influences of parameters such as interface contact ratio,nonlinear parameters and external disturbances on the primary resonance frequency characteristics were obtained,which provided a theoretical reference for the suppression of rolling mill vibration.
文摘The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condi- tion were established by von Karman plate theory, and then accordingly exact solution of static load and its numerical results were given. Based on time mode hypothesis and the variational method, the control equation of the space mode was derived, and then the amplitude frequency-load character relation of circular sandwich plate was obtained by the modified iteration method. Consequently the rule of the effect of the two kinds of load on the vibration character of the circular sandwich plate was investigated. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.
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.
文摘In this paper nonlinear analysis of a thin rectangular functionally graded piate is formulated in terms of von-Karman＇s dynamic equations. Functionaily Graded Material （FGM） properties vary through the constant thickness of the plate at ambient temperature. By expansion of the solution as a series of mode functions, we reduce the governing equations of motion to a Duffing＇s equation. The homotopy perturbation solution of generated Duffing＇s equation is also obtained and compared with numerical solutions. The sufficient conditions for the existence of periodic oscillatory behavior of the plate are established by using Green＇s function and Schauder＇s fixed point theorem.
基金supported by the National Natural Science Foundation of China(Project Nos.12022213 and 11902203)Liaoning Educational Committee Scientific Research Project in General(JYT2020035).
文摘As a novel vibration absorber,Nitinol-steel wire rope(NiTi-ST)has rarely been studied on vibration suppression for lattice sandwich beams in supersonic airflow.In this paper,NiTi-ST with nonlinear stiffness and hysteretic damping is embedded in a lattice sandwich beam to control the beam's vibration.The nonlinear restoring and hysteretic damping force of NiTi-ST are treated as polynomials.The dynamic equation is established based on Hamilton's principle.The amplitude responses of the beam with different NiTi-ST configurations are calculated.The vibration-suppression effects and energy dissipation of lattice sandwich beam with different NiTi-ST configurations under different air velocities are also compared.The frequency-domain and time-domain methods are used to analyze the structural aeroelastic properties.Simulation results show that the use of NiTi-ST can significantly suppress excessive vibration of a lattice sandwich beam in supersonic airflow.
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 optimal time-delay feedback control method is provided to mitigate the primary resonance of a single-walled carbon nanotube （SWCNT） subjected to a Lorentz force excited by a longitudinal magnetic field. The nonlinear governing equations of motion for the SWCNT under longitudinal magnetic field are derived and the modulation equations are obtained by using the method of multiple scales. The regions of the stable feedback gain are worked out by using the stability conditions of eigenvalue equation. Taking the attenuation ratio as the objective function and the stable vibration regions as constrained conditions, the optimal control parameters are worked out by using minimum optimal method. The optimal controllers are designed to control the dynamic behaviors of tile nonlinear vibration systems. It is found that the optimal feedback gain obtained by the optimal method can enhance the control performance of the primary resonance of SWCNT devices.
基金国家自然科学基金，Technology Item of Ministry of Communications of China
文摘Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-parameter foundation. Under the condition of free boundary, a set of trial functions satisfying all boundary conditions and crack＇s continuous conditions were proposed. By employing the Galerkin method and the harmonic balance method, the nonlinear vibration equations were solved and the nonlinear vibration behaviors of the plate were analyzed. In numerical computation, the effects of the different location and depth of crack, the different structural parameters of plates and the different physical parameters of foundation on the nonlinear amplitude frequency response curves of the plate were discussed.
基金Project supported by the National Basic Research Program of China (No. 2011CB610300)the National Natural Science Foundation of China (Nos. 10972182, 11172239, and 10902089)+3 种基金the 111 Project of China (No. B07050)the Ph. D. Programs Foundation of Ministry of Education of China (No. 20106102110019)the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment (No. GZ0802)the Doctorate Foundation of Northwestern Polytechnical University (No. CX201224)
文摘Based on the nonlocal continuum theory, the nonlinear vibration of an embedded single-walled carbon nanotube （SWCNT） subjected to a harmonic load is in- vestigated. In the present study, the SWCNT is assumed to be a curved beam, which is unlike previous similar work. Firstly, the governing equations of motion are derived by the Hamilton principle, meanwhile, the Galerkin approach is carried out to convert the nonlinear integral-differential equation into a second-order nonlinear ordinary differ- ential equation. Then, the precise integration method based on the local linearzation is appropriately designed for solving the above dynamic equations. Besides, the numerical example is presented, the effects of the nonlocal parameters, the elastic medium constants, the waviness ratios, and the material lengths on the dynamic response are analyzed. The results show that the above mentioned effects have influences on the dynamic behavior of the SWCNT.
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Based on von Karman plate theory, the issue about nonlinear vibration for circular sandwich plates under circumjacent load with the loosely clamped boundary condition was researched. Nonlinear differential eigenvalue equations and boundary conditions of the problem were formulated by variational method and then their exact static solution can be got. The solution was derived by modified iteration method, so the analytic relations between amplitude and nonlinear oscillating frequency for circular sandwich plates were obtained. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.
文摘The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied. Based on the large deflection theories of von Krmn and the theory of thermoelasticity, the whole governing equations and their simplified type are derived. The time-spatial variables are separated by Galerkin's technique, thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation. By means of regular perturbation method and multiple-scales method, the first-order approximate analytical solution for characteristic relation of frequency vs amplitude parameters along with the decay rate of amplitude are obtained, and the effects of different geometric parameters and coupling factors as well as boundary conditions on thermoelastically coupled nonlinear vibration behaviors are discussed.
