Abstract:The Schrodinger equations is a basic equation of quantum mechanics. It’s just as important as Newton’s equation of motion of classical physics in quantum mechanics. In this paper, we use variable separation method to obtain the stationary solution of the quantum mechanical system with time independent Hamiltonian. We separately give solutions of Schrdinger equations with Kerr type, saturation type and quintic nonlinearity. And the obtained analytical solutions are compared with the numerical solutions. They agree well with each other.

Abstract:The constraints default phenomenon is a serious problem in solving the Itype Lagrange equation with traditional numerical method. For the simplified 2D model of the solar power receiver of Solar Power Satellite (SPS), the symplectic method is used to analyze the deploying process of the solar power receiver and the constraints default is discussed in this paper. Firstly, based on the Hamilton variational principle, the canonical equation is derived from the EulerLagrange equation that describe the deploying process of the solar power receiver. And then, the symplectic PRK scheme for the canonical equation is constructed. Finally, the deploying process of the solar power receiver is simulated by the symplectic PRK scheme. From the simulation results, it can be concluded that the symplectic PRK scheme constructed in this paper can satisfy the displacement constraint of the 2D system well for a long time.

Abstract:This paper studies the Noether symmetry and corresponding conserved quantity for fractional Birkhoffian systems in terms of Caputo fractional derivatives. Firstly, the fractional Pfaff action is defined within Caputo fractional derivatives. The fractional Birkhoff’s equations and corresponding transversality conditions are also established. Secondly, based on the invariance of the Pfaff action under the infinitesimal transformations, the conditions of invariance are given under a special oneparameter group of infinitesimal transformations without transforming the time as well as a general oneparameter group with transforming the time, respectively. Finally, according to the notion of fractional conserved quantity presented by Frederico and Torres, the Noether theorem for the fractional Birkhoffian systems is constructed, which states the relationship between a fractional Noether symmetry and a fractional conserved quantity.

Abstract:moving loads pass through the rough surface of beam. Considering the characteristics of random excitation, present nonlinear model of moving loads different beam roughness. The critical condition in of mean square is obtained by random Melnikov process. The response of structure under the combin of random and periodic excitation is simulated, and used to the variation of dynamic behaviors. It is concluded that speed, nonlinear dynamic behaviors midspan of beam are severely influenced by the random excitation. Therefore poor flatness of surface would increase the probability of occurrence of chaos.

Abstract:This paper studied a beltdrive system containing a translating belt, two pulleys, accessory systems, and a oneway clutch. The driven pulley and the accessory system were coupled by the oneway clutch. Moreover, the transverse vibration of the translating belt was taken into account. Therefore, the derived coupled discretecontinuous nonlinear equations consist of integropartialdifferential equations and piecewise ordinary differential equations. The continuous nonlinear equations were truncated to a set of nonlinear ordinary differential equations by using the Galerkin method. The steadystate responses of the coupled vibration of the beltdrive system were investigated by the numerical harmonic balance method. Moreover, the effects of the oneway clutch on the power system were studied by comparing the frequencyresponse curve of the translating belt with and without oneway clutch device. The nonlinear dynamic characteristics of the beltdrive system were studied. Furthermore, the steadystate responses of the beltdrive system were investigated at the higher excitation frequency for the first time. In addition, the steadystate responses based on the harmonic balance method were confirmed by the RungeKutta algorithm.

Abstract:To solve the dynamic problem for the out-of-plane vibrations of a rotating thin ring, this paper studied the basic transmission characteristics of elastic wave propagation, and analyzed the dispersion equation, wave numbers, cutoff frequencies, phase velocity and the ratio of axial vibration displacement to torsional vibration displacement, which is valuable in the free vibration analysis of the solid cage in a high speed roller bearing. Based on the wave propagation method, the positive and negative wave numbers were separated by the criterion of positivegoing waves. The characteristic equation of a rotating thin ring was established by the phaseclosed principle and the transfer matrices. One example was given to solve the natural frequencies of the rotating ring, and the result is consistent with the result of the given literature.

Abstract:This paper focuses on the influence of joint clearance on the satellite dashes when the space environment alternates between cool and hot. Since the whole truss structure is complex and has many kinds of clearance,this paper only studied the nonlinear dynamical behavior of synchronous straight bevel gears which have clearance after the synchronous straight bevel gears is locked. The first model is Hertz contact force model; the second one is coefficient of restitution model; the last one is nonlinear springdamping model. Then the physical model was simplified, the dynamic one was obtained, and the dynamic equation with the nonlinear springdamping model was established. Due to the existence of segmentation in the dynamic equations, direct solve analytically is difficult, so this paper used numerical simulation method to analyze the model. From the analysis, it is obtained that the system of synchronous straight bevel gears with clearance will appear complex nonlinear phenomena such as Singleperiodic, perioddoubling bifurcation and chaotic responses.

Abstract:Aiming at the uncertainty problem caused by model uncertainties and external disturbances in actual control process of chaotic ship steering, this paper combined the adaptive control method with sliding mode control method, and also transferred the sign function to the first derivative of control input when designing the switching function, which eliminates the chattering problem in common sliding mode control method, so a single input adaptive sliding mode control method for chaotic ship steering control was proposed. The experiment results show that, compared with the traditional sliding mode control method, the proposed method has a good performance on chaotic ship steering control with model uncertainties and external disturbances, which provides a more reliable way for chaotic ship steering control.

Abstract:In this paper, the vibration suppression of torsional vibrating system is investigated through the delayed vibration absorber of neutral type. The stability theory of dynamic system was applied to study the stability of the neutral delayed vibration absorber and the torsional vibrating system, and their stable regions were obtained, respectively, by taking time delay as a parameter. Moreover, The absorbing effect of dynamic vibration absorber with the delay changing was obtained. It is shown that the stable region of the vibration absorber and vibration reduction system became larger when compared with the general delayed vibration absorber. Finally, the numerical simulations were also carried out to verify the analytic results.

Abstract:A threelegged resonant vibration driven robot using piezoelectric actuator is presented in this paper. The dynamical equations of the horizontal locomotion is established as one of the three legs vibrating in resonant condition. Numerical results illustrates the motion mechanism and the effect of anisotropic friction on direction and velocity of the robot. The approximate relationship between the frequency of piezoelectric actuator and the velocity of locomotion is obtained. The governing equation of inplane vibration for a curved beam is developed to calculate the natural frequencies and the corresponding mode shapes. Based on this equation, three sets of geometrical parameters for the curved legs are devised. It is found that their frequencies are respectively different. The robot prototype is also created according to these parameters. The planar locomotion is accomplished through robot testing by switching the frequencies of alternating voltage applied on piezoelectric actuator to the shift resonant among the legs. Experimental results reasonably match with the numerical simulation.

Abstract:We explore the nontrivial effects of coupling strength and timedelayed coupling on bursting synchronization of modular neuronal network with hybrid chemical and electrical synapses by nonlinear dynamics and numerical simulation. The results show that the intra and intercoupling between different neurons can induce bursting neurons to achieve bursting synchronization in modular neuronal network. However, time delays in the coupling have negative influences on the couplinginduced bursting synchronization. Furthermore, these two results are verified to be robust against the number of subnetworks and the number of neurons within each subnetwork. Note that the degraded impact of timedelayed coupling on bursting synchronization may have potential theoretical significance for curing some neuronal diseases (such as Parkinson＇s Disease, epilepsy) caused by bursting synchronization.

Abstract:The nonlinear response of delaminated buckling beams with different delamination locations under axial periodic excitation was examined through experimental investigation. The time history of displacement, phase diagrams and spectrum are described and discussed. The research demonstrates the delaminated buckled beam performs nonlinear dynamic motions, such as period, perioddoubling as well as chaos. The experimental results show that in the case of the same delamination length, the delaminated location greatly affect the dynamic characteristics of delaminated buckled beam. And when the central of the delamination region is closer the midspan of beam, the first order frequency of delaminated beam is lower. Moreover, the delaminated buckled beam more easily experiences the periodic motion, doubling periodic motion and chaotic motion at lower excited frequency and loads.

Abstract:Based onphysical simulation experiment, an attitude control problem concerning the inplane motion of a tethered satellite system with short distance deployment is studied by means of dynamics similarity between the ground-based experiments and the onorbit system. Starting with nonlinear dynamic of the tethered satellite system with controllable arm, dynamics similarity conditions between the groundbased experiments and the onorbit system are obtained. using the proportion differential feedback control strategy, a numerical simulation is performed to the attitude motion of the controlled tethered satellite. Subsequently, the similar onorbit environment is realized by experimental platform. The groundbased test is conducted, the control of the attitude motion tethered satellite the tether swing is achieved only using single rigid arm. Finally, the comparison of experimental and numerical results demonstrate that the of rigid arm can effectively control the deployment of the tethered satellite.