Abstract:The paper firstly obtained the first kind of elliptic equation for the longshortwave interaction equations through travelling wave transformation. Based on the solutions and Bcklund transformation of the first kind of elliptic equation, the new infinite sequence solutions of the longshortwave interaction equations were constructed, including the Jacobi elliptic function, hyperbolic function, exponential function and rational function.

Abstract:A harmonic-energy balance method is put forward to solve the strong nonlinear pendulum equation. The difference from the classical perturbation method is that the harmonic balance method does not account the differential equation and initial conditions separately, but it considers both simultaneously. Through the harmonic-balance method, two-order ordinary differential equations describing dynamic systems become a set of nonlinear algebraic equations with the variables of angular frequency and amplitude. Considering the balance of energy, the close equations with angular frequency and amplitude as the variables can be solved. The harmonic-energy balance method is a combination of harmonic-balance and energy balance. It overcomes the shortcomings of both methods and takes their advantages. A case study also shows that the harmonicenergy balance method is simpler with higher precision although it takes less harmonics.

Abstract:With the development of MEMS fabricating technology, MEMS structure now has a wide application in manufacturing industry. Meanwhile, because of no any characteristic length scale parameters in constitutive relationship, the classical theory of continuum mechanics is unlikely to predict the size effect under micro scale. This paper investigates the nonlinear problems of micro Mindlin plates based on the firstorder shear deformation theory and von Karman nonlinearity, and the strain gradient theory is also utilized to take size effect into consideration. Nonlinear dynamic model of the micro Mindlin plate along with its boundary conditions are obtained by taking strain energy, including strain energy of both macro and micro deformation, kinetic energy and external work into Hamilton′s principle.

Abstract:The dynamical response including the motion and the destruction of the electro-active polymer cylindrical shells subjected to the periodic pressure on the inner surface are studied within the framework of finite elasto-dynamics. It is proved that there exists a certain critical value of the internal pressure and the electric field through numerical computing and dynamic qualitative analysis based on the nonlinear differential equation for the motion of the inner surface of the shell. The motion of the shell is nonlinear quasi-periodic oscillation when the mean pressure of the periodic pressure and the voltage are less than their critical values, respectively. In contrast, the shell is destroyed when the pressure or the voltage exceeds the corresponding critical value. Moreover, the effect of the electric field and the pressure parameters on the critical values and the oscillation of the shell are then discussed.

Abstract:Stickslip and friction of the joint interface pay a significant role not only on structure nonlinear stiffness and damping but also on structure passive damping. Iwan model provides a preferable recurrence of the stickslip and friction characteristics of the joint interface. The alternating frequency/time domain method (AFT) is used to study the steadystate response of single degree of freedom oscillator system containing Iwan nonlinear model in this paper. This method takes both advantages of the effectiveness of calculating response for linear system by frequency domain method and the ease of evaluating nonlinear force by time domain method. The discrete Fourier transform alternating from the time domain to the frequency domain is applied through iterating to obtain the steadystate response of the system. The result of AFT is compared with that from the central difference method, and the influence of excitation amplitude on nonlinear characteristic is also examined in this paper. The results show that the steadystate response by AFT method agrees well with that of the central difference method. Moreover, the AFT method performs better computational efficiency, as the timeconsuming is reduced by 50 percent. In a whole, it is found that the application of higher excitation amplitude results in the increase of the system energy dissipation and the reduces stiffness and natural frequency.

Abstract:A similarity model considering the nonlinear dynamic characteristics of rolling ball bearing in rotorbearing system was put forward to examine the problem of dynamic similarity. The nonlinear vibration differential equation of rolling ball bearing was firstly established. The similarity relationship on the nonlinear dynamic characteristics was deduced by the integral simulation method, and the similarity design criteria of the rolling ball bearing was then achieved. Afterwards, the groove ball bearing of C204JUT and 6208 were set as a prototype and a model for numerical simulation, respectively. The effect of rotational speed, radial load Fr, damping C and radial clearance on the vibration displacement and velocity of rolling ball bearing system were investigated by bifurcation. Finally, through comparing the bifurcation range, the stable parameter value, the response value for the stable motion in the bifurcation diagram, the similarity criteria was verified. The conclusions were obtained as follow: i)The similarity relationship of the nonlinear vibration characteristics for the rolling ball bearing can be established by its structural similarity. ii)The bifurcation shape of the prototype and the model was consistent, and the steady response of the model matched that of the prototype very well.

Abstract:In order to obtain the resonance frequency of a new designed last-stage blade on marine turbine, the blade is excited by compressed air in the highspeed dynamic balance test bench. The signal of blade vibration is transferred to a signal analysis system by the telemetry transmitter and receiver when it is picked up by the inductive components, and the information of blade vibration is then obtained under multiple channels. The test data show that the "triple point" resonance speed is a modal family for pitch diameter number k=7 and k=8, and the range of resonance speed is beyond the working speed, respectively. Compared with the results from the numerical calculation and the testing, the tolerance of dynamic frequencies does not exceed 5% for pitch diameter number k=7&8. Numerical and experimental analysis prove that the blades in the operating speed are safe and reliable.

Abstract:The transient dynamic characteristics of the torpedo turbine rotor system are predicted and analyzed in this paper. The transient motion equations of the whole rotor system are established based on the transfer matrix method and then solved by Newmark-β numerical integral method. Three different startup processes, including linear, exponent as well as staged accelerations, are involved in the simulation. The numerical results show that the critical speeds of turbine rotor system for three start-up processes are relatively close to each other. However, the peak values and oscillatory convergence time are quite different. The prediction of the staged acceleration process provides the lowest peak value at the second critical rotation rate, which is consistent with the actual situation. This paper provides an essential reference for the further design and optimization of torpedo turbine rotor system.

Abstract:The Very Flexible Aircraft (VFA) may result in large elastic deformation during flight, which has a great influence on aeroelastic properties and flight dynamics characteristic of the aircraft, especially on its stability. Based on the threestage rigid hypothesis, the longitudinal dynamic model is developed, where the dihedral angle is employed to describe the wing bending deformation. The relations among the control surface, thrust, angle of attack and dihedral angle are further examined, with emphasis on the influence of dihedral angle on the flight stability. The results show that the dihedral angle has a great effect on the stability for unchanged flight speed and height. Excessive deformation may lead to dynamic instability. In order to maintain the longitudinal stability, it is necessary to control the deformation of the VFA.

Abstract:Tires are the only carrier of the contact between the vehicle and road surface. Their mechanical property is important for analysis and control on the vehicle dynamic response. At present, the tire simulation mostly focuses on the steadystate model. But it can not describe the dynamic characteristic of the tire accurately. Therefore, it plays a significant role to add the dynamic tire model in the vehicle dynamics simulation. The tire friction model in the multibody dynamical software ADAMS is static, where the friction is regarded as a static value. However, in actual, the friction between the tire and road surface is dynamic, and it should be a dynamic function of the relative velocity and displacement. To this end, in this paper, the dynamic tire LuGre model using the Matlab/Simulink software is constructed. Through connecting the interface with Adams/Car, cosimulation between the vehicle model and the simulink tire model is carried out in order to achieve the dynamic contact between tire and road and improve the accuracy of vehicle system analysis.

Abstract:Due to the existence of computer virus, large numbers of computers cannot run normally. It usually results in huge loss. To this end, an control model for a new type of computer virus based on a general computer virus model is proposed in this paper. Firstly, a new type of computer virus model is improved, and the control is taken into account. The optimal control problem is then proposed. Meanwhile, the existence of optimal control is proved. Pontryagin’s minimal principal is employed to analyze the optimal control. Finally, the theory analysis is also supplemented as a comparison work. The simulating results shows that under the condition without control, the basic reproductive number is obtained from the original model, and it is bigger than 1. Moreover, above conclusion indicates that there exists the endemic equilibrium, and it leads to the outbreak of the computer virus finally. The numerical modeling shows that through the optimal control strategy, the spread of computer virus can be prevented effectively.

Abstract:Based on the telemetry data, the technology to select the real modes for the aircraft operational mode derived by ambient excitation is investigated through ARMANExT method in this paper. Firstly, the theory of the ARMANExT method is introduced. Secondly, the mode indication is proposed, and the filter strategy is studied based on stabilization diagram, frequency and timefrequency analysis. Eventually, a case study is carried out. It is found that the identified modes reasonably match with the result of the frequency and timefrequency analysis.

Abstract:A dynamic model of flexible translational joint with Karnopp friction is presented in this paper. The slider of translational joint is treated as flexible body, while the guides are treated as rigid. Meanwhile, the influences of clearance on the dynamics of systems are considered. Since the friction forces and contact states between the slider and guides are complicated, a mechanical model is proposed using finite element method, where a contact model is developed based on Penalty method and the timevarying contact states of nodes are determined by applying trialanderror algorithm. Based on KED method and Newmark method, a simulation method is proposed to solve kinetic equations of the translational joint. Eventually, a planar sliderbar system with Karnopp friction and flexible slider is simulated, and the dynamic response of the mechanical system is analyzed. Moreover, the numerical results reveal the reasonability of the new developed method.

Abstract:In this paper, synchronous dynamic behavior of three Ringcoupled and Linearcoupled HR neuronal system is examined. Through constructing a suitable Lyapunov function as well as applying linear matrix inequalities and matrix theory, the global exponential stability and the global asymptotic stability of linearised error system at zero solution is obtained, respectively, and the relative criterion is theoretically provided for global asymptotic synchronization and global exponential synchronization of HR neuronal system. Furthermore, Ringcoupled network is synchronized more easily than Linearcoupled network. Numerical simulations also verifies the effectiveness of the results in this paper.

Abstract:The stability of a Harrison predator-prey model driven by symmetric trichotomous noises is studied in this paper. Using the ShapiroLoginov formula, the firstorder and secondorder moments of the linearized system are obtained. Then, the stability condition of the Harrison predator-prey model is given by using RouthHurwitz stability criterion. It is found that the stability of the system depends on the noise intensities and correlation time. Finally, some numerical results are performed to support the theoretical analyses.

Abstract:The effect of the traditional weak signal detection on low SNR is undesirable. this paper proposes an improved method for the detection of the weak signal under strong noise background. It replaces the nonlinear restoring force of a chaotic system by a equation of -x5+x7 by means of a single Duffing oscillator. Compared with the traditional Duffing oscillator detection system, this method performs stronger robustness. It states the working principle of weak signal detection based on the phase plane changes, and any unknown weak periodic signal detection can be achieved through the conversion of the time scale. The simulation study on the weak periodic signal detection under the noise background is also carried out, and verified against the detecting results of the real bearing fault signal. It is found that the proposed method obtains good effect. It provides a reasonable method for the engineering application.