Search Results (5)

This study explores the dynamic behavior of a vertical pipe conveying gas-liquid two-phase flow with rotationally restrained boundaries, employing the generalized integral transform technique (GITT). The rotationally restrained boundary conditions are more realistic for practical engineering applications in comparison to the classical simply-supported and clamped boundary conditions, which can be viewed as limiting scenarios of the rotationally restrained boundary conditions when rotational stiffness approaches zero and infinity, respectively. Utilizing the small-deflection Euler-Bernoulli beam theory, the governing equation of motion for the deflection of the pipe is transformed into an infinite set of coupled ordinary differential equations, which is then numerically solved following truncation at a finite order $NW$. The proposed integral transform solution was initially validated against extant literature results. Numerical findings demonstrate that as the gas volume fraction increases, there is a reduction in both the first-order critical flow velocity and the vibration frequency of the pipe conveying two-phase flow. Conversely, as the rotational stiffness factor enhances, both the first-order critical velocity and vibration frequency increase, resulting in improved stability of the pipe. The impact of the bottom-end rotational stiffness factor $r_2$ on the dynamic stability of the pipe is more pronounced compared to the top-end rotational factor $r_1$. The variation in two-phase flow parameters is closely associated with the damping and stiffness matrices. Modifying the gas volume fraction in the two-phase flow alters the distribution of centrifugal and Coriolis forces within the pipeline system, thereby affecting the pipeline’s natural frequency. The results illustrate that an increase in the gas volume fraction leads to a decrease in both the pipeline’s critical velocity and vibration frequency, culminating in reduced stability. The findings suggest that both the gas volume fraction and boundary rotational stiffness exert a significant influence on the dynamic behavior and stability of the pipe conveying gas-liquid two-phase flow. Full article

The suppression of torque ripples in an interior permanent magnet synchronous motor (IPMSM) is essential to improve its efficiency and responsiveness. Here, we report on the development of an electromagnetic energy harvester incorporated into an IPMSM to suppress its torque ripples. The proposed harvester is driven to oscillations by the speed ripple of the AC motor. We derived the motion and circuit equations for the motor and the harvester according to Euler–Lagrange equations. We discussed the principle of electrical power generation and used MATLAB/Simulink numerical simulations to investigate the dynamic behavior of the proposed harvester. Our findings revealed that the active Coriolis force unnecessarily reduces the motor’s original torque, leading to unsuccessful power generation. Nevertheless, our results demonstrated that the reactive Coriolis force successfully suppresses the motor torque ripple. Full article

The dynamic equation of a mass point in the circular restricted three-body problem is governed by Coriolis and centrifugal force, in addition to a co-rotating potential relative to the frame. In this paper, we provide an explicit, symmetric integrator for this problem. Such an integrator is more efficient than the symplectic Euler method and the Gauss Runge–Kutta method as regards this problem. In addition, we proved the integrator is symplectic by the discrete Hamilton’s principle. Several groups of numerical experiments demonstrated the precision and high efficiency of the integrator in the examples of the quadratic potential and the bounded orbits in the circular restricted three-body problem. Full article

The effect of the lateral walls of a Lab-On-a-Disc device on the dynamics of a model system of particles with a density lower than that of the solvent (modelling parasites eggs) is analyzed theoretically and experimentally. In the absence of lateral walls, a particle always moves in the direction of the centrifugal force, while its trajectory is deflected in the tangential direction by the inertial Coriolis and Euler forces. Lateral walls, depending on the angle forming with the radial direction, can guide the particle either in the same or in the opposite direction to the centrifugal force, thus resulting in unusual particle trajectories including zig-zag or backwards particle motion. The effect is pronounced in the case of short operation times when the acceleration of the angular rotation, and thus the Euler force, is considerable. The predicted unusual motion is demonstrated by numerically solving the equation of motion in the presence of lateral walls and verified in the experiment with particles of density lower than that of the solvent. Our analysis is useful for design and operational considerations of Lab-On-a-Disc devices aiming for or involving (bio)particle handling. Full article

As a powerful tool that can be used to solve both continuous and discrete equations, the Lie symmetry analysis of dynamical systems on a time scale is investigated. Applying the method to the Burgers equation and Euler equation, we get the symmetry of the equation and single parameter groups on a time scale. Some group invariant solutions in explicit form for the traffic flow model simulated by a Burgers equation and Euler equation with a Coriolis force on a time scale are studied. Full article