This paper concerns the existence of affine-periodic solutions for perturbed affine-periodic systems.This kind of affine-periodic solutions has the form of x(t+T)≡Qx(t) with some nonsingular matrix Q,which may be qua...This paper concerns the existence of affine-periodic solutions for perturbed affine-periodic systems.This kind of affine-periodic solutions has the form of x(t+T)≡Qx(t) with some nonsingular matrix Q,which may be quasi-periodic when Q is an orthogonal matrix. It can be even unbounded but x(t)/|x(t)| is quasi-periodic,like a helical line. for example x(t)=e^(at)(cos ωt, sin ωt), when Q is not an orthogonal matrix. The averaging method of higher order for finding affine-periodic solutions is given by topological degree.展开更多
The paper studies the parametric stochastic roll motion in the random waves.The differential equation of the ship parametric roll under random wave is established with considering the nonlinear damping and ship speed....The paper studies the parametric stochastic roll motion in the random waves.The differential equation of the ship parametric roll under random wave is established with considering the nonlinear damping and ship speed.Random sea surface is treated as a narrow-band stochastic process,and the stochastic parametric excitation is studied based on the effective wave theory.The nonlinear restored arm function obtained from the numerical simulation is expressed as the approximate analytic function.By using the stochastic averaging method,the differential equation of motion is transformed into Ito’s stochastic differential equation.The steady-state probability density function of roll motion is obtained,and the results are validated with the numerical simulation and model test.展开更多
The energy preserving average vector field （AVF） method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction di...The energy preserving average vector field （AVF） method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants.展开更多
Numerical properties of the time integration method proposed by the first author of this paper in 2007 are the same as those of the constant average acceleration method （AAM） for linear elastic systems, except that ...Numerical properties of the time integration method proposed by the first author of this paper in 2007 are the same as those of the constant average acceleration method （AAM） for linear elastic systems, except that the capability to capture dynamic loading was not explored. It was found that there were different quadrature equations to predict the next step displacement increment. A modified quadrature equation of this method was derived so that the equation to determine the next step displacement was numerically equivalent to the equation used in the constant AAM. It was verified that the original form of this method, in general, had a better capability to capture dynamic loadings than the constant AAM. This excellent property, in addition to computational efficiency, will help to make this method competitive with general secondorder accurate integration methods.展开更多
A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise （fGn） with the Hurst index 1/2 〈 H 〈 1 is proposed. First, the definition and the ba...A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise （fGn） with the Hurst index 1/2 〈 H 〈 1 is proposed. First, the definition and the basic property of fGn and related fractional Brownian motion （iBm） are briefly introduced. Then, the averaged fractional stochastic differential equations （SDEs） for the first integrals and combinations of angle variables of the associated Hamiltonian systems are derived. The stationary probability density and statistics of the original systems are then obtained approximately by simulating the averaged SDEs numerically. An example is worked out to illustrate the proposed stochastic averaging method. It is shown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of original system agree well.展开更多
This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize co...This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize computer program easily. Results can be applied in both autonomous and non-autonomous systems. At last, an example is resolved to verify the method.展开更多
We consider the persistence of affine periodic solutions for perturbed affine periodic systems.Such(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T>0 is fixed and Q is a nonsingular ma...We consider the persistence of affine periodic solutions for perturbed affine periodic systems.Such(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T>0 is fixed and Q is a nonsingular matrix.These are a kind of spatiotemporal symmetric solutions,e.g.spiral waves.We give the averaging method for the existence of affine periodic solutions in two situations:one in which the initial values of the affine periodic solutions of the unperturbed system form a manifold,and another that does not rely on the structure of the initial values of the unperturbed system's affine periodic solutions.The transversal condition is determined using the Brouwer degree.We also present a higher order averaging method for general degenerate systems by means of the Brouwer degree and a Lyapunov-Schmidt reduction.展开更多
The averaging analysis was carried out to study the motion of a quasi axisymmetrical gyrostat under a small magnitude self excited control torque. The common approach to investigating the problem of rigid body rot...The averaging analysis was carried out to study the motion of a quasi axisymmetrical gyrostat under a small magnitude self excited control torque. The common approach to investigating the problem of rigid body rotation under the action of a small torque known in the body frame was described. Using this approach, the problem (Grammel's problem for the case of small torque) that is maintaining the angular velocity of a quasi axisymmetrical gyrostat using a control torque quadratic in the angular velocity was solved.展开更多
A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming probl...A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.展开更多
Piecewise linear systems are prevalent in engineering practice,and can be categorized into symmetric and asymmetric piecewise linear systems.Considering that symmetry is a special case of asymmetry,it is essential to ...Piecewise linear systems are prevalent in engineering practice,and can be categorized into symmetric and asymmetric piecewise linear systems.Considering that symmetry is a special case of asymmetry,it is essential to investigate the broader model,namely the asymmetric piecewise linear system.The traditional averaging method is frequently used for studying nonlinear systems,particularly symmetric piecewise linear systems,with the harmonic response of the oscillator serving as a key prerequisite for calculating steady-state solutions.However,asymmetric systems inherently exhibit nonharmonic,asymmetric responses,rendering the traditional averaging method inapplicable.To overcome this limitation,this paper introduces an improved averaging method tailored for an oscillator characterized by asymmetric gaps and springs.Unlike the traditional method,which assumes a purely harmonic response,the improved averaging method redefines the system response as a superposition of a direct current(DC)term and a first harmonic component.Herein,the DC term can be regarded as the offset induced by model asymmetry.Furthermore,the DC term is treated as a slow variable function of time,with its time derivative assumed to be zero when calculating the steady-state solution,akin to the amplitude and phase in the traditional averaging method.Numerical validation demonstrates that the responses computed in both time and frequency domains with the improved averaging method exhibit greater accuracy compared with those derived from the traditional method.Leveraging these improved results,the study also examines the parameter effect,stability,and bifurcation phenomena within the amplitude-frequency responses.展开更多
Fluid-conveying pipes generally face combined excitations caused by periodic loads and random noises.Gaussian white noise is a common random noise excitation.This study investigates the random vibration response of a ...Fluid-conveying pipes generally face combined excitations caused by periodic loads and random noises.Gaussian white noise is a common random noise excitation.This study investigates the random vibration response of a simply-supported pipe conveying fluid under combined harmonic and Gaussian white noise excitations.According to the generalized Hamilton’s principle,the dynamic model of the pipe conveying fluid under combined harmonic and Gaussian white noise excitations is established.Subsequently,the averaged stochastic differential equations and Fokker–Planck–Kolmogorov(FPK)equations of the pipe conveying fluid subjected to combined excitations are acquired by the modified stochastic averaging method.The effectiveness of the analysis results is verified through the Monte Carlo method.The effects of fluid speed,noise intensity,amplitude of harmonic excitation,and damping factor on the probability density functions of amplitude,displacement,as well as velocity are discussed in detail.The results show that with an increase in fluid speed or noise intensity,the possible greatest amplitude for the fluid-conveying pipe increases,and the possible greatest displacement and velocity also increase.With an increase in the amplitude of harmonic excitation or damping factor,the possible greatest amplitude for the pipe decreases,and the possible greatest displacement and velocity also decrease.展开更多
Anthropogenic aluminum cycle in China was analyzed by the aluminum flow diagram based on the life cycle of aluminum products. The whole anthropogenic aluminum cycle consists of four stages： alumina and aluminum produ...Anthropogenic aluminum cycle in China was analyzed by the aluminum flow diagram based on the life cycle of aluminum products. The whole anthropogenic aluminum cycle consists of four stages： alumina and aluminum production, fabrication and manufacture, use and reclamation. Based on the investigation on the 2003-2007 aluminum cycles in China, a number of changes can be found. For instance, resources self-support ratio （RSR） in alumina production dropped from 95.42%to 55.50%, while RSR in the aluminum production increased from 52.45%to 79.25%. However, RSR in the Chinese aluminum industry leveled off at 50%in the period of 2003-2007. The respective use ratios of domestic and imported aluminum scrap in the aluminum industry of 2007 were 5.38% and 9.40%. In contrast, both the net imported Al-containing resources and the lost quantity of Al-containing materials in aluminum cycle increased during the same period, as well as the net increased quantity of Al-containing materials in social stock and recycled Al-scrap. Proposals for promoting aluminum cycle were put forward. The import/export policy and reducing the loss of Al-containing materials for the aluminum industry in China in the future were discussed.展开更多
Parametric vibration of an axially moving, elastic, tensioned beam with pulsating speed was investigated in the vicinity of subharmonic and combination resonance. The method of averaging was used to yield a set of aut...Parametric vibration of an axially moving, elastic, tensioned beam with pulsating speed was investigated in the vicinity of subharmonic and combination resonance. The method of averaging was used to yield a set of autonomous equations when the parametric excitation frequency is twice or the combination of the natural frequencies. Instability boundaries were presented in the plane of parametric frequency and amplitude. The analytical results were numerically verified. The effects of the viscoelastic damping, steady speed and tension on the instability boundaries were numerically demonsWated. It is found that the viscoelastic damping decreases the instability regions and the steady speed and the tension make the instability region drift along the frequency axis.展开更多
In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the l...In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.展开更多
This paper investigates the stochastic P-bifurcation(SPB)of a fractionally damped oscillator subjected to additive and multiplicative Gaussian white noise.Variable transformation and the stochastic averaging technique...This paper investigates the stochastic P-bifurcation(SPB)of a fractionally damped oscillator subjected to additive and multiplicative Gaussian white noise.Variable transformation and the stochastic averaging technique are applied to derive the expression of probability density function(PDF)of the system response.Critical conditions of the stochastic bifurcation induced by system parameters are presented based on the change in the number of extreme points of the probability density function.Numerical results are given to show the effectiveness of the proposed approach.Stochastic P-bifurcations for additive and multiplicative noise are studied in detail according to the critical conditions.展开更多
Identification of modal parameters of a linear structure with output-only measurements has received much attention over the past decades. In the paper, the Natural Excitation Technique (NExT) is used for acquisition o...Identification of modal parameters of a linear structure with output-only measurements has received much attention over the past decades. In the paper, the Natural Excitation Technique (NExT) is used for acquisition of the impulse signals from the structural responses. Then Eigensystem Realization Algorithm (ERA) is utilized for modal identification. For disregarding the fictitious ‘computational modes', a procedure, Statistically Averaging Modal Frequency Method (SAMFM), is developed to distinguish the true modes from noise modes, and to improve the precision of the identified modal frequencies of the structure. An offshore platform is modeled with the finite element method. The theoretical modal parameters are obtained for a comparison with the identified values. The dynamic responses of the platform under random wave loading are computed for providing the output signals used for identification with ERA. Results of simulation demonstrate that the proposed method can determine the system modal frequency with high precision.展开更多
The energy approach is used to theoretically verify that the average acceleration method （AAM）, which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical ...The energy approach is used to theoretically verify that the average acceleration method （AAM）, which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical nonlinear damping, including the special case of velocity power type damping with a bilinear restoring force model. Based on the energy approach, the stability of the AAM is proven for SDOF structures using the mathematical features of the velocity power function and for MDOF structures by applying the virtual displacement theorem. Finally, numerical examples are given to demonstrate the accuracy of the theoretical analysis.展开更多
Response and bifurcation of fractional Duffing oscillator under recycling noise and time-delayed feedback control are investigated. Firstly, based on the principle of the minimum mean square error and small time-delay...Response and bifurcation of fractional Duffing oscillator under recycling noise and time-delayed feedback control are investigated. Firstly, based on the principle of the minimum mean square error and small time-delayed approximation and linearize the cubic stiffness term, the fractional derivative is equivalent to a linear combination of damping and restoring forces, and the original system is simplified into an equivalent integer order system. Secondly, the Ito differential equations and one-dimensional Markov process are obtained according to stochastic averaging method, and the stochastic stability and stochastic bifurcation of the system are analyzed. Lastly, through joint probability density function diagram and the stationary probability density function diagram, the stochastic bifurcation behavior of system under the different time-delay, fractional order and noise intensity are discussed respectively, the validity of the theory and the occurrence of bifurcation phenomenon are verified.展开更多
Decomposing co-seismic deformation is an immediate need for researchers who are interested in earthquake inversion analysis and geo-hazard mapping. However, conventional InSAR or digital elevation models （DEMs） imag...Decomposing co-seismic deformation is an immediate need for researchers who are interested in earthquake inversion analysis and geo-hazard mapping. However, conventional InSAR or digital elevation models （DEMs） imagery analyses only provide the displacement in the Line-of-Sight （LOS） direction or elevation changes. The 2004 Mid-Niigata earthquake in Japan provides lessons on how to decompose co-seismic deformation from two sets of DEMs. If three adjacent points undergo a rigid-body-translation movement, their co-seismic deformation can be decomposed by solving simultaneous equations. Although this method has been successfully used to discuss tectonic deformations, the algorithm needed improvement and a more rigorous algorithm, including a new definition of nominal plane, DEMs comparability improvement and matrix condition check is provided. Even with these procedures, the obtained decomposed displacement often showed remarkable scatter prompting the use of the moving average method, which was used to determine both tectonic and localized displacement characteristics. A cut-off window and a pair of band-pass windows were selected according to the regional geology and construction activities to ease the tectonic and localized displacement calculations, respectively. The displacement field of the tectonic scale shows two major clusters of large lateral components, and coincidently major visible landslides were found mostly within them. The localized displacement helps to reveal hidden landslides in the target area. As far as the Kizawa hamlet is concerned, the obtained vectors show down-slope movements, which are consistent with the observed traces of dislocations that were found in the Kizawa tunnel and irrigation wells. The method proposed has great potential to be applied to understanding post-earthquake rehabilitation in other areas.展开更多
Hemispherical Resonator Gyroscope(HRG)is a classical high precision Coriolis Vibration Gyroscope(CVG),which performs attitude estimation of carrier by detecting the precession of standing wave of resonator,thus,the dr...Hemispherical Resonator Gyroscope(HRG)is a classical high precision Coriolis Vibration Gyroscope(CVG),which performs attitude estimation of carrier by detecting the precession of standing wave of resonator,thus,the drift of standing wave of resonator has a great influence on the output accuracy of gyroscope,where the quality factor non-uniformity of resonator is one of main error sources.Ring electrode is a classical excitation structure of HRG because the standing wave can precess freely under its excitation,which makes the gyroscope have more accurate scale factor,larger measurement range and better dynamic characteristics.In this paper,the equations of motion of an ideal resonator excited by a ring electrode are derived by the elastic thin shell theory and Lagrange mechanical principle,then the corresponding equivalent mechanical model is established.According to the“average method”,it can be seen that the ideal resonator excited by the ring electrode works in integral mode,and any position in the circumferential direction of resonator can be a working point,which means that the quality factor non-uniformity has a great effect on the drift of standing wave.Therefore,the equations of motion of resonator with quality factor non-uniformity under the ring electrode excitation are deduced by the equivalent mechanical model,and the drift model of standing wave is established by the“average method”,it can be found that both the amplitude of quality factor non-uniformity and angle between the“inherent damping axis”and antinode axis of standing wave can affect the drift rate of standing wave.Moreover,the drift model indicates that if the input angular rate does not reach the threshold,the precession angular rate of standing wave will appear“self-locking”phenomenon,that is,the gyroscope will lose the integral effect.展开更多
基金supported by National Basic Research Program of China (Grant No. 2013CB834100)National Natural Science Foundation of China (Grant Nos. 11571065,11171132 and 11201173)
文摘This paper concerns the existence of affine-periodic solutions for perturbed affine-periodic systems.This kind of affine-periodic solutions has the form of x(t+T)≡Qx(t) with some nonsingular matrix Q,which may be quasi-periodic when Q is an orthogonal matrix. It can be even unbounded but x(t)/|x(t)| is quasi-periodic,like a helical line. for example x(t)=e^(at)(cos ωt, sin ωt), when Q is not an orthogonal matrix. The averaging method of higher order for finding affine-periodic solutions is given by topological degree.
基金the State Administration of Science,Technology and Industry for National Defense of China(Grant No.B2420132001).
文摘The paper studies the parametric stochastic roll motion in the random waves.The differential equation of the ship parametric roll under random wave is established with considering the nonlinear damping and ship speed.Random sea surface is treated as a narrow-band stochastic process,and the stochastic parametric excitation is studied based on the effective wave theory.The nonlinear restored arm function obtained from the numerical simulation is expressed as the approximate analytic function.By using the stochastic averaging method,the differential equation of motion is transformed into Ito’s stochastic differential equation.The steady-state probability density function of roll motion is obtained,and the results are validated with the numerical simulation and model test.
基金supported by the National Natural Science Foundation of China(Grant No.91130013)the Open Foundation of State Key Laboratory of HighPerformance Computing of China
文摘The energy preserving average vector field （AVF） method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants.
基金Science Council (NSC),Chinese Taipei Under Grant No.NSC-96-2221-E-027-030
文摘Numerical properties of the time integration method proposed by the first author of this paper in 2007 are the same as those of the constant average acceleration method （AAM） for linear elastic systems, except that the capability to capture dynamic loading was not explored. It was found that there were different quadrature equations to predict the next step displacement increment. A modified quadrature equation of this method was derived so that the equation to determine the next step displacement was numerically equivalent to the equation used in the constant AAM. It was verified that the original form of this method, in general, had a better capability to capture dynamic loadings than the constant AAM. This excellent property, in addition to computational efficiency, will help to make this method competitive with general secondorder accurate integration methods.
基金supported by the National Natural Science Foundation of China under grants nos.:11272279,11321202 and 11432012
文摘A stochastic averaging method of quasi integrable and resonant Hamiltonian systems under excitation of fractional Gaussian noise （fGn） with the Hurst index 1/2 〈 H 〈 1 is proposed. First, the definition and the basic property of fGn and related fractional Brownian motion （iBm） are briefly introduced. Then, the averaged fractional stochastic differential equations （SDEs） for the first integrals and combinations of angle variables of the associated Hamiltonian systems are derived. The stationary probability density and statistics of the original systems are then obtained approximately by simulating the averaged SDEs numerically. An example is worked out to illustrate the proposed stochastic averaging method. It is shown that the results obtained by using the proposed stochastic averaging method and those from digital simulation of original system agree well.
文摘This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize computer program easily. Results can be applied in both autonomous and non-autonomous systems. At last, an example is resolved to verify the method.
基金supported by the National Natural Science Foundation of China(1237119112071175)+4 种基金supported by the NSFC(1207117511901080)supported by the NSFC(12071175)the Fundamental Research Funds For the Central Universities(2412023YQ003)the Natural Science Foundation of Jilin Province(20200201253JC)。
文摘We consider the persistence of affine periodic solutions for perturbed affine periodic systems.Such(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T>0 is fixed and Q is a nonsingular matrix.These are a kind of spatiotemporal symmetric solutions,e.g.spiral waves.We give the averaging method for the existence of affine periodic solutions in two situations:one in which the initial values of the affine periodic solutions of the unperturbed system form a manifold,and another that does not rely on the structure of the initial values of the unperturbed system's affine periodic solutions.The transversal condition is determined using the Brouwer degree.We also present a higher order averaging method for general degenerate systems by means of the Brouwer degree and a Lyapunov-Schmidt reduction.
文摘The averaging analysis was carried out to study the motion of a quasi axisymmetrical gyrostat under a small magnitude self excited control torque. The common approach to investigating the problem of rigid body rotation under the action of a small torque known in the body frame was described. Using this approach, the problem (Grammel's problem for the case of small torque) that is maintaining the angular velocity of a quasi axisymmetrical gyrostat using a control torque quadratic in the angular velocity was solved.
文摘A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.
基金Project supported by the National Natural Science Foundation of China(Nos.12272242 and U1934201)。
文摘Piecewise linear systems are prevalent in engineering practice,and can be categorized into symmetric and asymmetric piecewise linear systems.Considering that symmetry is a special case of asymmetry,it is essential to investigate the broader model,namely the asymmetric piecewise linear system.The traditional averaging method is frequently used for studying nonlinear systems,particularly symmetric piecewise linear systems,with the harmonic response of the oscillator serving as a key prerequisite for calculating steady-state solutions.However,asymmetric systems inherently exhibit nonharmonic,asymmetric responses,rendering the traditional averaging method inapplicable.To overcome this limitation,this paper introduces an improved averaging method tailored for an oscillator characterized by asymmetric gaps and springs.Unlike the traditional method,which assumes a purely harmonic response,the improved averaging method redefines the system response as a superposition of a direct current(DC)term and a first harmonic component.Herein,the DC term can be regarded as the offset induced by model asymmetry.Furthermore,the DC term is treated as a slow variable function of time,with its time derivative assumed to be zero when calculating the steady-state solution,akin to the amplitude and phase in the traditional averaging method.Numerical validation demonstrates that the responses computed in both time and frequency domains with the improved averaging method exhibit greater accuracy compared with those derived from the traditional method.Leveraging these improved results,the study also examines the parameter effect,stability,and bifurcation phenomena within the amplitude-frequency responses.
基金supported by the National Natural Science Foundation of China(Nos.12272211 and 12072181).
文摘Fluid-conveying pipes generally face combined excitations caused by periodic loads and random noises.Gaussian white noise is a common random noise excitation.This study investigates the random vibration response of a simply-supported pipe conveying fluid under combined harmonic and Gaussian white noise excitations.According to the generalized Hamilton’s principle,the dynamic model of the pipe conveying fluid under combined harmonic and Gaussian white noise excitations is established.Subsequently,the averaged stochastic differential equations and Fokker–Planck–Kolmogorov(FPK)equations of the pipe conveying fluid subjected to combined excitations are acquired by the modified stochastic averaging method.The effectiveness of the analysis results is verified through the Monte Carlo method.The effects of fluid speed,noise intensity,amplitude of harmonic excitation,and damping factor on the probability density functions of amplitude,displacement,as well as velocity are discussed in detail.The results show that with an increase in fluid speed or noise intensity,the possible greatest amplitude for the fluid-conveying pipe increases,and the possible greatest displacement and velocity also increase.With an increase in the amplitude of harmonic excitation or damping factor,the possible greatest amplitude for the pipe decreases,and the possible greatest displacement and velocity also decrease.
基金Projects (71003018,71373003) supported by the National Natural Science Foundation of ChinaProjects (N110402003,N120302004) supported by the Fundamental Research Funds for the Central Universities,ChinaProject (13YJCZH172) supported by the Ministry of Education of China of Humanities and Social Sciences
文摘Anthropogenic aluminum cycle in China was analyzed by the aluminum flow diagram based on the life cycle of aluminum products. The whole anthropogenic aluminum cycle consists of four stages： alumina and aluminum production, fabrication and manufacture, use and reclamation. Based on the investigation on the 2003-2007 aluminum cycles in China, a number of changes can be found. For instance, resources self-support ratio （RSR） in alumina production dropped from 95.42%to 55.50%, while RSR in the aluminum production increased from 52.45%to 79.25%. However, RSR in the Chinese aluminum industry leveled off at 50%in the period of 2003-2007. The respective use ratios of domestic and imported aluminum scrap in the aluminum industry of 2007 were 5.38% and 9.40%. In contrast, both the net imported Al-containing resources and the lost quantity of Al-containing materials in aluminum cycle increased during the same period, as well as the net increased quantity of Al-containing materials in social stock and recycled Al-scrap. Proposals for promoting aluminum cycle were put forward. The import/export policy and reducing the loss of Al-containing materials for the aluminum industry in China in the future were discussed.
文摘Parametric vibration of an axially moving, elastic, tensioned beam with pulsating speed was investigated in the vicinity of subharmonic and combination resonance. The method of averaging was used to yield a set of autonomous equations when the parametric excitation frequency is twice or the combination of the natural frequencies. Instability boundaries were presented in the plane of parametric frequency and amplitude. The analytical results were numerically verified. The effects of the viscoelastic damping, steady speed and tension on the instability boundaries were numerically demonsWated. It is found that the viscoelastic damping decreases the instability regions and the steady speed and the tension make the instability region drift along the frequency axis.
文摘In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.
基金This work was supported by the National Natural Science Foundation of China(Grants 12002089,11902081 and 11872305).
文摘This paper investigates the stochastic P-bifurcation(SPB)of a fractionally damped oscillator subjected to additive and multiplicative Gaussian white noise.Variable transformation and the stochastic averaging technique are applied to derive the expression of probability density function(PDF)of the system response.Critical conditions of the stochastic bifurcation induced by system parameters are presented based on the change in the number of extreme points of the probability density function.Numerical results are given to show the effectiveness of the proposed approach.Stochastic P-bifurcations for additive and multiplicative noise are studied in detail according to the critical conditions.
文摘Identification of modal parameters of a linear structure with output-only measurements has received much attention over the past decades. In the paper, the Natural Excitation Technique (NExT) is used for acquisition of the impulse signals from the structural responses. Then Eigensystem Realization Algorithm (ERA) is utilized for modal identification. For disregarding the fictitious ‘computational modes', a procedure, Statistically Averaging Modal Frequency Method (SAMFM), is developed to distinguish the true modes from noise modes, and to improve the precision of the identified modal frequencies of the structure. An offshore platform is modeled with the finite element method. The theoretical modal parameters are obtained for a comparison with the identified values. The dynamic responses of the platform under random wave loading are computed for providing the output signals used for identification with ERA. Results of simulation demonstrate that the proposed method can determine the system modal frequency with high precision.
基金National Natural Science Foundation of ChinaUnder Grant No. 50578047, 50338020 China Ministry ofEducation (Program for New Century Excellent Talents inUniversity) China Ministry of Science and Technology UnderGrant No.2003AA602150
文摘The energy approach is used to theoretically verify that the average acceleration method （AAM）, which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical nonlinear damping, including the special case of velocity power type damping with a bilinear restoring force model. Based on the energy approach, the stability of the AAM is proven for SDOF structures using the mathematical features of the velocity power function and for MDOF structures by applying the virtual displacement theorem. Finally, numerical examples are given to demonstrate the accuracy of the theoretical analysis.
基金Supported by the National Natural Science Foundation of China(61863022)the Key Project of Gansu Province Natural Science Foundation(23JRRA882)。
文摘Response and bifurcation of fractional Duffing oscillator under recycling noise and time-delayed feedback control are investigated. Firstly, based on the principle of the minimum mean square error and small time-delayed approximation and linearize the cubic stiffness term, the fractional derivative is equivalent to a linear combination of damping and restoring forces, and the original system is simplified into an equivalent integer order system. Secondly, the Ito differential equations and one-dimensional Markov process are obtained according to stochastic averaging method, and the stochastic stability and stochastic bifurcation of the system are analyzed. Lastly, through joint probability density function diagram and the stationary probability density function diagram, the stochastic bifurcation behavior of system under the different time-delay, fractional order and noise intensity are discussed respectively, the validity of the theory and the occurrence of bifurcation phenomenon are verified.
文摘Decomposing co-seismic deformation is an immediate need for researchers who are interested in earthquake inversion analysis and geo-hazard mapping. However, conventional InSAR or digital elevation models （DEMs） imagery analyses only provide the displacement in the Line-of-Sight （LOS） direction or elevation changes. The 2004 Mid-Niigata earthquake in Japan provides lessons on how to decompose co-seismic deformation from two sets of DEMs. If three adjacent points undergo a rigid-body-translation movement, their co-seismic deformation can be decomposed by solving simultaneous equations. Although this method has been successfully used to discuss tectonic deformations, the algorithm needed improvement and a more rigorous algorithm, including a new definition of nominal plane, DEMs comparability improvement and matrix condition check is provided. Even with these procedures, the obtained decomposed displacement often showed remarkable scatter prompting the use of the moving average method, which was used to determine both tectonic and localized displacement characteristics. A cut-off window and a pair of band-pass windows were selected according to the regional geology and construction activities to ease the tectonic and localized displacement calculations, respectively. The displacement field of the tectonic scale shows two major clusters of large lateral components, and coincidently major visible landslides were found mostly within them. The localized displacement helps to reveal hidden landslides in the target area. As far as the Kizawa hamlet is concerned, the obtained vectors show down-slope movements, which are consistent with the observed traces of dislocations that were found in the Kizawa tunnel and irrigation wells. The method proposed has great potential to be applied to understanding post-earthquake rehabilitation in other areas.
文摘Hemispherical Resonator Gyroscope(HRG)is a classical high precision Coriolis Vibration Gyroscope(CVG),which performs attitude estimation of carrier by detecting the precession of standing wave of resonator,thus,the drift of standing wave of resonator has a great influence on the output accuracy of gyroscope,where the quality factor non-uniformity of resonator is one of main error sources.Ring electrode is a classical excitation structure of HRG because the standing wave can precess freely under its excitation,which makes the gyroscope have more accurate scale factor,larger measurement range and better dynamic characteristics.In this paper,the equations of motion of an ideal resonator excited by a ring electrode are derived by the elastic thin shell theory and Lagrange mechanical principle,then the corresponding equivalent mechanical model is established.According to the“average method”,it can be seen that the ideal resonator excited by the ring electrode works in integral mode,and any position in the circumferential direction of resonator can be a working point,which means that the quality factor non-uniformity has a great effect on the drift of standing wave.Therefore,the equations of motion of resonator with quality factor non-uniformity under the ring electrode excitation are deduced by the equivalent mechanical model,and the drift model of standing wave is established by the“average method”,it can be found that both the amplitude of quality factor non-uniformity and angle between the“inherent damping axis”and antinode axis of standing wave can affect the drift rate of standing wave.Moreover,the drift model indicates that if the input angular rate does not reach the threshold,the precession angular rate of standing wave will appear“self-locking”phenomenon,that is,the gyroscope will lose the integral effect.
