Resonance problems encountered in vehicle-bridge interaction (VBI) have attracted widespread concern over the past decades. Due to system random characteristics, the prediction of resonant speeds and responses will become more complicated. To this end, this study presents stochastic analysis on the resonance of railway trains moving over a series of simply supported bridges with consideration of the randomness of system parameters. A train-slab track-bridge (TSB) vertically coupled dynamics model is established following the basic principle of vehicle-track-coupled dynamics. The railway train is composed of multiple vehicles, and each of them is built by seven rigid parts assigned with a total of 10 degrees of freedom. The rail, track slab, and bridge are considered as Euler–Bernoulli beams, and the vibration equations of which are established by the modal superposition method (MSM). Except for the nonlinear wheel-rail interaction based on the Hertz contact theory, the other coupling relations between each subsystem are assumed to be linear elastic. The number theory method is employed to obtain the representative sample point sets of the random parameters, and the flow trajectories of probabilities for the TSB dynamics system are captured by a probability density evolution method (PDEM). Numerical results indicate that the maximum bridge and vehicle responses are mainly dominated by the primary train-induced resonant speed; the last vehicle of a train will be more seriously excited when the bridges are set in resonance by the train; the resonant speeds and responses are rather sensitive to the system randomness, and the possible maximum amplitudes predicted by the PDEM are significantly underestimated by the traditional deterministic method; optimized parameters of the TSB system are preliminary obtained based on the representative point sets and imposed screening conditions.
Introducing the Lagrangian approach to acoustic simulation is supposed to reduce the difficulty in solving problems with deformable boundaries, complex topologies, or multiphase media. Specific examples are sound generation in the vocal track and bubble acoustics. As a Lagrangian meshfree particle method, the traditional smoothed particle hydrodynamics (SPH) method has been applied in acoustic computation but in a quiescent medium. This study presents two Lagrangian approaches for modeling sound propagation in moving fluid. In the first approach, which can be regarded as a direct numerical simulation method, both standard SPH and the corrective smoothed particle method (CSPM) are utilized to solve the fluid dynamic equations and obtain pressure change directly. In the second approach, both SPH and CSPM are used to solve the Lagrangian acoustic perturbation equations; the particle motion and the acoustic perturbation are separated and controlled by two sets of governing equations. Subsequently, sound propagation in flows with different Mach numbers is simulated with several boundary conditions including the perfected matched layers. Computational results show clear Doppler effects. The two Lagrangian approaches demonstrate convergence with exact solutions, and the different boundary conditions are validated to be effective.
Computational acoustic methods based on Eulerian description are widely used in industrial applications. However, some special acoustic problems, such as transient acoustic problems with moving or deformable boundaries, object separation, or for multiphase systems, are still cannot ideally solved with these Eulerian methods. The present work aims at using a Lagrangian meshfree method, the smoothed particle hydrodynamics (SPH), to simulate a time-domain acoustic problems with moving boundaries which is the sound of a rigid body falling on water. First, Lagrangian acoustic wave equations considering the sound source based on the hydrodynamic/acoustic splitting method are given and represented in the SPH form. Then, two-dimensional simulation of a rigid object falling on the free surface of water is computed by the SPH method. Noise sources are obtained from the flow field information of each fluid particle. Finally, acoustic experiments with measuring the sound of the rigid body falling on water are used to test and validate the SPH results. The accuracy and efficiency of the SPH acoustic computation are evaluated, and a comparison of cases with different impact velocities is also discussed.
The single-gimbal control moment gyros (SGCMGs) steering law has been a standing topic in the field of spacecraft attitude control for several decades. A practical steering law should meet the following requirements simultaneously: powerful singularity avoidance ability, high precision torque output ability and fast singularity escape ability. Moreover, the angular velocity commands generated by the steering law should not jitter sharply. In this paper, a vector control-based singularity avoidance and escape steering law for SGCMGs is proposed to satisfy these goals. In addition, a system angular momentum state evaluation function for command torque is defined for the first time, which can be used to effectively evaluate the remaining angular momentum resources for the command torque. We demonstrate the effectiveness and superiority of the proposed steering law with detailed comparisons to existing efforts.
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