The coexisting periodic impacting motions and their multiplicity of a kind of dual component systems under harmonic excitation are analytically derived. The stability condition of a periodic impacting motion is given ...The coexisting periodic impacting motions and their multiplicity of a kind of dual component systems under harmonic excitation are analytically derived. The stability condition of a periodic impacting motion is given by analyzing the propagation of small, arbitrary perturbation from that motion. In numerical simulations, the periodic impacting motions are classified according to the system states before and after an impact. The numerical results show that there exist many types of vibro-impacts and the bifurcation of periodic vibro-impacts is not smooth.展开更多
This paper addresses the problem of Hopf-flip bifurcation of high dimensional maps. Using the center manifold theorem, we obtain a three dimensional reduced map through the projection technique. The reduced map is fur...This paper addresses the problem of Hopf-flip bifurcation of high dimensional maps. Using the center manifold theorem, we obtain a three dimensional reduced map through the projection technique. The reduced map is further transformed into its normal form whose coefficients are determined by that of the original system. The dynamics of the map near the Hopf-flip bifurcation point is approximated by a so called “time-2τ^2 map” of a planar autonomous differential equation. It is shown that high dimensional maps may result in cycles of period two, tori T^1 （Hopf invariant circles）, tori 2T^1 and tori 2T^2 depending both on how the critical eigenvalues pass the unit circle and on the signs of resonant terms＇ coefficients. A two-degree-of-freedom vibro-impact system is given as an example to show how the procedure of this paper works. It reveals that through Hopf-flip bifurcations, periodic motions may lead directly to different types of motion, such as subharmonic motions, quasi-periodic motions, motions on high dimensional tori and even to chaotic motions depending both on change in direction of the parameter vector and on the nonlinear terms of the first three orders.展开更多
A two-degree-of-freedom vibro-impact system having symmetrical rigid stops and subjected to periodic excitation is investigated in this paper. By introducing local maps between different stages of motion in the whole ...A two-degree-of-freedom vibro-impact system having symmetrical rigid stops and subjected to periodic excitation is investigated in this paper. By introducing local maps between different stages of motion in the whole impact process, the Poincare map of the system is constructed. Using the Poincare map and the Gram Schmidt orthonormalization, a method of calculating the spectrum of Lyapunov exponents of the above vibro-impact system is presented. Then the phase portraits of periodic and chaotic attractors for the system and the corresponding convergence diagrams of the spectrum of Lyapunov exponents are given out through the numerical simulations. To further identify the validity of the aforementioned computation method, the bifurcation diagram of the system with respect to the bifurcation parameter and the corresponding largest Lyapunov exponents are shown.展开更多
The existing researches on the damping wheel mainly focus on investigating the influence of damping structure change on the vibro-acoustic control.The changes include the geometric size of the damping structure,the da...The existing researches on the damping wheel mainly focus on investigating the influence of damping structure change on the vibro-acoustic control.The changes include the geometric size of the damping structure,the damping material parameters,and the placement,and so on.In order to further understand the mechanism in reducing the acoustic radiation of railway wheel with layer damping treatment,in this paper,the wheel is simply modified by a full-sized circular plate.The circle plate side has stuck circumference constrained damping ridges and radial constrained damping ridges on it.Based on a hybrid finite element method-boundary element method（FEM-BEM）,the paper develops a vibro-acoustic radiation model for such a distributed constrained damping structure.The vibration and acoustic radiation of the circular plate is analyzed.In the analysis,the dynamic response of the system is obtained by using the 3D finite model superposition method.The obtained vibration response is used as the initial boundary condition in solving Helmholtz boundary integral equation for the sound radiation analysis.In the procedure,firstly,the modal analysis of the circular plate is performed to get the distribution of the system modal strain energy.Secondly,the vibro-acoustic radiation characteristics of the plate with different kinds of circumference damping ridges and radial damping ridges are compared in order to try to find the best effective damping ridge structure.Thirdly,using the distribution of the plate modal strain energy investigates the effect of the ridge distribution locations on the circular plate on its vibro-acoustic radiation.The calculation and analysis research results show that,the sticking circumference and radial damping ridges on the plate can control the vibro-acoustic radiation of the plate effectively in different frequency range.The distribution of the constrained damping ridge has an effect on reduction in vibro-acoustic radiation of the circular plate.The present research is very useful in the design of railway wheel with low noise level.展开更多
A mass-spring-damper linear oscillator with a limiting stop barrier is presented. Modeling non-smooth processes in mechanical engineering is a complex problem. It is especially for the systems with more than a single ...A mass-spring-damper linear oscillator with a limiting stop barrier is presented. Modeling non-smooth processes in mechanical engineering is a complex problem. It is especially for the systems with more than a single degree of freedom. But recent studies in dynamical systems have been applied to single degree of freedom systems. The vibrating system, consisting of an oscillator with amplitude of motion limited by a barrier, is known as a vibro-impact system. The amount of force and kinetic energy transferred to a barrier has an important application in designing of engineering systems that undergo the vibro-impact phenomenon. The results show the effect of changing restitution coefficient of a barrier on the amount of force and energy absorbed.展开更多
In this paper, multi-valued responses and dynamic properties of a nonlinear vibro-impact system with a unilateral nonzero offset barrier are studied. Based on the Krylov-Bogoliubov averaging method and Zhuravlev non-s...In this paper, multi-valued responses and dynamic properties of a nonlinear vibro-impact system with a unilateral nonzero offset barrier are studied. Based on the Krylov-Bogoliubov averaging method and Zhuravlev non-smooth trans- formation, the frequency response, stability conditions, and the equation of backbone curve are derived. Results show that in some conditions impact system may have two or four steady-state solutions, which are interesting and not mentioned for a vibro-impact system with the existence of frequency island phenomena. Then, the classification of the steady-state solutions is discussed, and it is shown that the nontrivial steady-state solutions may lose stability by saddle node bifurcation and Hopf bifurcation. Furthermore, a criterion for avoiding the jump phenomenon is derived and verified. Lastly, it is found that the distance between the system＇s static equilibrium position and the barrier can lead to jump phenomenon under hardening type of nonlinearity stiffness.展开更多
A response analysis procedure is developed for a vibro-impact system excited by colored noise. The non-smooth transformation is used to convert the vibro-impact system into a new system without impact term. With the h...A response analysis procedure is developed for a vibro-impact system excited by colored noise. The non-smooth transformation is used to convert the vibro-impact system into a new system without impact term. With the help of the modified quasi-conservative averaging, the total energy of the new system can be approximated as a Markov process, and the stationary probability density function （PDF） of the total energy is derived. The response PDFs of the original system are obtained using the analytical solution of the stationary PDF of the total energy. The validity of the theoretical results is tested through comparison with the corresponding simulation results. Moreover, stochastic bifurcations are also explored.展开更多
The resonant response of a single-degree-of-freedom nonlinear vibro-impact oscillator with a one-sided barrier to a narrow-band random parametric excitation is investigated. The narrow-band random excitation used here...The resonant response of a single-degree-of-freedom nonlinear vibro-impact oscillator with a one-sided barrier to a narrow-band random parametric excitation is investigated. The narrow-band random excitation used here is a bounded random noise. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, thereby permitting the applications of random averaging over ＂fast＂ variables. The averaged equations are solved exactly and an algebraic equation of the amplitude of the response is obtained for the ease without random disorder. The methods of linearization and moment are used to obtain the formula of the mean-square amplitude approximately for the case with random disorder. The effects of damping, detuning, restitution factor, nonlinear intensity, frequency and magnitude of random excitations are analysed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak response amplitudes will reduce at large damping or large nonlinear intensity and will increase with large amplitude or frequency of the random excitations. The phenomenon of stochastic jump is observed, that is, the steady-state response of the system will jump from a trivial solution to a large non-trivial one when the amplitude of the random excitation exceeds some threshold value, or will jump from a large non-trivial solution to a trivial one when the intensity of the random disorder of the random excitation exceeds some threshold value.展开更多
In this paper, we give a controlled two-degree-of-freedom （TDOF） vibro-impact system based on the damping control law, and then investigate the dynamical behaviour of this system. According to numerical simulation, ...In this paper, we give a controlled two-degree-of-freedom （TDOF） vibro-impact system based on the damping control law, and then investigate the dynamical behaviour of this system. According to numerical simulation, we find that this control scheme can suppress chaos to periodic orbit successfully. Furthermore, the feasibility and the robustness of the controller are confirmed, separately. We also find that this scheme cannot only suppress chaos, but also generate chaos in this system.展开更多
The present paper reviews the vibro-acoustic modelling of extruded aluminium train floor structures including the state-of-the-art of its industrial applications, as well as the most recent developments on mid-frequen...The present paper reviews the vibro-acoustic modelling of extruded aluminium train floor structures including the state-of-the-art of its industrial applications, as well as the most recent developments on mid-frequency mod- elling techniques in general. With the common purpose to predict mid-frequency vibro-acoustic responses of stiffened panel structures to an acceptable accuracy at a reasonable computational cost, relevant techniques are mainly based on one of the following three types of mid-frequency vibro- acoustic modelling principles： （1） enhanced deterministic methods, （2） enhanced statistical methods, and （3） hybrid deterministic/statistical methods. It is shown that, although recent developments have led to a significant step forward in industrial applicability, mature and adequate prediction tech- niques, however, are still very much required for solving sound transmission through, and radiation from, extruded aluminium panels used on high-speed trains. Due to their great potentials for predicting mid-frequency vibro-acoustics of stiffened panel structures, two of recently developed mid-frequency modelling approaches, i.e. the so-called hybrid finite element-statistical energy analysis （FE-SEA） and hybrid wave-based method- statistical energy analysis （WBM-SEA）, are then recapitulated.展开更多
A method is presented to seek for coexisting periodic orbits which may be stable or unstable in piecewise-linear vibro-impacting systems. The conditions for coexistence of single impact periodic orbits are derived, an...A method is presented to seek for coexisting periodic orbits which may be stable or unstable in piecewise-linear vibro-impacting systems. The conditions for coexistence of single impact periodic orbits are derived, and in particular, it is investigated in details how to assure that no other impacts will happen in an evolution period of a single impact periodic motion. Furthermore, some criteria for nonexistence of single impact periodic orbits with specific periods are also established. Finally, the stability of coexisting periodic orbits is discussed, and the corresponding computation formula is given. Examples of numerical simulation are in good agreement with the theoretic analysis.展开更多
Based on Mindlin stress solution, a numerical computational method was proposed to calculate the stresses in the ground induced by side friction and the resistance of Y-shaped vibro-pile. The improved Terzaghi's a...Based on Mindlin stress solution, a numerical computational method was proposed to calculate the stresses in the ground induced by side friction and the resistance of Y-shaped vibro-pile. The improved Terzaghi's and ЪерезанцевВГ's methods for ultimate bearing capacity evaluation were proposed by considering the stress strength induced by friction resistance at pile head level of Y-pile. A new method to calculate the ultimate bearing capacity of Y-pile was also proposed based on the assumptions of soil failure mode at the tip of Y-pile and the use of Mohr-Coulomb soil yield criterion and Vesic compressive correction coefficient with the induced stresses in the ground. Based on the comparisons with the field static load test results, it is found that the improved Terzaghi's method gives higher ultimate capacity, while the other two methods shows good agreement with the field results.展开更多
基金Project supported in part by National Natural Science Foundation of China under the grant 59572024in part by Trans-century Training Program Foundation for the Talents by the State Education Commission of China
文摘The coexisting periodic impacting motions and their multiplicity of a kind of dual component systems under harmonic excitation are analytically derived. The stability condition of a periodic impacting motion is given by analyzing the propagation of small, arbitrary perturbation from that motion. In numerical simulations, the periodic impacting motions are classified according to the system states before and after an impact. The numerical results show that there exist many types of vibro-impacts and the bifurcation of periodic vibro-impacts is not smooth.
基金The project supported by the Nutional Natural Science Foundation of China(10472096)
文摘This paper addresses the problem of Hopf-flip bifurcation of high dimensional maps. Using the center manifold theorem, we obtain a three dimensional reduced map through the projection technique. The reduced map is further transformed into its normal form whose coefficients are determined by that of the original system. The dynamics of the map near the Hopf-flip bifurcation point is approximated by a so called “time-2τ^2 map” of a planar autonomous differential equation. It is shown that high dimensional maps may result in cycles of period two, tori T^1 （Hopf invariant circles）, tori 2T^1 and tori 2T^2 depending both on how the critical eigenvalues pass the unit circle and on the signs of resonant terms＇ coefficients. A two-degree-of-freedom vibro-impact system is given as an example to show how the procedure of this paper works. It reveals that through Hopf-flip bifurcations, periodic motions may lead directly to different types of motion, such as subharmonic motions, quasi-periodic motions, motions on high dimensional tori and even to chaotic motions depending both on change in direction of the parameter vector and on the nonlinear terms of the first three orders.
基金supported by the National Natural Science Foundation of China (Grant No. 10972059)the Natural Science Foundation of the Guangxi Zhuang Autonmous Region of China (Grant Nos. 0640002 and 2010GXNSFA013110)+1 种基金the Guangxi Youth Science Foundation of China (Grant No. 0832014)the Project of Excellent Innovating Team of Guangxi University
文摘A two-degree-of-freedom vibro-impact system having symmetrical rigid stops and subjected to periodic excitation is investigated in this paper. By introducing local maps between different stages of motion in the whole impact process, the Poincare map of the system is constructed. Using the Poincare map and the Gram Schmidt orthonormalization, a method of calculating the spectrum of Lyapunov exponents of the above vibro-impact system is presented. Then the phase portraits of periodic and chaotic attractors for the system and the corresponding convergence diagrams of the spectrum of Lyapunov exponents are given out through the numerical simulations. To further identify the validity of the aforementioned computation method, the bifurcation diagram of the system with respect to the bifurcation parameter and the corresponding largest Lyapunov exponents are shown.
基金supported by National Natural Science Foundation of China (Grant No. 50821063)Technological Research and Development Programs of Railway Ministry of China (Grant No. 2008J001-A,Grant No. 2009J001)Natural Science Foundation of State Key Laboratory of Traction Power,China (Grant No. 2008TPL-Z07)
文摘The existing researches on the damping wheel mainly focus on investigating the influence of damping structure change on the vibro-acoustic control.The changes include the geometric size of the damping structure,the damping material parameters,and the placement,and so on.In order to further understand the mechanism in reducing the acoustic radiation of railway wheel with layer damping treatment,in this paper,the wheel is simply modified by a full-sized circular plate.The circle plate side has stuck circumference constrained damping ridges and radial constrained damping ridges on it.Based on a hybrid finite element method-boundary element method（FEM-BEM）,the paper develops a vibro-acoustic radiation model for such a distributed constrained damping structure.The vibration and acoustic radiation of the circular plate is analyzed.In the analysis,the dynamic response of the system is obtained by using the 3D finite model superposition method.The obtained vibration response is used as the initial boundary condition in solving Helmholtz boundary integral equation for the sound radiation analysis.In the procedure,firstly,the modal analysis of the circular plate is performed to get the distribution of the system modal strain energy.Secondly,the vibro-acoustic radiation characteristics of the plate with different kinds of circumference damping ridges and radial damping ridges are compared in order to try to find the best effective damping ridge structure.Thirdly,using the distribution of the plate modal strain energy investigates the effect of the ridge distribution locations on the circular plate on its vibro-acoustic radiation.The calculation and analysis research results show that,the sticking circumference and radial damping ridges on the plate can control the vibro-acoustic radiation of the plate effectively in different frequency range.The distribution of the constrained damping ridge has an effect on reduction in vibro-acoustic radiation of the circular plate.The present research is very useful in the design of railway wheel with low noise level.
文摘A mass-spring-damper linear oscillator with a limiting stop barrier is presented. Modeling non-smooth processes in mechanical engineering is a complex problem. It is especially for the systems with more than a single degree of freedom. But recent studies in dynamical systems have been applied to single degree of freedom systems. The vibrating system, consisting of an oscillator with amplitude of motion limited by a barrier, is known as a vibro-impact system. The amount of force and kinetic energy transferred to a barrier has an important application in designing of engineering systems that undergo the vibro-impact phenomenon. The results show the effect of changing restitution coefficient of a barrier on the amount of force and energy absorbed.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11472212,11532011,11302171,and 11302172)
文摘In this paper, multi-valued responses and dynamic properties of a nonlinear vibro-impact system with a unilateral nonzero offset barrier are studied. Based on the Krylov-Bogoliubov averaging method and Zhuravlev non-smooth trans- formation, the frequency response, stability conditions, and the equation of backbone curve are derived. Results show that in some conditions impact system may have two or four steady-state solutions, which are interesting and not mentioned for a vibro-impact system with the existence of frequency island phenomena. Then, the classification of the steady-state solutions is discussed, and it is shown that the nontrivial steady-state solutions may lose stability by saddle node bifurcation and Hopf bifurcation. Furthermore, a criterion for avoiding the jump phenomenon is derived and verified. Lastly, it is found that the distance between the system＇s static equilibrium position and the barrier can lead to jump phenomenon under hardening type of nonlinearity stiffness.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11172233,10932009,and 11202160)the Natural Science Foundation of Shaanxi Province,China(Grant No.2012JQ1004)
文摘A response analysis procedure is developed for a vibro-impact system excited by colored noise. The non-smooth transformation is used to convert the vibro-impact system into a new system without impact term. With the help of the modified quasi-conservative averaging, the total energy of the new system can be approximated as a Markov process, and the stationary probability density function （PDF） of the total energy is derived. The response PDFs of the original system are obtained using the analytical solution of the stationary PDF of the total energy. The validity of the theoretical results is tested through comparison with the corresponding simulation results. Moreover, stochastic bifurcations are also explored.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10772046 and 50978058)Natural Science Foundation of Guangdong Province of China (Grant No. 102528000010000)
文摘The resonant response of a single-degree-of-freedom nonlinear vibro-impact oscillator with a one-sided barrier to a narrow-band random parametric excitation is investigated. The narrow-band random excitation used here is a bounded random noise. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, thereby permitting the applications of random averaging over ＂fast＂ variables. The averaged equations are solved exactly and an algebraic equation of the amplitude of the response is obtained for the ease without random disorder. The methods of linearization and moment are used to obtain the formula of the mean-square amplitude approximately for the case with random disorder. The effects of damping, detuning, restitution factor, nonlinear intensity, frequency and magnitude of random excitations are analysed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak response amplitudes will reduce at large damping or large nonlinear intensity and will increase with large amplitude or frequency of the random excitations. The phenomenon of stochastic jump is observed, that is, the steady-state response of the system will jump from a trivial solution to a large non-trivial one when the amplitude of the random excitation exceeds some threshold value, or will jump from a large non-trivial solution to a trivial one when the intensity of the random disorder of the random excitation exceeds some threshold value.
基金supported by the National Natural Science Foundation of China (Grant No 10472091)
文摘In this paper, we give a controlled two-degree-of-freedom （TDOF） vibro-impact system based on the damping control law, and then investigate the dynamical behaviour of this system. According to numerical simulation, we find that this control scheme can suppress chaos to periodic orbit successfully. Furthermore, the feasibility and the robustness of the controller are confirmed, separately. We also find that this scheme cannot only suppress chaos, but also generate chaos in this system.
基金sponsored by the NationalNatural foundation of China(Grant Nos.U1434201 and 51175300)
文摘The present paper reviews the vibro-acoustic modelling of extruded aluminium train floor structures including the state-of-the-art of its industrial applications, as well as the most recent developments on mid-frequency mod- elling techniques in general. With the common purpose to predict mid-frequency vibro-acoustic responses of stiffened panel structures to an acceptable accuracy at a reasonable computational cost, relevant techniques are mainly based on one of the following three types of mid-frequency vibro- acoustic modelling principles： （1） enhanced deterministic methods, （2） enhanced statistical methods, and （3） hybrid deterministic/statistical methods. It is shown that, although recent developments have led to a significant step forward in industrial applicability, mature and adequate prediction tech- niques, however, are still very much required for solving sound transmission through, and radiation from, extruded aluminium panels used on high-speed trains. Due to their great potentials for predicting mid-frequency vibro-acoustics of stiffened panel structures, two of recently developed mid-frequency modelling approaches, i.e. the so-called hybrid finite element-statistical energy analysis （FE-SEA） and hybrid wave-based method- statistical energy analysis （WBM-SEA）, are then recapitulated.
文摘A method is presented to seek for coexisting periodic orbits which may be stable or unstable in piecewise-linear vibro-impacting systems. The conditions for coexistence of single impact periodic orbits are derived, and in particular, it is investigated in details how to assure that no other impacts will happen in an evolution period of a single impact periodic motion. Furthermore, some criteria for nonexistence of single impact periodic orbits with specific periods are also established. Finally, the stability of coexisting periodic orbits is discussed, and the corresponding computation formula is given. Examples of numerical simulation are in good agreement with the theoretic analysis.
文摘Based on Mindlin stress solution, a numerical computational method was proposed to calculate the stresses in the ground induced by side friction and the resistance of Y-shaped vibro-pile. The improved Terzaghi's and ЪерезанцевВГ's methods for ultimate bearing capacity evaluation were proposed by considering the stress strength induced by friction resistance at pile head level of Y-pile. A new method to calculate the ultimate bearing capacity of Y-pile was also proposed based on the assumptions of soil failure mode at the tip of Y-pile and the use of Mohr-Coulomb soil yield criterion and Vesic compressive correction coefficient with the induced stresses in the ground. Based on the comparisons with the field static load test results, it is found that the improved Terzaghi's method gives higher ultimate capacity, while the other two methods shows good agreement with the field results.
