The parametric dynamic stability of resonant beams with various parameters under periodic axial force is studied. It is assumed that the theoretical formulations are based on Euler-Bernoulli beam theory. The governing...The parametric dynamic stability of resonant beams with various parameters under periodic axial force is studied. It is assumed that the theoretical formulations are based on Euler-Bernoulli beam theory. The governing equations of motion are derived by using the Rayleigh-Ritz method and transformed into Mathieu equations, which are formed to determine the stability criterion and stability regions for parametricallyexcited linear resonant beams. An improved stability criterion is obtained using periodic Lyapunov functions. The boundary points on the stable regions are determined by using a small parameter perturbation method. Numerical results and discussion are presented to highlight the effects of beam length, axial force and damped coefficient on the stability criterion and stability regions. While some stability rules are easy to anticipate, we draw some conclusions： with the increase of damped coefficient, stable regions arise; with the decrease of beam length, the conditions of the damped coefficient arise instead. These conclusions can provide a reference for the robust design of parametricallyexcited linear resonant sensors.展开更多
In this paper,we report the frequency comb response experimentally and analytically in a rhombic micro-resonator with parametrical modulation.When the electrostatically actuated rhombic micro-resonator is modulated ax...In this paper,we report the frequency comb response experimentally and analytically in a rhombic micro-resonator with parametrical modulation.When the electrostatically actuated rhombic micro-resonator is modulated axially by a low-frequency periodic excitation,a comb-like vibration response with few equidistant positioned fingers in the frequency domain is observed.The finger spacing of frequency comb response is exactly consistent with modulation frequency and the number and amplitude of the fingers can be tuned by modulation strength.A mixed frequency comb with extra comb fingers is further generated when the resonator is modulated simultaneously by two different low-frequency excitation signals.By adjusting the relation of the two modulation frequencies,unequal spacing frequency combs are achieved for the first time,which leads to a more flexible tunability of the comb spacing for different applications.Theoretical analysis based on the dynamic model well explains the corresponding observations.展开更多
This paper discusses a simple way to suppress the parametrically excited lateral vibration of a mass-loaded string. Supposing that the mass at the lower end of the string is subjected to a vertical harmonic excitation...This paper discusses a simple way to suppress the parametrically excited lateral vibration of a mass-loaded string. Supposing that the mass at the lower end of the string is subjected to a vertical harmonic excitation and neglecting the higher order vibration modes, the equation of motion for the mass-loaded string can be represented by a Mathieus equation with cubic nonlinearity. According to the theory of the Mathieus equation, in the mass-loaded string system, when the vertical vibration frequency of the mass approaches twice the natural frequency of the string lateral vibration, once the vertical vibration amplitude of the mass exceeds a critical value, the parametric resonance will occur in the string. To avoid the parametric resonance, a vibration absorber, composed of a thin beam and two mass blocks attached at both sides of the beam symmetrically, is proposed to install with the mass to reduce its vertical vibration, and ultimately suppress the lateral vibration of the string. Such a suppression strategy is finally validated by experiments.展开更多
In the present work, we investigate the nonlinear parametrically excited vibration and active control of a gear pair system involving backlash, time-varying meshing stiffness and static transmission error. Firstly, a ...In the present work, we investigate the nonlinear parametrically excited vibration and active control of a gear pair system involving backlash, time-varying meshing stiffness and static transmission error. Firstly, a gear pair model is established in a strongly nonlinear form, and its nonlinear vibration characteristics are systematically investigated through different approaches. Several complicated phenomena such as period doubling bifurcation, anti period doubling bifurcation and chaos can be observed under the internal parametric excitation. Then, an active compensation controller is designed to suppress the vibration, including the chaos. Finally, the effectiveness of the proposed controller is verified numerically.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
This paper presents a nonlinear dynamic model for simulation and analysis of a kind of parametrically excited vibration of stay cable caused by support motion in cable-stayed bridges. The sag, inclination angle of the...This paper presents a nonlinear dynamic model for simulation and analysis of a kind of parametrically excited vibration of stay cable caused by support motion in cable-stayed bridges. The sag, inclination angle of the stay cable are considered in the model, based on which, the oscillation mechanism and dynamic response characteristics of this kind of vibration are analyzed through numerical calculation. It is noted that parametrically excited oscillation of a stay cable with certain sag, inclination angle and initial static tension force may occur in cable-stayed bridges due to deck vibration under the condition that the natural frequency of a cable approaches to about half of the first model frequency of the bridge deck system. A new vibration control system installed on the cable anchorage is proposed as a possible damping system to suppress the cable parametric oscillation. The numerical calculation results showed that with the use of this damping system, the cable oscillation due to the vibration of the deck and/or towers will be considerably reduced.展开更多
If the constraint boundary relates to a bifurcation parameter, a bifurcation is said to be parametrically constrained. Relying upon some substitution, a parametrically constrained bifurcation is transformed to an unco...If the constraint boundary relates to a bifurcation parameter, a bifurcation is said to be parametrically constrained. Relying upon some substitution, a parametrically constrained bifurcation is transformed to an unconstrained bifurcation about new variables. A general form of transition sets of the parametrically constrained bifurcation is derived. The result indicates that only the constrained bifurcation set is influenced by parametric constraints, while other transition sets are the same as those of the corresponding nonparametrically constrained bifurcation. Taking parametrically constrained pitchfork bifurcation problems as examples, effects of parametric constraints on bifurcation classification are discussed.展开更多
The dynamical behaviour of a parametrically excited Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay is concerned. By means of the method of averaging together with t...The dynamical behaviour of a parametrically excited Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay is concerned. By means of the method of averaging together with truncation of Taylor expansions, two slow-flow equations on the amplitude and phase of response were derived for the case of principal parametric resonance, it is shown that the stability condition for the trivial solution is only associated with the linear terms in the original systems besides the amplitude and frequency of parametric excitation. And the trivial solution can be stabilized by appreciate choice of gains and time delay in feedback control. Different from the case of the trivial solution, the stability condition for nontrivial solutions is also associated with nonlinear terms besides linear terms in the original system. It is demonstrated that nontrivial steady state responses may lose their stability by saddle-node （SN） or Hopf bifurcation （HB） as parameters vary. The simulations, obtained by numerically integrating the original system, are in good agreement with the analytical results.展开更多
The nonlinear response of a two_degree_of_freedom nonlinear oscillating system to parametric excitation is examined for the case of 1∶2 internal resonance and, principal parametric resonance with respect to the lower...The nonlinear response of a two_degree_of_freedom nonlinear oscillating system to parametric excitation is examined for the case of 1∶2 internal resonance and, principal parametric resonance with respect to the lower mode. The method of multiple scales is used to derive four first_order autonomous ordinary differential equations for the modulation of the amplitudes and phases. The steady_state solutions of the modulated equations and their stability are investigated. The trivial solutions lose their stability through pitchfork bifurcation giving rise to coupled mode solutions. The Melnikov method is used to study the global bifurcation behavior, the critical parameter is determined at which the dynamical system possesses a Smale horseshoe type of chaos.展开更多
For a co_dimension two bifurcation system on a three_dimensional central manifold, which is parametrically excited by a real noise, a rather general model is obtained by assuming that the real noise is an output of a ...For a co_dimension two bifurcation system on a three_dimensional central manifold, which is parametrically excited by a real noise, a rather general model is obtained by assuming that the real noise is an output of a linear filter system_a zeromean stationary Gaussian diffusion process which satisfies detailed balance condition. By means of the asymptotic analysis approach given by L. Arnold and the expression of the eigenvalue spectrum of Fokker_Planck operator, the asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are obtained.展开更多
For a real noise parametrically excited co_dimension two bifurcation system on a three_dimensional central manifold, a model of enhanced generality is developed in the present paper by assuming the real noise to be an...For a real noise parametrically excited co_dimension two bifurcation system on a three_dimensional central manifold, a model of enhanced generality is developed in the present paper by assuming the real noise to be an output of a linear filter system, namely,a zero_mean stationary Gaussian diffusion process that satisfies the detailed balance condition. On such basis, asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are established by use of Arnold asymptotic analysis approach in parallel with the eigenvalue spectrum of Fokker_Planck operator.展开更多
In response to the identification problem concerning multi-degree of freedom （MDOF） nonlinear systems, this study presents the extended forward orthogonal regression （EFOR） based on predicted residual sums of squa...In response to the identification problem concerning multi-degree of freedom （MDOF） nonlinear systems, this study presents the extended forward orthogonal regression （EFOR） based on predicted residual sums of squares （PRESS） to construct a nonlinear dynamic parametrical model. The proposed parametrical model is based on the non-linear autoregressive with exogenous inputs （NARX） model and aims to explicitly reveal the physical design parameters of the system. The PRESSbased EFOR algorithm is proposed to identify such a model for MDOF systems. By using the algorithm, we built a common-structured model based on the fundamental concept of evaluating its generalization capability through cross-validation. The resulting model aims to prevent over-fitting with poor generalization performance caused by the average error reduction ratio （AERR）-based EFOR algorithm. Then, a functional relationship is established between the coefficients of the terms and the design parameters of the unified model. Moreover, a 5- DOF nonlinear system is taken as a case to illustrate the modeling of the proposed algorithm. Finally, a dynamic parametrical model of a cantilever beam is constructed from experimental data. Results indicate that the dynamic parametrical model of nonlinear systems, which depends on the PRESS-based EFOR, can accurately predict the output response, thus providing a theoretical basis for the optimal design of modeling methods for MDOF nonlinear systems.展开更多
Some of the up-to-date experimental results on the parametrically-excited solitons in arectangular trough of water are provided, including the periodical reflection of a soliton at an end wall of a trough, the collisi...Some of the up-to-date experimental results on the parametrically-excited solitons in arectangular trough of water are provided, including the periodical reflection of a soliton at an end wall of a trough, the collision dynamics of two solitons of like polarity and the existence of mirror effect at boundaries. Attempts are made to explain the observed phenomena and a conception of virtual solitons is proposed.展开更多
A new mode of nonpropagating solitary waves in circular tank, which are forcedly ex-cited in tbe vertical direction, is described. The waveform is measured and the data accordwell with the hyperbolic secant function.A...A new mode of nonpropagating solitary waves in circular tank, which are forcedly ex-cited in tbe vertical direction, is described. The waveform is measured and the data accordwell with the hyperbolic secant function.Analyses of the vibration modes of the wave showthat the mode is not a pure mode of circular container. A wax cone was inserted in themiddle of tank in order to keep down the plateau. The hysteresis phenomenon of excitation ofsolitary wave has been observed as well.展开更多
Water plays a vital role in biological metabolism and it would be essential to trace the water content non-invasively,such as leveraging the vibrational absorption peak of the O-H bond.However,due to the lack of an ef...Water plays a vital role in biological metabolism and it would be essential to trace the water content non-invasively,such as leveraging the vibrational absorption peak of the O-H bond.However,due to the lack of an efficient laser source,it was challenging to image the water content in the deep tissue with micron-level spatial resolution.To address this problem,we develop a high-power hybrid optical parametrically-oscillating emitter(HOPE)at 1930 nm,at which the vibrational absorption peak of the O-H bond locates.The maximum pulse energy is over 1.74μJ with a pulse repetition rate of 50 kHz and a pulse width of 15 ns.We employ this laser source in the optical-resolution photoacoustic microscopy(OR-PAM)system to image the water content in the phantom and the biological tissue in vitro.Our 1930-nm OR-PAM could map the water content in the complex tissue environment at high spatial resolution,deep penetration depth,improved sensitivity,and suppressed artifact signal of the lipid.展开更多
Nonlinear dynamic analysis is performed on moving belts subjected to geometric nonlinearity and initial tension fluctuation. To incorporate more accurately the damping mechanism of belt material, linear viscoelastic m...Nonlinear dynamic analysis is performed on moving belts subjected to geometric nonlinearity and initial tension fluctuation. To incorporate more accurately the damping mechanism of belt material, linear viscoelastic models are adopted in a unified form of differential operators. To circumvent high-order differential vibration equation of time-varying coefficients and with gyroscopic and nonlinear terms, where analytical solution is almost impossible, a systematic approach is presented by reforming the motion equation and directly using the method of multiple scales. To exemplify the procedure, the solutions at principal resonance are obtained and their stability conditions are derived for employing a Kelvin-Voigt model to reflect the property of the belt material. The solutions and stability conditions successfully reduce to those for using Kelvin model and elastic model, which validate the present approaches. Numerical simulations highlight the effects of tension fluctuations and translating speeds on the stability of the belt vibration.展开更多
A high-temperature and high-pressure valve is the key equipment of a wind tunnel system;it controls the generation of high-temperature and high-pressure gas.To reduce the adverse impact of high-temperature and high-pr...A high-temperature and high-pressure valve is the key equipment of a wind tunnel system;it controls the generation of high-temperature and high-pressure gas.To reduce the adverse impact of high-temperature and high-pressure gas on the strength of the valve body,a cooling structure is set on the valve seat.This can significantly reduce the temperature of the valve body and valve seat.The effects of its structure on the cooling characteristics and stress of the valve seat are studied,and six main parameters that can completely describe the geometry of the cooling structure are proposed.The central composite design method is used to select sample points,and the multi-objective genetic algorithm(MOGA)method is used for optimal structural design.A modification method according to the main parameters for the valve seat is proposed.The results show that the cooling structure weakens the pressure-bearing capability of the valve seat.Among the six main parameters of the valve seat,the distance from the end face of the lower hole to the Z-axis and the distance from the axis of the lower hole to the origin of the coordinates have the most obvious effects on the average stress of the valve seat.An optimum design value is proposed.This work can provide a reference for the design of high-temperature and high-pressure valves.展开更多
In recent years,the concept of digital human has attracted widespread attention from all walks of life,and the modelling of high-fidelity human bodies,heads,and hands has been intensively studied.This paper focuses on...In recent years,the concept of digital human has attracted widespread attention from all walks of life,and the modelling of high-fidelity human bodies,heads,and hands has been intensively studied.This paper focuses on head modelling and proposes a generic head parametric model based on neural radiance fields.Specifically,we first use face recognition networks and 3D facial expression database FaceWarehouse to parameterize identity and expression semantics,respectively,and use both as conditional inputs to build a neural radiance field for the human head,thereby improving the head model’s representation ability while ensuring editing capabilities for the identity and expression of the rendered results;then,through a combination of volume rendering and neural rendering,the 3D representation of the head is rapidly rendered into the 2D plane,producing a high-fidelity image of the human head.Thanks to the well-designed loss functions and good implicit representation of the neural radiance field,our model can not only edit the identity and expression independently,but also freely modify the virtual camera position of the rendering results.It has excellent multi-view consistency,and has many applications in novel view synthesis,pose driving and more.展开更多
An experimental investigation of the dynamics of the interface between two low-viscosity fluids with high density contrast oscillating in a fixed vertical slotted channel has been conducted.It has been found that as t...An experimental investigation of the dynamics of the interface between two low-viscosity fluids with high density contrast oscillating in a fixed vertical slotted channel has been conducted.It has been found that as the amplitude of the liquid column oscillations increases,parametric oscillations of the interface are excited in the form of a standing wave located in the channel plane.In particular,depending on the interfacial tension,the standing waves have a frequency equal to that of liquid piston oscillations(harmonic response),or half of the frequency of oscillations of the liquid column in the channel(subharmonic response).The detected type of instability has a gravitational-capillary nature and is analogous to Faraday waves.The analysis of the overcritical dynamics of wave oscillations indicates that interfacial tension plays a crucial role in determining the type of parametric instability.At high interfacial tension,only synchronous(harmonic)wave modes are observed,and the threshold of the wave excitation is determined by the amplitude of piston oscillations of the liquid column.In this case,the oscillation acceleration does not play a role and has a small value in the threshold of the synchronous mode response.In the case of weak surface tension,subharmonic oscillations are observed.The threshold for the development of these oscillations is determined by the dimensionless acceleration of the oscillating liquid column and remains almost constant with variations in the dimensionless frequency of oscillations.At moderate values of interfacial tension(in the region of moderate dimensionless frequencies),a synchronous wave mode emerges in the stability threshold of the oscillating interface.As the dimensionless acceleration is increased further,a subharmonic mode is excited.The growth of subharmonic oscillations occurs against the background of harmonic wave oscillations,with the oscillations of the interface representing a combination of two standing waves.展开更多
Tensegrity structures,embodying the principles of continuous tensioning and discrete compression,have emerged as fundamental frameworks in locomotive soft robotics for navigating uneven and unpredictable environments,...Tensegrity structures,embodying the principles of continuous tensioning and discrete compression,have emerged as fundamental frameworks in locomotive soft robotics for navigating uneven and unpredictable environments,owing to their flexible and resilient traits.By means of a straightforward and cost-effective method to achieve structure-driven,vibration-driven tensegrity shows great potential,particularly in tasks demanding random exploration.However,the design guidance for vibration-driven tensegrity and their performance evaluation in unstructured terrain remain unrevealed due to the complex dynamics of the structure.This paper presents a small six-bar tensegrity robot,driven by wireless vibration motors,designed for deployment in disaster rescue and search scenarios.Finite element simulation is used to investigate how structural characteristics,excitation parameters,and the arrangement of motors affect the kinematic performance of this tensegrity system.A prototype of the six-bar tensegrity robot with three motors located on the lower ends of the three lower struts is designed and manufactured after the numerical simulations.A simple control policy which adjusts the motion of the tensegrity robot by turning on or off the motors on different locations is proposed.The prototype with and without the control policy is tested in man-made environments of various complexity.It shows that the ability and efficiency of the tensegrity robot in exploring unstructured environments is significantly enhanced by the proposed control policy.It is believed that the potential of the vibration-driven tensegrity robot could be further exploited by integrating multi-source sensors and more intelligent control policies.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 60927005)the 2012 Innovation Foundation of BUAA for PhD Graduatesthe Fundamental Research Funds for the Central Universities,China (Grant No. YWF-10-01-A17)
文摘The parametric dynamic stability of resonant beams with various parameters under periodic axial force is studied. It is assumed that the theoretical formulations are based on Euler-Bernoulli beam theory. The governing equations of motion are derived by using the Rayleigh-Ritz method and transformed into Mathieu equations, which are formed to determine the stability criterion and stability regions for parametricallyexcited linear resonant beams. An improved stability criterion is obtained using periodic Lyapunov functions. The boundary points on the stable regions are determined by using a small parameter perturbation method. Numerical results and discussion are presented to highlight the effects of beam length, axial force and damped coefficient on the stability criterion and stability regions. While some stability rules are easy to anticipate, we draw some conclusions： with the increase of damped coefficient, stable regions arise; with the decrease of beam length, the conditions of the damped coefficient arise instead. These conclusions can provide a reference for the robust design of parametricallyexcited linear resonant sensors.
基金the National Natural Science Foundation of China(Grant Nos.12172323 and 52075432)Zhejiang Provincial Natural Science Foundation of China(Grant No.LZ22A020003)+1 种基金Fundamental Research Funds for the Central Universities(Grant No.G2022KY05104)Program for Innovation Team of Shaanxi Province(Grant No.2021TD-23).
文摘In this paper,we report the frequency comb response experimentally and analytically in a rhombic micro-resonator with parametrical modulation.When the electrostatically actuated rhombic micro-resonator is modulated axially by a low-frequency periodic excitation,a comb-like vibration response with few equidistant positioned fingers in the frequency domain is observed.The finger spacing of frequency comb response is exactly consistent with modulation frequency and the number and amplitude of the fingers can be tuned by modulation strength.A mixed frequency comb with extra comb fingers is further generated when the resonator is modulated simultaneously by two different low-frequency excitation signals.By adjusting the relation of the two modulation frequencies,unequal spacing frequency combs are achieved for the first time,which leads to a more flexible tunability of the comb spacing for different applications.Theoretical analysis based on the dynamic model well explains the corresponding observations.
文摘This paper discusses a simple way to suppress the parametrically excited lateral vibration of a mass-loaded string. Supposing that the mass at the lower end of the string is subjected to a vertical harmonic excitation and neglecting the higher order vibration modes, the equation of motion for the mass-loaded string can be represented by a Mathieus equation with cubic nonlinearity. According to the theory of the Mathieus equation, in the mass-loaded string system, when the vertical vibration frequency of the mass approaches twice the natural frequency of the string lateral vibration, once the vertical vibration amplitude of the mass exceeds a critical value, the parametric resonance will occur in the string. To avoid the parametric resonance, a vibration absorber, composed of a thin beam and two mass blocks attached at both sides of the beam symmetrically, is proposed to install with the mass to reduce its vertical vibration, and ultimately suppress the lateral vibration of the string. Such a suppression strategy is finally validated by experiments.
基金Project supported by the National Natural Science Foundation of China(Grant No.61104040)the Natural Science Foundation of Hebei Province,China(Grant No.E2012203090)the University Innovation Team of Hebei Province Leading Talent Cultivation Project,China(Grant No.LJRC013)
文摘In the present work, we investigate the nonlinear parametrically excited vibration and active control of a gear pair system involving backlash, time-varying meshing stiffness and static transmission error. Firstly, a gear pair model is established in a strongly nonlinear form, and its nonlinear vibration characteristics are systematically investigated through different approaches. Several complicated phenomena such as period doubling bifurcation, anti period doubling bifurcation and chaos can be observed under the internal parametric excitation. Then, an active compensation controller is designed to suppress the vibration, including the chaos. Finally, the effectiveness of the proposed controller is verified numerically.
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.
文摘This paper presents a nonlinear dynamic model for simulation and analysis of a kind of parametrically excited vibration of stay cable caused by support motion in cable-stayed bridges. The sag, inclination angle of the stay cable are considered in the model, based on which, the oscillation mechanism and dynamic response characteristics of this kind of vibration are analyzed through numerical calculation. It is noted that parametrically excited oscillation of a stay cable with certain sag, inclination angle and initial static tension force may occur in cable-stayed bridges due to deck vibration under the condition that the natural frequency of a cable approaches to about half of the first model frequency of the bridge deck system. A new vibration control system installed on the cable anchorage is proposed as a possible damping system to suppress the cable parametric oscillation. The numerical calculation results showed that with the use of this damping system, the cable oscillation due to the vibration of the deck and/or towers will be considerably reduced.
基金Project supported by the National Natural Science Foundation of China (Nos. 10872142 and10632040)the New Century Excellent Talents Plan of the Ministry of Education of China(No. NCET-05-0247)the Key Project of Tianjin (No. 09JCZDJC26800)
文摘If the constraint boundary relates to a bifurcation parameter, a bifurcation is said to be parametrically constrained. Relying upon some substitution, a parametrically constrained bifurcation is transformed to an unconstrained bifurcation about new variables. A general form of transition sets of the parametrically constrained bifurcation is derived. The result indicates that only the constrained bifurcation set is influenced by parametric constraints, while other transition sets are the same as those of the corresponding nonparametrically constrained bifurcation. Taking parametrically constrained pitchfork bifurcation problems as examples, effects of parametric constraints on bifurcation classification are discussed.
基金Project supported by the Scientific Research Foundation for Returned Overseas Chinese Scholar of Ministry of Eduction, China (No.2006-331)
文摘The dynamical behaviour of a parametrically excited Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay is concerned. By means of the method of averaging together with truncation of Taylor expansions, two slow-flow equations on the amplitude and phase of response were derived for the case of principal parametric resonance, it is shown that the stability condition for the trivial solution is only associated with the linear terms in the original systems besides the amplitude and frequency of parametric excitation. And the trivial solution can be stabilized by appreciate choice of gains and time delay in feedback control. Different from the case of the trivial solution, the stability condition for nontrivial solutions is also associated with nonlinear terms besides linear terms in the original system. It is demonstrated that nontrivial steady state responses may lose their stability by saddle-node （SN） or Hopf bifurcation （HB） as parameters vary. The simulations, obtained by numerically integrating the original system, are in good agreement with the analytical results.
文摘The nonlinear response of a two_degree_of_freedom nonlinear oscillating system to parametric excitation is examined for the case of 1∶2 internal resonance and, principal parametric resonance with respect to the lower mode. The method of multiple scales is used to derive four first_order autonomous ordinary differential equations for the modulation of the amplitudes and phases. The steady_state solutions of the modulated equations and their stability are investigated. The trivial solutions lose their stability through pitchfork bifurcation giving rise to coupled mode solutions. The Melnikov method is used to study the global bifurcation behavior, the critical parameter is determined at which the dynamical system possesses a Smale horseshoe type of chaos.
文摘For a co_dimension two bifurcation system on a three_dimensional central manifold, which is parametrically excited by a real noise, a rather general model is obtained by assuming that the real noise is an output of a linear filter system_a zeromean stationary Gaussian diffusion process which satisfies detailed balance condition. By means of the asymptotic analysis approach given by L. Arnold and the expression of the eigenvalue spectrum of Fokker_Planck operator, the asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are obtained.
基金the National Natural Science Foundation of China
文摘For a real noise parametrically excited co_dimension two bifurcation system on a three_dimensional central manifold, a model of enhanced generality is developed in the present paper by assuming the real noise to be an output of a linear filter system, namely,a zero_mean stationary Gaussian diffusion process that satisfies the detailed balance condition. On such basis, asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are established by use of Arnold asymptotic analysis approach in parallel with the eigenvalue spectrum of Fokker_Planck operator.
基金Acknowledgements This work was supported by the National Science Foundation of China （Grant No. 11572082）, the Excellent Talents Support Program in Institutions of Higher Learning in Liaoning Province, China （Grant No. LJQ2015038）, the Fundamental Research Funds for the Central Universities of China （Grant Nos. N150304004 and N140301001）, and the Key Laboratory for Precision and Non-traditional Machining of the Ministry of Education, Dalian University of Technology （Grant No. JMTZ201602）.
文摘In response to the identification problem concerning multi-degree of freedom （MDOF） nonlinear systems, this study presents the extended forward orthogonal regression （EFOR） based on predicted residual sums of squares （PRESS） to construct a nonlinear dynamic parametrical model. The proposed parametrical model is based on the non-linear autoregressive with exogenous inputs （NARX） model and aims to explicitly reveal the physical design parameters of the system. The PRESSbased EFOR algorithm is proposed to identify such a model for MDOF systems. By using the algorithm, we built a common-structured model based on the fundamental concept of evaluating its generalization capability through cross-validation. The resulting model aims to prevent over-fitting with poor generalization performance caused by the average error reduction ratio （AERR）-based EFOR algorithm. Then, a functional relationship is established between the coefficients of the terms and the design parameters of the unified model. Moreover, a 5- DOF nonlinear system is taken as a case to illustrate the modeling of the proposed algorithm. Finally, a dynamic parametrical model of a cantilever beam is constructed from experimental data. Results indicate that the dynamic parametrical model of nonlinear systems, which depends on the PRESS-based EFOR, can accurately predict the output response, thus providing a theoretical basis for the optimal design of modeling methods for MDOF nonlinear systems.
基金Project supported by the National Natural Science Foundation of China and the Youth Foundation of Nanjing University.
文摘Some of the up-to-date experimental results on the parametrically-excited solitons in arectangular trough of water are provided, including the periodical reflection of a soliton at an end wall of a trough, the collision dynamics of two solitons of like polarity and the existence of mirror effect at boundaries. Attempts are made to explain the observed phenomena and a conception of virtual solitons is proposed.
基金Project supported in part by the National Natural Science Foundation of China.
文摘A new mode of nonpropagating solitary waves in circular tank, which are forcedly ex-cited in tbe vertical direction, is described. The waveform is measured and the data accordwell with the hyperbolic secant function.Analyses of the vibration modes of the wave showthat the mode is not a pure mode of circular container. A wax cone was inserted in themiddle of tank in order to keep down the plateau. The hysteresis phenomenon of excitation ofsolitary wave has been observed as well.
基金This project is funded by Research Grants Council of the Hong Kong Special Administrative Region,China(HKU 17200219,HKU 17209018,E-HKU701/17,CityU T42-103/16-N,and HKU C7047-16G)Natural Science Foundation of China(N_HKU712/16)。
文摘Water plays a vital role in biological metabolism and it would be essential to trace the water content non-invasively,such as leveraging the vibrational absorption peak of the O-H bond.However,due to the lack of an efficient laser source,it was challenging to image the water content in the deep tissue with micron-level spatial resolution.To address this problem,we develop a high-power hybrid optical parametrically-oscillating emitter(HOPE)at 1930 nm,at which the vibrational absorption peak of the O-H bond locates.The maximum pulse energy is over 1.74μJ with a pulse repetition rate of 50 kHz and a pulse width of 15 ns.We employ this laser source in the optical-resolution photoacoustic microscopy(OR-PAM)system to image the water content in the phantom and the biological tissue in vitro.Our 1930-nm OR-PAM could map the water content in the complex tissue environment at high spatial resolution,deep penetration depth,improved sensitivity,and suppressed artifact signal of the lipid.
基金Supported by the Basic Research Fund of Tsinghua University
文摘Nonlinear dynamic analysis is performed on moving belts subjected to geometric nonlinearity and initial tension fluctuation. To incorporate more accurately the damping mechanism of belt material, linear viscoelastic models are adopted in a unified form of differential operators. To circumvent high-order differential vibration equation of time-varying coefficients and with gyroscopic and nonlinear terms, where analytical solution is almost impossible, a systematic approach is presented by reforming the motion equation and directly using the method of multiple scales. To exemplify the procedure, the solutions at principal resonance are obtained and their stability conditions are derived for employing a Kelvin-Voigt model to reflect the property of the belt material. The solutions and stability conditions successfully reduce to those for using Kelvin model and elastic model, which validate the present approaches. Numerical simulations highlight the effects of tension fluctuations and translating speeds on the stability of the belt vibration.
基金supported by the National Natural Science Foundation of China(No.52175067)the Zhejiang Key Research&Development Project(No.2021C01021)+1 种基金the Natural Science Foundation of Zhejiang Province(No.LY20E050016)the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation(CPSF)(No.GZC20241478)。
文摘A high-temperature and high-pressure valve is the key equipment of a wind tunnel system;it controls the generation of high-temperature and high-pressure gas.To reduce the adverse impact of high-temperature and high-pressure gas on the strength of the valve body,a cooling structure is set on the valve seat.This can significantly reduce the temperature of the valve body and valve seat.The effects of its structure on the cooling characteristics and stress of the valve seat are studied,and six main parameters that can completely describe the geometry of the cooling structure are proposed.The central composite design method is used to select sample points,and the multi-objective genetic algorithm(MOGA)method is used for optimal structural design.A modification method according to the main parameters for the valve seat is proposed.The results show that the cooling structure weakens the pressure-bearing capability of the valve seat.Among the six main parameters of the valve seat,the distance from the end face of the lower hole to the Z-axis and the distance from the axis of the lower hole to the origin of the coordinates have the most obvious effects on the average stress of the valve seat.An optimum design value is proposed.This work can provide a reference for the design of high-temperature and high-pressure valves.
文摘In recent years,the concept of digital human has attracted widespread attention from all walks of life,and the modelling of high-fidelity human bodies,heads,and hands has been intensively studied.This paper focuses on head modelling and proposes a generic head parametric model based on neural radiance fields.Specifically,we first use face recognition networks and 3D facial expression database FaceWarehouse to parameterize identity and expression semantics,respectively,and use both as conditional inputs to build a neural radiance field for the human head,thereby improving the head model’s representation ability while ensuring editing capabilities for the identity and expression of the rendered results;then,through a combination of volume rendering and neural rendering,the 3D representation of the head is rapidly rendered into the 2D plane,producing a high-fidelity image of the human head.Thanks to the well-designed loss functions and good implicit representation of the neural radiance field,our model can not only edit the identity and expression independently,but also freely modify the virtual camera position of the rendering results.It has excellent multi-view consistency,and has many applications in novel view synthesis,pose driving and more.
基金supported by the Ministry of Education of the Russian Federation(Project No.1023032300071-6-2.3.1).
文摘An experimental investigation of the dynamics of the interface between two low-viscosity fluids with high density contrast oscillating in a fixed vertical slotted channel has been conducted.It has been found that as the amplitude of the liquid column oscillations increases,parametric oscillations of the interface are excited in the form of a standing wave located in the channel plane.In particular,depending on the interfacial tension,the standing waves have a frequency equal to that of liquid piston oscillations(harmonic response),or half of the frequency of oscillations of the liquid column in the channel(subharmonic response).The detected type of instability has a gravitational-capillary nature and is analogous to Faraday waves.The analysis of the overcritical dynamics of wave oscillations indicates that interfacial tension plays a crucial role in determining the type of parametric instability.At high interfacial tension,only synchronous(harmonic)wave modes are observed,and the threshold of the wave excitation is determined by the amplitude of piston oscillations of the liquid column.In this case,the oscillation acceleration does not play a role and has a small value in the threshold of the synchronous mode response.In the case of weak surface tension,subharmonic oscillations are observed.The threshold for the development of these oscillations is determined by the dimensionless acceleration of the oscillating liquid column and remains almost constant with variations in the dimensionless frequency of oscillations.At moderate values of interfacial tension(in the region of moderate dimensionless frequencies),a synchronous wave mode emerges in the stability threshold of the oscillating interface.As the dimensionless acceleration is increased further,a subharmonic mode is excited.The growth of subharmonic oscillations occurs against the background of harmonic wave oscillations,with the oscillations of the interface representing a combination of two standing waves.
基金supported by the National Natural Science Foundation of China(Grant Nos.52178175 and 52108182)the National Natural Science Foundation of Zhejiang Province(Grant No.LZ23E080003).
文摘Tensegrity structures,embodying the principles of continuous tensioning and discrete compression,have emerged as fundamental frameworks in locomotive soft robotics for navigating uneven and unpredictable environments,owing to their flexible and resilient traits.By means of a straightforward and cost-effective method to achieve structure-driven,vibration-driven tensegrity shows great potential,particularly in tasks demanding random exploration.However,the design guidance for vibration-driven tensegrity and their performance evaluation in unstructured terrain remain unrevealed due to the complex dynamics of the structure.This paper presents a small six-bar tensegrity robot,driven by wireless vibration motors,designed for deployment in disaster rescue and search scenarios.Finite element simulation is used to investigate how structural characteristics,excitation parameters,and the arrangement of motors affect the kinematic performance of this tensegrity system.A prototype of the six-bar tensegrity robot with three motors located on the lower ends of the three lower struts is designed and manufactured after the numerical simulations.A simple control policy which adjusts the motion of the tensegrity robot by turning on or off the motors on different locations is proposed.The prototype with and without the control policy is tested in man-made environments of various complexity.It shows that the ability and efficiency of the tensegrity robot in exploring unstructured environments is significantly enhanced by the proposed control policy.It is believed that the potential of the vibration-driven tensegrity robot could be further exploited by integrating multi-source sensors and more intelligent control policies.
