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EN
A point mass added to a plate may have a significant effect on its linear and nonlinear dynamics, including frequencies, mode shapes and the forced response to external loading. In the present paper, a simply supported clamped simply supported clamped rectangular plate (SCSCRP) carrying a point mass is examined. The expressions for the kinetic, linear and non-linear strain energies are derived by taking into account the effect of the added mass on the kinetic energy and the effect of the membrane forces induced by the non-linearity on the strain energy. The discretization of these expressions makes the mass tensor, the linear and non-linear rigidity tensors appear in a non-linear algebraic multimode amplitude equation, the iterative solution of which permit to obtain, in the neighborhood of the first non-linear mode, the basic SCSCRP function amplitude dependent contribution coefficients. Nonlinear frequency response functions have been obtained for the first time, based on an iterative numerical solution in each case of the associated complete set of nonlinear algebraic equations. Such new results are useful for a better qualitative understanding allowing an optimal dynamic design of the rectangular plates with added masses.
EN
A propeller shaft generally experiences three linear forces and three moments, the most important of which are thrust, torque, and lateral forces (horizontal and vertical). Thus, we consider 4DOFs (degrees of freedom) of propeller shaft vibrations. This paper is presented to obtain the vibration equations of the various coupled vibrations of the propeller shaft at the stern of a ship (including coupled torsional-axial, torsional-lateral, axial-lateral, torsional-axial, and lateral vibrations). We focused on the added hydrodynamic forces (added mass and added damping forces) due to the location of the propeller behind the ship. In this regard, the 4DOFs of the coupled vibration (torsional-longitudinal and lateral vibrations in the horizontal and vertical directions) equations of shaft and propeller systems located behind a ship were extracted with and without added mass and damping forces. Also, the effect of mass eccentricity was considered on vibrations occurring at the rear of the ship.
EN
Simulation of the hydrodynamic performance of a floating current turbine in a combined wave and flow environment is important. In this paper, ANSYS-CFX software is used to analyse the hydrodynamic performance of a vertical-axis turbine with various influence factors such as tip speed ratio, pitching frequency and amplitude. Time-varying curves for thrust and lateral forces are fitted with the least squares method; the added mass and damping coefficients are refined to analyse the influence of the former factors. The simulation results demonstrate that, compared with nonpitching and rotating turbines under constant inflow, the time-varying load of rotating turbines with pitching exhibits an additional fluctuation. The pitching motion of the turbine has a positive effect on the power output. The fluctuation amplitudes of thrust and lateral force envelope curves have a positive correlation with the frequency and amplitude of the pitching motion and tip speed ratio, which is harmful to the turbine’s structural strength. The mean values of the forces are slightly affected by pitching frequencies and amplitudes, but positively proportional to the tip speed ratio of the turbine. Based upon the least squares method, the thrust and lateral force coefficients can be divided into three components, uniform load coefficient, added mass and damping coefficients, the middle one being significantly smaller than the other two. Damping force plays a more important role in the fluctuation of loads induced by pitching motion. These results can facilitate study of the motion response of floating vertical-axis tidal current turbine systems in waves.
EN
The numerical approach for determination of influence of deformation of the gas bubble (radius 0.74 mm) on added mass coefficient in (i) steady-state conditions and (ii) during approach to the horizontal wall, is proposed. It is shown that the bubble deformation can be tuned numerically (within the range 1.06 - 1.88) via proper variations of the Laplace pressure, without changing the bubble radius. Influence of the bubble deformation on its motion parameters is discussed and compared to theoretical predictions regarding the bubble drag coefficient and Reynolds number. Moreover, the approach allowing determination of the added mass of rising bubble, on the basis of variations in fluid kinetic energy, is described. It is shown that calculated added mass variations strongly depends on the interplay between (i) the bubble deformation ratio and (ii) its rising velocity. This effect is especially important for added mass of a gas bubble approaching a solid wall, because it can affect the kinetics of drainage of the separating liquid film formed under dynamic conditions, when Re >> 1.
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