We consider a pair of nonidentical mechanical pendulums. The bob of each pendulum in addition to its own mass electrically is charged. The pendulums are hung from a common pivot in a vertical plane forming a slanted a...We consider a pair of nonidentical mechanical pendulums. The bob of each pendulum in addition to its own mass electrically is charged. The pendulums are hung from a common pivot in a vertical plane forming a slanted asymmet-ric ??shaped figure. For arbitrary initial swings that are not necessarily confined to small angles, we analyze the dy-namics of each bob under the influence of gravity’s pull as well as the mutual repulsive Coulombian internal force. The equations describing the motion of the system are a set of highly, supper nonlinear coupled differential equations. Applying Mathematica we solve the equations numerically. For nonidentical parameters describing the pendulums, namely, we show the system behaves chaotically;i.e. the angular position of each pendulum leaves a non-repeatable, chaotic pattern in time. For this coupled two-particle interactive system we show also by folding the time axis, the angular position of one of the pendulums vs. the other traces a Lissajous type curve. Our report includes various traditional phase diagrams and a set of newly designed, useful, phase-type diagrams as well. For a comprehensive understanding about the dynamics of the problem at hand, we provide Mathematica codes conducive to animating the chaotic motion of the system. The generic format of the codes allows adjusting the relevant pa-rameters at will and addressing the “what-if” scenarios.展开更多
Nonlinear stability criteria for the motions geoverned by three-dimensional quasigeostrophic model in spherical geometry are obtained by using Arnol＇d＇s variational principle and a priori estimate method. The result...Nonlinear stability criteria for the motions geoverned by three-dimensional quasigeostrophic model in spherical geometry are obtained by using Arnol＇d＇s variational principle and a priori estimate method. The results gained in this paper are parallel to Arnol＇d＇s second theorem and better than the known results. Especially, under the approximation of vertically integrated nondivergency, criteria corresponding to Arnol＇d＇s second theorem are first established by a detailed analysis.展开更多
Some more proper criteria for the nonlinear stability of three-dimensional quasi-geostrophic motions are given by combining variational principle with a prior estimates method. The criteria are suitable for perturbati...Some more proper criteria for the nonlinear stability of three-dimensional quasi-geostrophic motions are given by combining variational principle with a prior estimates method. The criteria are suitable for perturbations of initial condition as well as parameters in the model. The basic flow can be steady or unsteady. Particularly the difficulty due to the nonlinear boundary condition is completely overcome by the use of our method.展开更多
Motion cueing algorithms(MCA)are often applied in the motion simulators.In this paper,a nonlinear optimal MCA,taking into account translational and rotational motions of a simulator within its physical limitation,is d...Motion cueing algorithms(MCA)are often applied in the motion simulators.In this paper,a nonlinear optimal MCA,taking into account translational and rotational motions of a simulator within its physical limitation,is designed for the motion platform aiming to minimize human’s perception error in order to provide a high degree of fidelity.Indeed,the movement sensation center of most MCA is placed at the center of the upper platform,which may cause a certain error.Pilot’s station should be paid full attention to in the MCA.Apart from this,the scaling and limiting module plays an important role in optimizing the motion platform workspace and reducing false cues during motion reproduction.It should be used along within the washout filter to decrease the amplitude of the translational and rotational motion signals uniformly across all frequencies through the MCA.A nonlinear scaling method is designed to accurately duplicate motions with high realistic behavior and use the platform more efficiently without violating its physical limitations.The simulation experiment is verified in the longitudinal/pitch direction for motion simulator.The result implies that the proposed method can not only overcome the problem of the workspace limitations in the simulator motion reproduction and improve the realism of movement sensation,but also reduce the false cues to improve dynamic fidelity during the motion simulation process.展开更多
The periodic motion and stability for a class of two-degree-of-freedom nonlinear oscillating systems are studied by using the method of Liapunov function. The sufficient conditions which guarantee the existence, uniqu...The periodic motion and stability for a class of two-degree-of-freedom nonlinear oscillating systems are studied by using the method of Liapunov function. The sufficient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions are obtained.展开更多
This paper investigates the behavior and the failure mechanism of a double deck bridge constructed in China through nonlinear time history analysis. A parametric study was conducted to evaluate the influence of differ...This paper investigates the behavior and the failure mechanism of a double deck bridge constructed in China through nonlinear time history analysis. A parametric study was conducted to evaluate the influence of different structural characteristics on the behavior of the double deck bridge under transverse seismic motions, and to detect the effect of bi- directional loading on the seismic response of this type of bridge. The results showed that some characteristics, such as the variable lateral stiffness, the foundation modelling, and the longitudinal reinforcement ratio of the upper and lower columns of the bridge pier bents have a major impact on the double deck bridge response and its failure mechanism under transverse seismic motions. It was found that the soft story failure mechanism ：is not unique to the double deck bridge and its occurrence is related to some conditions and structural characteristics of the bridge structure. The analysis also showed that the seismic vulnerability of the double deck bridge under bi-directional loading： was severely increased compared to the bridge response under unidirectional transverse loading, and out-of-phase movements were triggered between adjacent girders.展开更多
This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochas...This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.展开更多
Nonlinear amphibious vehicle rolling under regular waves and wind load is analyzed by a single degree of freedom system.Considering nonlinear damping and restoring moments,a nonlinear rolling dynamical equation of amp...Nonlinear amphibious vehicle rolling under regular waves and wind load is analyzed by a single degree of freedom system.Considering nonlinear damping and restoring moments,a nonlinear rolling dynamical equation of amphibious vehicle is established.The Hamiltonian function of the nonlinear rolling dynamical equation of amphibious vehicle indicate when subjected to joint action of periodic wave excitation and crosswind,the nonlinear rolling system degenerates into being asymmetric.The threshold value of excited moment of wave and wind is analyzed by the Melnikov method.Finally,the nonlinear rolling motion response and phase portrait were simulated by four order Runge-Kutta method at different excited moment parameters.展开更多
Due to the importance of vibration effects on the functional accuracy of mechanical systems,this research aims to develop a precise model of a nonlinearly vibrating single-link mobile flexible manipulator.The manipula...Due to the importance of vibration effects on the functional accuracy of mechanical systems,this research aims to develop a precise model of a nonlinearly vibrating single-link mobile flexible manipulator.The manipulator consists of an elastic arm,a rotary motor,and a rigid carrier,and undergoes general in-plane rigid body motion along with elastic transverse deformation.To accurately model the elastic behavior,Timoshenko’s beam theory is used to describe the flexible arm,which accounts for rotary inertia and shear deformation effects.By applying Newton’s second law,the nonlinear governing equations of motion for the manipulator are derived as a coupled system of ordinary differential equations(ODEs)and partial differential equations(PDEs).Then,the assumed mode method(AMM)is used to solve this nonlinear system of governing equations with appropriate shape functions.The assumed modes can be obtained after solving the characteristic equation of a Timoshenko beam with clamped boundary conditions at one end and an attached mass/inertia at the other.In addition,the effect of the transverse vibration of the inextensible arm on its axial behavior is investigated.Despite the axial rigidity,the effect makes the rigid body dynamics invalid for the axial behavior of the arm.Finally,numerical simulations are conducted to evaluate the performance of the developed model,and the results are compared with those obtained by the finite element approach.The comparison confirms the validity of the proposed dynamic model for the system.According to the mentioned features,this model can be reliable for investigating the system’s vibrational behavior and implementing vibration control algorithms.展开更多
Nonlinear behaviors of a free-floating body in waves were experimentally investigated in the present study. The experiments were carried out for 6 different wave heights and 6 different wave periods to cover a relativ...Nonlinear behaviors of a free-floating body in waves were experimentally investigated in the present study. The experiments were carried out for 6 different wave heights and 6 different wave periods to cover a relatively wide range of wave nonlinearities. A charge-coupled device （CCD） camera was used to capture the real-time motion of the floating body. The measurement data show that the sway, heave and roll motions of the floating body are all harmonic oscillations while the equilibrium position of the sway motion drifts in the wave direction. The drift speed is proportional to wave steepness when the size of the floating body is comparable to the wavelength, while it is proportional to the square of wave steepness when the floating body is relatively small. In addition, the drift motion leads to a slightly longer oscillation period of the floating body than the wave period of nonlinear wave and the discrepancy increases with the increment of wave steepness.展开更多
High-resolution seismic models of sediment basins are critical inputs for earthquake ground motion prediction and petroleum resource exploration.In this study we employed a newly developed technique that utilizes the ...High-resolution seismic models of sediment basins are critical inputs for earthquake ground motion prediction and petroleum resource exploration.In this study we employed a newly developed technique that utilizes the frequency-dependent nonlinear P-wave particle motion to estimate sedimentary structure beneath the Bohai Bay basin.A recent study suggests that the delay of the P wave on the horizontal component relative the vertical component and its variations over frequency are caused by interference of the direct P wave with waves generated at the sediment base.The frequency-dependent delay time can be used to constrain sediment thickness and seismic velocity beneath recording stations.We measured the particle motions of teleseismic P waves recorded by 249 broadband stations of the North China Array,which covers the western Bohai Bay basin and its surrounding areas.We found that the P waves of 90 stations inside the Bohai Bay basin and other local basins within the Taihang and Yanshan mountain ranges exhibit significant frequency-dependent nonlinear particle motions,and used the particle motion data to invert the sediment thickness(Z0)and surface S-wave velocity(β0).The estimated sediment thickness inside the Bohai Bay Basin varies from 1.02 km to 3.72 km,with an average of 3.20 km,which roughly agrees with previous active source studies.展开更多
文摘We consider a pair of nonidentical mechanical pendulums. The bob of each pendulum in addition to its own mass electrically is charged. The pendulums are hung from a common pivot in a vertical plane forming a slanted asymmet-ric ??shaped figure. For arbitrary initial swings that are not necessarily confined to small angles, we analyze the dy-namics of each bob under the influence of gravity’s pull as well as the mutual repulsive Coulombian internal force. The equations describing the motion of the system are a set of highly, supper nonlinear coupled differential equations. Applying Mathematica we solve the equations numerically. For nonidentical parameters describing the pendulums, namely, we show the system behaves chaotically;i.e. the angular position of each pendulum leaves a non-repeatable, chaotic pattern in time. For this coupled two-particle interactive system we show also by folding the time axis, the angular position of one of the pendulums vs. the other traces a Lissajous type curve. Our report includes various traditional phase diagrams and a set of newly designed, useful, phase-type diagrams as well. For a comprehensive understanding about the dynamics of the problem at hand, we provide Mathematica codes conducive to animating the chaotic motion of the system. The generic format of the codes allows adjusting the relevant pa-rameters at will and addressing the “what-if” scenarios.
文摘Nonlinear stability criteria for the motions geoverned by three-dimensional quasigeostrophic model in spherical geometry are obtained by using Arnol＇d＇s variational principle and a priori estimate method. The results gained in this paper are parallel to Arnol＇d＇s second theorem and better than the known results. Especially, under the approximation of vertically integrated nondivergency, criteria corresponding to Arnol＇d＇s second theorem are first established by a detailed analysis.
文摘Some more proper criteria for the nonlinear stability of three-dimensional quasi-geostrophic motions are given by combining variational principle with a prior estimates method. The criteria are suitable for perturbations of initial condition as well as parameters in the model. The basic flow can be steady or unsteady. Particularly the difficulty due to the nonlinear boundary condition is completely overcome by the use of our method.
基金Supported by Natural Science Foundation of Hubei Province(2019CFB693)Scientific Research Guiding Project of Education Department of Hubei Province(B2020418)。
文摘Motion cueing algorithms(MCA)are often applied in the motion simulators.In this paper,a nonlinear optimal MCA,taking into account translational and rotational motions of a simulator within its physical limitation,is designed for the motion platform aiming to minimize human’s perception error in order to provide a high degree of fidelity.Indeed,the movement sensation center of most MCA is placed at the center of the upper platform,which may cause a certain error.Pilot’s station should be paid full attention to in the MCA.Apart from this,the scaling and limiting module plays an important role in optimizing the motion platform workspace and reducing false cues during motion reproduction.It should be used along within the washout filter to decrease the amplitude of the translational and rotational motion signals uniformly across all frequencies through the MCA.A nonlinear scaling method is designed to accurately duplicate motions with high realistic behavior and use the platform more efficiently without violating its physical limitations.The simulation experiment is verified in the longitudinal/pitch direction for motion simulator.The result implies that the proposed method can not only overcome the problem of the workspace limitations in the simulator motion reproduction and improve the realism of movement sensation,but also reduce the false cues to improve dynamic fidelity during the motion simulation process.
文摘The periodic motion and stability for a class of two-degree-of-freedom nonlinear oscillating systems are studied by using the method of Liapunov function. The sufficient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions are obtained.
文摘This paper investigates the behavior and the failure mechanism of a double deck bridge constructed in China through nonlinear time history analysis. A parametric study was conducted to evaluate the influence of different structural characteristics on the behavior of the double deck bridge under transverse seismic motions, and to detect the effect of bi- directional loading on the seismic response of this type of bridge. The results showed that some characteristics, such as the variable lateral stiffness, the foundation modelling, and the longitudinal reinforcement ratio of the upper and lower columns of the bridge pier bents have a major impact on the double deck bridge response and its failure mechanism under transverse seismic motions. It was found that the soft story failure mechanism ：is not unique to the double deck bridge and its occurrence is related to some conditions and structural characteristics of the bridge structure. The analysis also showed that the seismic vulnerability of the double deck bridge under bi-directional loading： was severely increased compared to the bridge response under unidirectional transverse loading, and out-of-phase movements were triggered between adjacent girders.
基金National Natural Science Foundation of China for Innovative Research Groups Under Grant No.50321803 & 50621062National Natural Science Foundation of China Under Grant No.50808113 & 10872148
文摘This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.
基金The Pre-research Project of the General Armament DepartmentThe Science Fund of North University of China(No.20130105)
文摘Nonlinear amphibious vehicle rolling under regular waves and wind load is analyzed by a single degree of freedom system.Considering nonlinear damping and restoring moments,a nonlinear rolling dynamical equation of amphibious vehicle is established.The Hamiltonian function of the nonlinear rolling dynamical equation of amphibious vehicle indicate when subjected to joint action of periodic wave excitation and crosswind,the nonlinear rolling system degenerates into being asymmetric.The threshold value of excited moment of wave and wind is analyzed by the Melnikov method.Finally,the nonlinear rolling motion response and phase portrait were simulated by four order Runge-Kutta method at different excited moment parameters.
文摘Due to the importance of vibration effects on the functional accuracy of mechanical systems,this research aims to develop a precise model of a nonlinearly vibrating single-link mobile flexible manipulator.The manipulator consists of an elastic arm,a rotary motor,and a rigid carrier,and undergoes general in-plane rigid body motion along with elastic transverse deformation.To accurately model the elastic behavior,Timoshenko’s beam theory is used to describe the flexible arm,which accounts for rotary inertia and shear deformation effects.By applying Newton’s second law,the nonlinear governing equations of motion for the manipulator are derived as a coupled system of ordinary differential equations(ODEs)and partial differential equations(PDEs).Then,the assumed mode method(AMM)is used to solve this nonlinear system of governing equations with appropriate shape functions.The assumed modes can be obtained after solving the characteristic equation of a Timoshenko beam with clamped boundary conditions at one end and an attached mass/inertia at the other.In addition,the effect of the transverse vibration of the inextensible arm on its axial behavior is investigated.Despite the axial rigidity,the effect makes the rigid body dynamics invalid for the axial behavior of the arm.Finally,numerical simulations are conducted to evaluate the performance of the developed model,and the results are compared with those obtained by the finite element approach.The comparison confirms the validity of the proposed dynamic model for the system.According to the mentioned features,this model can be reliable for investigating the system’s vibrational behavior and implementing vibration control algorithms.
基金financially supported by the National Natural Science Foundation of China(Grant No.11272079)the National Basic Research Program of China(973 Program,Grant No.2011CB013702)
文摘Nonlinear behaviors of a free-floating body in waves were experimentally investigated in the present study. The experiments were carried out for 6 different wave heights and 6 different wave periods to cover a relatively wide range of wave nonlinearities. A charge-coupled device （CCD） camera was used to capture the real-time motion of the floating body. The measurement data show that the sway, heave and roll motions of the floating body are all harmonic oscillations while the equilibrium position of the sway motion drifts in the wave direction. The drift speed is proportional to wave steepness when the size of the floating body is comparable to the wavelength, while it is proportional to the square of wave steepness when the floating body is relatively small. In addition, the drift motion leads to a slightly longer oscillation period of the floating body than the wave period of nonlinear wave and the discrepancy increases with the increment of wave steepness.
文摘High-resolution seismic models of sediment basins are critical inputs for earthquake ground motion prediction and petroleum resource exploration.In this study we employed a newly developed technique that utilizes the frequency-dependent nonlinear P-wave particle motion to estimate sedimentary structure beneath the Bohai Bay basin.A recent study suggests that the delay of the P wave on the horizontal component relative the vertical component and its variations over frequency are caused by interference of the direct P wave with waves generated at the sediment base.The frequency-dependent delay time can be used to constrain sediment thickness and seismic velocity beneath recording stations.We measured the particle motions of teleseismic P waves recorded by 249 broadband stations of the North China Array,which covers the western Bohai Bay basin and its surrounding areas.We found that the P waves of 90 stations inside the Bohai Bay basin and other local basins within the Taihang and Yanshan mountain ranges exhibit significant frequency-dependent nonlinear particle motions,and used the particle motion data to invert the sediment thickness(Z0)and surface S-wave velocity(β0).The estimated sediment thickness inside the Bohai Bay Basin varies from 1.02 km to 3.72 km,with an average of 3.20 km,which roughly agrees with previous active source studies.
