STABILITY AND LOCAL BIFURCATION IN A SIMPLY-SUPPORTED BEAM CARRYING A MOVING MASS

The stability and local bifurcation of a simply-supported flexible beam （Bernoulli- Euler type） carrying a moving mass and subjected to harmonic axial excitation are investigated. In the theoretical analysis, the partial differential equation of motion with the fifth-order nonlinear term is solved using the method of multiple scales （a perturbation technique）. The stability and local bifurcation of the beam are analyzed for 1/2 sub harmonic resonance. The results show that some of the parameters, especially the velocity of moving mass and external excitation, affect the local bifurcation significantly. Therefore, these parameters play important roles in the system stability.

Dynamic simulation of beam-like structure with a crack subjected to a random moving mass oscillator

In this paper, dynamic simulation of a beam-like structure with a transverse open crack subjected to a random moving mass oscillator is investigated. The simultaneous effect of a crack and a random oscillator has not been addressed up to now. The crack in the beam at different locations and with different depths is considered as one group of damage, each as an individual imperfection. In addition, bearing immobility is considered as another type of problem in the beam. Mass, stiffness, damping and velocity of the oscillator are assumed to be random parameters. An improved perturbation technique is applied to reduce the simulation time. It was found that there is a maximum value of the variance of each uncertain parameter, in which the maximum reliability of the perturbation method can be achieved, and that this maximum value can be obtained by the Alpha-Hilber Monte-Carlo simulation method. The simulation results reveal that the mass and the velocity uncertainty cause high uncertainty in the deflection of the beam. Also, the pattern of the deflection is not affected by different random oscillator parameters, and as a result, the type of damage can be identified even with high uncertainty. Moreover, the deflection in the nodes around the mid-span of the beam provides the best information regarding the imperfections, and consequently leads to the best sensor locations in an actual experiment.

Second order sliding mode control with back stepping approach for moving mass spinning missiles

An attitude controller using the second order sliding mode control methodology with a backstepping approach（SOSMCB）is designed and implemented for a spinning missile with two internal moving mass blocks.The system consists of a rigid body and two radial internal moving mass blocks and its mathematical model is established based on Newtonian mechanics.The control scheme integrates a second order sliding mode control algorithm into the last step of the backstepping approach,and its stability is proved by means of a Lyapunov function.The performance of the controller is demonstrated by numerical simulations,the results show that the attitude controller is stable and effective.

Coupling Vibration of Simply-Supported Damping Beam Carrying a Moving Mass

The coupling dynamic problems,such as the vehicle-bridge interaction problem,are difficult to be analyzed.In this paper,the generalized multi-symplectic approach is employed to investigate the coupling dynamic behaviors in the vehicle-bridge interaction system.A simply-supported damping beam model carrying a moving mass is considered and the generalized multi-symplectic form with the dynamical symmetry breaking factors is deduced firstly.And then,Preissmann’s scheme is employed to discretize the generalized multi-symplectic form,and the discrete structure-preserving condition for the numerical scheme is presented.According to the discrete structure-preserving condition,the permitted moving speed of the mass with different damping factors and different time step lengths is obtained to ensure the structure-preserving properties of the numerical scheme.Finally,the effects of the damping factor of the beam and the moving speed of the mass on the vibration of the beam are investigated by Preissmann’s scheme.The main contribution of this work is to provide a structure-preserving analysis approach for the vehicle-bridge interaction problem.

Energy shaping for coordinating internally actuated vehicles

This paper considers the stable coordination problem of two vehicles equipping with internal moving mass actuators.The coordinating and stabilizing control are derived by energy shaping. The proposed method is physically motivated and avoids cancelation or domination of nonlinearities.

Steady state response of an infinite beam on a viscoelastic foundation with moving distributed mass and load

Compared with the moving concentrated load model,it is more realistic and proper to use the moving distributed mass and load model to simulate the dynamics of a train moving along a railway track.In the problem of a moving concentrated load,there is only one critical velocity,which divides the load moving velocity into two categories:subcritical and supercritical.The locus of a concentrated load demarcates the space into two parts:the waves in these two domains are called the front and rear waves,respectively.In comparison,in the problem of moving distributed mass and load,there are two critical velocities,which results in three categories of the distributed mass moving velocity.Due to the presence of the distributed mass and load,the space is divided into three domains,in which three different waves exist.Much richer and different variation patterns of wave shapes arise in the problem of the moving distributed mass and load.The mechanisms responsible for these variation patterns are systematically studied.A semi-analytical solution to the steady-state is also obtained,which recovers that of the classical problem of a moving concentrated load when the length of the distributed mass and load approaches zero.

MOVING THE MASSES

Providing adequate transportation for visitors and athletes at the 2008 Olympics is proving the capital's biggest challenge Seven million. That's the number of tickets the Beijing Organizing Committee for the Games of the 29th Olympiad (BOCOG) expects to sell to audiences flooding into the capital during the Olympics in 2008.