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
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
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
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
In a previous article,an R script was developed and divided into three parts to implement the multivariate normality(MVN)Q-test based on both the chisquare approximation and the bootstrap approach,using either the Sha...In a previous article,an R script was developed and divided into three parts to implement the multivariate normality(MVN)Q-test based on both the chisquare approximation and the bootstrap approach,using either the Shapiro-Wilk W statistic(QSWa and QSWb)or the Shapiro-Francia W’statistic(QSFa and QSFb).Royston’s H-test was included as a supplementary MVN test.The aim of this study is to compare the hit rate and statistical power of the four Qtest variants and the H-test using 200 samples drawn from multivariate stand-ard normal distributions and 200 samples from multivariate t-distributions with five degrees of freedom.The simulations vary in sample size(50,75,100,125,150,200,250,and 500),number of variables(from 2 to 6),and homoge-neous inter-variable correlation(0,0.3,0.5,0.7,and 0.9).The H-test outper-formed QSWb and QSFb,but not QSWa in the multivariate normal samples or QSFa in the multivariate t-distribution samples.QSFb performed better than QSWb.It is concluded that the bootstrap approach is conservative under the null hypothesis of multivariate normality.However,when the assumption of independence is violated,the bootstrap approach is theoretically more ap-propriate than QSWa and QSFa.A 10%significance level is recommended for QSFb in terms of hit rate,but in terms of statistical power,only when rejecting the null hypothesis.展开更多
The aim of this paper is to explore the effect of geometrical parameters on ultimate load-carrying capacity of a circular hollow section(CHS)X-joint under axial compression of the brace end.First of all,finite element...The aim of this paper is to explore the effect of geometrical parameters on ultimate load-carrying capacity of a circular hollow section(CHS)X-joint under axial compression of the brace end.First of all,finite element(FE)model to calculate ultimate load-carrying capacity of the CHS X-joint subjected to uniaxial load of the brace is constructed,and the calculated load–displacement curves are compared to the experimental ones.After validation of the FE model,46080 groups of FE calculation models with different geometrical parameters are generated by means of parametric modeling.Subsequently,eight variables including gusset thickness and chord thickness are set as input to predict load-carrying capacity of the CHS X-joint by four machine learning(ML)algorithms,i.e.,Generalized Regression Neural Network,Support Vector Machine,random forest(RF),and Extreme Gradient Boosting(XGBoost).Finally,the constructed ML prediction models are interpreted by SHapley Additive exPlanations,to explore the impact weight of each factor on ultimate load-carrying capacity of the joint.The results show that all the four models can predict the load-carrying capacity of the subject accurately,with all the R2 values greater than 0.97.In addition,RF model yields the minimum mean-square error,Root Mean Squared Error,Mean Absolute Error,and Mean Absolute Percentage Error values,and the greatest R2 value,while the prediction accuracy of XGBoost is relatively worse.Among all the eight considered geometrical parameters,brace diameter has the strongest impact on load-carrying capacity of the joint,followed by chord thickness,chord ring width,chord ring thickness,brace ring width,and brace thickness,while the thicknesses of the gusset plate and brace have marginal influence on load-carrying capacity.The study of the current paper can provide guidelines for dimension design of CHS X-joints.展开更多
Accurately modeling heavy-tailed data is critical across applied sciences,particularly in finance,medicine,and actuarial analysis.This work presents the heavy-tailed power XLindley distribution(HTPXLD),a unique heavy-...Accurately modeling heavy-tailed data is critical across applied sciences,particularly in finance,medicine,and actuarial analysis.This work presents the heavy-tailed power XLindley distribution(HTPXLD),a unique heavy-tailed distribution.Adding one more parameter to the power XLindley distribution improves this new distribution,especially when modeling leptokurtic lifetime data.The suggested density provides greater flexibility with asymmetric forms and different degrees of peakedness.Its statistical features,like the quantile function,moments,extropy measures,incomplete moments,stochastic ordering,and stress-strength parameters,are explored.We further investigate its use in actuarial science through the computation of pertinent metrics,such as value-at-risk,tail value-at-risk,tail variance,and tail variance premium.To obtain the point and interval parameter estimates,we use the maximum likelihood estimation approach.We do many simulation tests to evaluate the performance of our proposed estimator.Metrics like bias,relative bias,mean squared error,root mean squared error,average interval length,and coverage probability will be used in these tests to assess the estimator’s performance.To illustrate the practical value of our proposed model,we apply it to analyze three real-world datasets.We then compare its performance to established competing models,highlighting its advantages.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.
文摘In a previous article,an R script was developed and divided into three parts to implement the multivariate normality(MVN)Q-test based on both the chisquare approximation and the bootstrap approach,using either the Shapiro-Wilk W statistic(QSWa and QSWb)or the Shapiro-Francia W’statistic(QSFa and QSFb).Royston’s H-test was included as a supplementary MVN test.The aim of this study is to compare the hit rate and statistical power of the four Qtest variants and the H-test using 200 samples drawn from multivariate stand-ard normal distributions and 200 samples from multivariate t-distributions with five degrees of freedom.The simulations vary in sample size(50,75,100,125,150,200,250,and 500),number of variables(from 2 to 6),and homoge-neous inter-variable correlation(0,0.3,0.5,0.7,and 0.9).The H-test outper-formed QSWb and QSFb,but not QSWa in the multivariate normal samples or QSFa in the multivariate t-distribution samples.QSFb performed better than QSWb.It is concluded that the bootstrap approach is conservative under the null hypothesis of multivariate normality.However,when the assumption of independence is violated,the bootstrap approach is theoretically more ap-propriate than QSWa and QSFa.A 10%significance level is recommended for QSFb in terms of hit rate,but in terms of statistical power,only when rejecting the null hypothesis.
文摘The aim of this paper is to explore the effect of geometrical parameters on ultimate load-carrying capacity of a circular hollow section(CHS)X-joint under axial compression of the brace end.First of all,finite element(FE)model to calculate ultimate load-carrying capacity of the CHS X-joint subjected to uniaxial load of the brace is constructed,and the calculated load–displacement curves are compared to the experimental ones.After validation of the FE model,46080 groups of FE calculation models with different geometrical parameters are generated by means of parametric modeling.Subsequently,eight variables including gusset thickness and chord thickness are set as input to predict load-carrying capacity of the CHS X-joint by four machine learning(ML)algorithms,i.e.,Generalized Regression Neural Network,Support Vector Machine,random forest(RF),and Extreme Gradient Boosting(XGBoost).Finally,the constructed ML prediction models are interpreted by SHapley Additive exPlanations,to explore the impact weight of each factor on ultimate load-carrying capacity of the joint.The results show that all the four models can predict the load-carrying capacity of the subject accurately,with all the R2 values greater than 0.97.In addition,RF model yields the minimum mean-square error,Root Mean Squared Error,Mean Absolute Error,and Mean Absolute Percentage Error values,and the greatest R2 value,while the prediction accuracy of XGBoost is relatively worse.Among all the eight considered geometrical parameters,brace diameter has the strongest impact on load-carrying capacity of the joint,followed by chord thickness,chord ring width,chord ring thickness,brace ring width,and brace thickness,while the thicknesses of the gusset plate and brace have marginal influence on load-carrying capacity.The study of the current paper can provide guidelines for dimension design of CHS X-joints.
基金supported by researchers Supporting Project Number(RSPD2025R548)King Saud University,Riyadh,Saudi Arabia.
文摘Accurately modeling heavy-tailed data is critical across applied sciences,particularly in finance,medicine,and actuarial analysis.This work presents the heavy-tailed power XLindley distribution(HTPXLD),a unique heavy-tailed distribution.Adding one more parameter to the power XLindley distribution improves this new distribution,especially when modeling leptokurtic lifetime data.The suggested density provides greater flexibility with asymmetric forms and different degrees of peakedness.Its statistical features,like the quantile function,moments,extropy measures,incomplete moments,stochastic ordering,and stress-strength parameters,are explored.We further investigate its use in actuarial science through the computation of pertinent metrics,such as value-at-risk,tail value-at-risk,tail variance,and tail variance premium.To obtain the point and interval parameter estimates,we use the maximum likelihood estimation approach.We do many simulation tests to evaluate the performance of our proposed estimator.Metrics like bias,relative bias,mean squared error,root mean squared error,average interval length,and coverage probability will be used in these tests to assess the estimator’s performance.To illustrate the practical value of our proposed model,we apply it to analyze three real-world datasets.We then compare its performance to established competing models,highlighting its advantages.
