Abstract:The multisymplectic formulations of the membrane forced vibration equation with periodic boundary conditions in Hamilton space were considered. Using the RungeKutta multisymplectic method, a semiimplicit ninemultiply threepoint scheme with a symplectic conservation law was constructed to discrete the partial differential equation (PDE), which was derived from the membrane forced vibration equation. The results of the numerical experiments show that the multisymplectic scheme can not only improve the numerical accuracy effectively but also maintain the local properties of the vibration system. From the simulation results, we can conclude that the multisymplectic method has excellent longtime numerical behavior.
Abstract:Joints of multibody systems can keep their constraints under the condition of very small clearances. However, the frictions in a joint are involved in the constraint forces, as the result of the correlations between the state of the systems and form of contact in the joint. Based on the equivalence of points contact and distributed contact, we presented the formulations of frictions in typical joints with small clearances on the assumption that the deformations of joints are negligible. An example was given to validate the presented formulations.
Abstract:The problem of P and PI feedback control to a time delay system was investigated,with the emphasis on the determination of the feedback gains that ensured the asymptotical stability of the delayed system. By means of Lambert W function,the feedback gain of P control can be expressed explicitly,so that the optimal feedback gain can be easily obtained. For the system under a PI control,the stable region of the feedback gains was determined on the basis of stability switches and Dsubdivision,and the optimal feedback gains that enabled the system to admit maximal stable margin were figured out numerically by using Lambert W function. From the viewpoint of computation,the present method is much simpler than the available methods.
Abstract:A new complex chaotic system was presented .Some of its basic dynamical properties,such as symmetry,dissipation,Lypanov exponents and chaotic attractors,were studied. The synchronization was achieved through design controller based on the passive control.The validity of this synchronous method was theoretically proved by Lyapunov method and the passive control theoty.Finally,a simulation was conducted with Matlab to prove the synchronization of the complex chaotic system. Simulation results show that the synchronization can be achieved quickly and well.
Abstract:This paper investigated the adaptive impulsive synchronization for a class of non-autonomous chaotic systems with unknown Lipschitz constant. Firstly, based on the Lyapunov stability theory, adaptive control theory and impulsive control theory, the adaptive controller, the impulsive controller and the parametric update law were designed respectively. Then, by the generalized Barbalat's lemma, the global asymptotic synchronization between the drive system and the response system was proved, and some corresponding sufficient conditions were also obtained. Two numerical examples were given to show the effectiveness of the proposed method.
Abstract:The problem of synchronization for chaotic system with mismatch uncertainties was discussed.Based on active control method,an active sliding mode control strategy was proposed,which enables uncertain chaotic systems to reach sliding mode plane within finite time.The stable sliding surface was designed by using linear matrix inequality (LMI) technique to reduce the influence of mismatched uncertainties. The sufficient condition for the existence of stable sliding surface was derived in terms of LMI.The simulation of the synchronization of the systems was presented to show the effectiveness of the proposed method.
Abstract:A new method for resolving nonproportionally damping matrix into proportional damping matrix and remainder dampng matrix and a new method for solving nonproportionally damped systems were proposed respectively.After introducing the perturbation method in to the nonproportional damping matrix and response vector, the nonproportionally damped system was reduced to a series of proportionally damped systems,which can be decoupled by using modal transformation. Based on this,an approximatelly analytical solution was obtined. The examples show that the solution obtained by this method agrees very well with that by the numerical method.
Abstract:According to the structure of human leg muscles, the Dingguo Zhang’s CPG model was modified. The CPG model was based on neural oscillator theory,which was developed from the combination of neuroscience and biomechanics’s perspective.The modified CPG model can overcome the limitations of movement that only reflect the rhythm of single leg,and can show the rhythm and harmony of two legs in gait movement,which is more approximate to the reality.By numerical simulation,the gait movement patterns were obtained.The result shows the rhythm characteristic of human gait movement,and can reflect the nervous system's regulatory role in human rhythm gait movement.
Abstract:Dynamical behaviors near saddlenode bifurcation point in nervous system, in both deterministic and stochastic neuronal model, were simulated. The characteristics of neural firing induced by noise were revealed and identified to be a stochastic renewal process. Correspondingly, the autonomous stochastic resonance induced by noise was also studied. The results not only reveal the dynamics and characteristics of firing patterns near the saddlenode bifurcation point, but also provide practical method to identify the saddlenode bifurcation point in nervous system.
Abstract:This paper investigated the control strategies for the active suppression of rotor/stator rubbing. First, the synchronous full annular rubbing solutions of a rotor/stator model, which took into account the dynamics of the rotor, the stator and the contact stiffness, were solved analytically. The stability of the solutions was then analyzed. Secondly, the stability characteristics of the model with cross-coupling damping or stiffness were studied, and their relations with the rubbing friction were revealed. Based on the results, two control methods by using the effects of the cross-coupling for the active suppression of rotor rubbing were proposed. The numerical simulations show the feasibility of the proposed control methods.
Abstract:The impact of axiallyloaded Euler Bernoulli beam with arbitrary impact position was investigated. The model of the impact system was simplified to a model of discrete concentrated masses linked with elastic elements. Firstly, based on the theory of integral transform, the differential equation of the collision system, the boundary conditions and the continuity conditions were transformed with Laplace transformation. Then, the analytical solution of the stress wave in frequency domain was obtained.The numerical inverse method was demonstrated by using the inversion of Laplace transformation with Crump,and the dynamic response in time domain was obtained. Curves of impact force, bending stress as well as shear varying with time were obtained by applying a numerical example, and this method was verified by comparing its results with those by using the finite element method. Finally, the effects of impact position, axiallyload, impact mass, impact velocity and flexibility coefficient on the impact force was studied, and several useful conclusions were obtained.
Abstract:Model reduction and active control of a flexible plate were investigated and experimented to verify the theoretical result. Firstly, the dynamic equation of the plate was presented using the assumed mode method. Then model reduction was studied using the modal cost analysis (MCA) method. Considering the system with small damping, a simplified approach for the MCA method was presented.An active controller was designed using the classical optimal control method. Simulation and experimental results indicate that the MCA method is able to demonstrate the relative importance of all the modes of the plate, so it can be used for model reduction of the plate.
Abstract:The energy principle was applied into the analyses of seismic response of one steel-concrete composite structure,and the dynamic response of the structure under earthquake load was analyzed by finite element software.The distribution regularity of hysteretic energy between columns and beams, plates,was investigated which took into account the structure damping ratio, peak ground shaking, strong motion duration and other influence factors. The results show that, the input energy is greatly affected by the damping ratio and peak ground shaking, but strong motion duration effect is relatively small. The storey distribution regularity of hysteretic energy is ladder-shaped distribution. The hysteretic energy dissipated by columns increases but the damping energy decreases with the increases of structure damping ratio, peak ground shaking and predominant period; beams and plates are contrary to columns. Ground motion duration has little effect on energy distribution.
Abstract:This paper presented an accurate method of calculating the earthquake force design sensitivity and Hessian matrix of the planar frame. The formulas for the earthquake force design sensitivity and Hessian matrix of the planar frame were deduced based on the finite element method and Newmarkβ method, and the corresponding calculating program was implemented with matlab language. Finally, a twostory planar frame was demonstrated as an example. The results indicate the method is effective.
Abstract:For the famous benchmark model of jointed beam proposed by the Sandia workshop on the modeling and simulation of structures with jointed interfaces, a symmetricmodalmodel and an antisymmetricmodalmodel were developed by the flexible support method in a relative description style separately. Then the modes were analyzed and the flexible parameters of the support were identified from the experimental data. A FEA was also carried out, in which the joint was modeled as a virtual material with identified parameters. The modes of the joined beam predicted by the analytical method and FEM are well coincident with the experimental results.
Abstract:A method based on linear matrix inequalities (LMI) constraints was presented for the re-entry longitudinal guidance law with intricate constraints. The nonlinear longitudinal dynamic equations were modeled pseudo-linearly for controllability in the standard trajectory neighborhood area,and then the guidance law was designed by solving LMI convex optimal. In each control period the feedback control law and input were obtained. The control input was used to guide the actual reentry trajectory, and closed-loop systems stability was proved. Simulation results show that the proposed guidance law is robust to deviations from reentry initial states.
Abstract:Considering the automobile suspension system with sinusoid excitation and hysteretic characteristic, we establish the dynamics model of 1/2 automobile suspension system with four degrees of freedom. The Poincare map is obtained by numerical emulation with the help of Matlab.The chaos response generated easily in the automobile suspension system is studied. The chaotic movement has adverse effect on the ride comfort of automobile and one is harmful to automobile moving.
Abstract:As a crucial link of the drivervehicleroad closedloop system, the driver model plays an important role in the simulation of vehicle closeloop system and the evaluation of vehicle active safety. Based on the Vehicle Handling Dynamics, the PreviewFollow theory and the Artificial Neural Network, this paper established a directional control driver model—TwoLayerFeedforward Artificial Neural Network Driver Model and the drivervehicle closed-loop system model. Using the closeloop system model, single and double lane change simulations were performed. The results show good agreement with the ideal data. It indicates that this driver model is reasonable enough to simulate the driver’s behavior property and provide a feasible way to the further investigation of the drivervehicleroad closedloop system.
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