Papers by Keyword: Nonlinear Dynamic System

Abstract: Friction damped (FD) structure is first design as the sub-structure in the mega-sub controlled (MSC) frame to further reduce structural dynamical responses. Three different building structures, i.e. a conventional mega-sub frame, the MSC frame and the MSC frame with FD sub-structure, are designed, with reference to the conventional mega-sub frame used in Tokyo City Hall The comparative dynamical analyses among the three building structures are made. The controlling effectiveness of the MSC frame with different sub-structural stiffness is examined. Moreover, the nonlinear dynamic equations and the method to assembling structural parameter matrixes for the MSC frame with FD sub-structure are presented. Researching results illustrate that the MSC frame with FD sub-structure has more excellent dynamic properties and more predominant controlling effectiveness, compared to the traditional mega-sub frame and the MSC frame.

Abstract: The characteristic of the drift error of inertial platform is a high-order nonlinear dynamic system, using the neural networks’ abilities of universal approximation of differentiable trajectory and capturing system dynamic information, this paper presents the drift error identifying project of inertial platform based on Elman networks structure. First, the drift error model of inertial platform is established, after selecting the input and output for network, momentum and alterable speed algorithm is used to speed up the network convergence. On the basis of the algorithm, the extended nonlinear node function in the hidden network does not only improve the learning speed of network, but also satisfies the need of accuracy on system identification. Through the drift error data measured on inertial platform, the training result shows that the scheme achieves satisfied identification results.

Abstract: The smooth-and-discontinue(SD) oscillator with time-dependent stiffness was put forward and founded to study dynamic characteristics of beam bridge under moving load. Mid-span deflection of beam bridge under moving load was described as vibration trace. Proper stiffness model function was elected and study nonlinear dynamic behaviors of mid-span deflection when several vehicles pass through bridge successively. The software MATLAB was used to simulate the model and obtain the bifurcation diagrams with parameter of vehicle speed and Poincare sections of the vehicle-bridge coupled system. The result shows the complicated nonlinear dynamics with periodic motion, quasi-periodic motion phenomena and chaos, the occurrence alternatively among these motions.

Abstract: The system model of flexible suspension bridge under several moving loads was founded according to SD oscillator with time –dependent stiffness. The model was simulated by the software MATLAB and the nonlinear dynamic behaviors of the system with different velocities were analyzed. Bifurcation diagram of the system is obtained with the changing of vehicle speed; meanwhile the phase trajectories and the Poincaré sections are also presented. The result shows the complicated nonlinear dynamics with periodic motion, quasi-periodic phenomena and chaos, the occurrence alternatively among these quasi-period and chaos, which reveals the reason that causes the S-shape deformation of flexible suspension bridge under moving load easily.

Abstract: The subharmonic resonance response of the strongly nonlinear delay differential equation is solved using the incremental harmonic balance method. The value of the exciting frequency when the subharmonic resonance occurs is discussed. The influences of the time delay and the feedback gain on the system subharmonic resonance response are studied. The variation of the subharmonic resonance response with the system parameters is obtained. The results show that the value of the exciting frequency when the subharmonic resonance occurs is affected by the system parameters. The proportion of the one third harmonic in the amplitude increases rapidly with the increase of the exciting frequency. The variation of the amplitude ratio of the one third harmonic and the first harmonic is wavy type. The proportion of the one third harmonic in the amplitude decreases with increasing the displacement feedback gain and increases with increasing the velocity feedback gain. The proportion of the one third harmonic in the amplitude occupies a dominant position in the subharmonic resonance response.

Abstract: With the development of analysis and identification way to nonlinear dynamic system, people uses many different method to build up mathematics model to simulate nonlinear dynamic system. This paper introduces some important nonlinear system identification ways and a kind of Volterra series expression type in detail. This kind of way adopts Hilbert reproducing kernel method to build up nonlinear dynamic system model. Hilbert space provides a kind of effective expression type for Fourier series and transfer based on anyorthogonal polynomial. Volterra series function has very strict theory basic, which can be applied into many nonlinear dynamic system analysis and identification filed, and has broad practicality and application prospect.