Showing papers on "Added mass published in 1998"

An Arbitrary Lagrangian-Eulerian finite element method

Abstract: This paper describes an Arbitrary Lagrangian- Eulerian (ALE) finite element method for the simulation of fluid domains with moving structures. The fluid is viscous, incompressible and unsteady and the fluid motion is solved by a fractional step discretization of the Navier-Stokes equations. The emphasis is on convection dominated flows, and a three-step method is used for the convection term. The moving structure causes the mesh of the fluid domain to move, and a new algorithm is proposed to solve the important and crucial problem of the calculation of the mesh velocities. Numerical calculations of the added mass and added damping of a vibrating two-dimensional circular cylinder in the frequency Reynolds number range Re w =20−2000 are performed to evaluate the proposed ALE finite element method. The numerically calculated added mass and added damping are compared to both analytical and numerical results. To further demonstrate the generality of the method, a numerical simulation of flow past an oscillating schematic sports car is presented.

Periodic behavior of a cantilever beam with end mass subjected to harmonic base excitation

Abstract: A massless cantilever beam with a lumped mass attached to its free end while being excited harmonically at the base is fully investigated. The derived equation of vibrating motion is found to be a non-linear parametric ordinary differential equation, having no closed form solution for it. We have, therefore, established the sufficient conditions for the existence of periodic oscillatory behavior of the beam using Green's function and employing Schauder's fixed point theorem.

Parametric response of cantilever Timoshenko beams with tip mass under harmonic support motion

Abstract: The parametric response of a thick cantilever beam with a tip mass subjected to harmonic axial support motion is investigated. The Timoshenko beam theory is used to assess the effects of rotary inertia and shear deformation for the beam. In this regard, different modal amplitudes for transverse displacement and angle of rotation of the cross-section are considered. This yields a more accurate description of the dynamic model. The governing equations of motion are then derived for an arbitrary axial support motion which provide the flexibility of choosing the number of characteristic modes of the beam. To formulate a simple, physically correct dynamic model for stability and periodicity analysis, the general governing equations are truncated to only the first mode of vibration. Using Green’s function and Schauder’s fixed point theorem, the necessary and sufficient conditions for the existence of periodic oscillatory behavior of the beam are established. Consequently, the phase domains of periodicity and stability for various values of the physical characteristics of the beam-mass system and harmonic base excitation are presented. Depending on the values of the excitation amplitude and frequency in the stable and unstable regions, the solution exhibits many shapes besides the transition periodic shapes. A numerical example assessing the role of slenderness ratio of the beam, is presented to demonstrate the effectiveness of the proposed study. Results indicate that for a given beam system with a known excitation, increasing the tip mass would almost always reduce the stable periodic region. The effect of the beam model assumption on the periodic domain is also studied. Results show that using purely flexural or even the Euler–Bernoulli model rather than Timoshenko, would produce an incorrect periodic region.

Development and Experimental Validation of an Underwater Manipulator Hydrodynamic Model

Abstract: Hydrodynamic forces can be large, and hence have a significant effect on the dynamic performance of underwater manipulation sys tems. This paper investigates these forces for a cylindrical single- link arm undergoing motions that are characteristic of a robotic manipulator. Based on flow visualization, theoretical analysis, and experimental measurements, a new model is developed that describes these forces. This model differs from previous models in that the drag and added mass coefficients are state-dependentfunctions that depend on the distance traveled by the arm. A factor of four improve ment in accuracy is demonstrated over standard constant-coefficient models.

Nonlinear Analysis of a Parametrically Excited Cantilever Beam. (Effect of the Tip Mass on Stationary Response).

Abstract: For a parametrically excited cantilever beam the effect of the tip mass on the nonlinear characteristics of the frequency-response is theoretically presented.The equation of motion governing the system is formulated by Hamilton's pronciple, taking into account the inertia and curvature nonlinearities and a quadratic damping effect of the beam.Using the method of multiple scales and center manifold theory, the bifurcation points of the frequency-response curve are analyzed.It follows that there are two transcritical bifurcations, and in addition to these bifurcations there are two saddle-node bifurcations, in the cases when the tip mass is relatively light and heavy, respectively.Experiments are also performed and the results show good qualitative agreement with the theoretical ones.

An analytical study of the transient motion of a dense rigid sphere in an incompressible newtonian fluid

Abstract: A theoretical study of the transient sphere motion (under the influence of gravity) through an incompressible Newtonian fluid subject to an Oseen-type drag relationship has been carried out. Exact closed form expressions for the instantaneous position, velocity and acceleration of the sphere are presented. An analytical expression developed herein also enables the delineation of the “best” sphere-fluid combination for the experimental observations of transient effects and these provide useful guidelines for designing laboratory experiments. However, this study is restricted to dense spheres falling in light liquids when the additional effects arising from the added mass and the Basset forces are negligible. Also, the boundary effects are altogether neglected.

Wave radiation and diffraction by a submerged sphere in a channel

Abstract: Wave radiation and diffraction by a submerged sphere is analysed based on the linearized velocity potential theory. The solution is obtained based on the multipole expansion which satisfies the boundary conditions on the free surface, at infinity and on side walls. The coefficients in the expansion are obtained by imposing the body surface boundary condition. Results are obtained for the added mass, the damping coefficient, the exciting force and the drift force. The effect of the trapped mode is also discussed

Free vibration of beams with two sections of distributed mass

Abstract: The equation of free transverse vibration of beams with two sections of partially distributed mass is derived and its exact solution has been obtained. Experimental data for a cantilever beam are given to verify the computational results. Using a cantilever beam as an example, some interesting features of changes of natural frequencies with mass length and position are described. The method is finally generalized for the case of beams with multiple spans of distributed mass.

Gravitational fall velocity of sphere in viscous fluid

Abstract: The gravitational transient fall velocity of a rigid sphere in an otherwise quiescent viscous fluid is studied through examining the physical reasonableness of simulated results and comparing the results to Moorman's 1955 free-fall experiments. The published sphere dynamic equations from low-to-moderate sphere Reynolds number are solved numerically by a fourth order predictor-corrector method and iterations on sphere velocity and acceleration. Among the published sphere dynamic expressions, Mei and Adrian's 1992 expression has the best agreement with Moorman's data. The relative importance of the steady and unsteady drags along the gravitational transient process is also discussed. It is found that neglecting the unsteady drag indeed simplifies the computational procedure, but the accuracy on the time-varying fall velocity is significantly compromised. The added mass and history terms are of great importance at early stages of gravitational transient falling for low sphere-to-fluid density ratio and low sphere Reynolds number.

Property Distribution Determination for Nonuniform Composite Beams From Vibration Response Measurements and Galerkin’s Method

Abstract: This paper presents initial results from a program to develop a rapid screening test for determining the in-plane fiber distributions in unidirectionally reinforced composite structures by the use of the vibration response measurements and Galerkin's method. Theoretical models and experimental data are generated on the basis of two methods: (1) the shifting method, in which the effective length of the beam is changed, and (2) the added mass method, in which the mass distribution of the beam is changed. The elastic constants and the density are all assumed to be junctions of fiber volume fraction, while the spatial distribution of the fiber volume fraction is assumed to be given by a polynomial function. The concept of an effective density is employed to obtain the appropriate solution to the coefficients of the polynomial function. Results show that the fundamental mode gives rise to better predictions of physical properties than the higher modes do. An error analysis includes discussion of the errors due to the influences of the mode number, the assumed order of the polynomial in the fiber volume fraction distribution, and the bending-extension coupling effect caused by the unsymmetrical distribution ofproperties about the beam middle surface.

On the complete radiation-diffraction problem and wave-drift damping of marine bodies in the yaw mode of motion

Abstract: The coupled radiation-diffraction problem due to a floating body with slow (time-dependent) rotation about the vertical axis in incoming waves is studied by means of potential theory. The water depth may be finite. First, the radiation problem is described. It is shown how the various components of the velocity potential may be obtained by means of integral equations. The first-order forces in the coupled radiation-diffraction problem are then considered. Generalized Haskind relations for the exciting forces and generalized Timman–Newman relations for the added mass and damping forces are deduced for bodies of arbitrary shape with vertical walls at the water line. The equation of motion is obtained, and the frequencies of the linear body responses superposed on the slow rotation are identified. Formulae for the wave-drift damping coefficients in the yaw mode of motion are derived in explicit form, and the energy equation is discussed. Computations illustrating the various aspects of the method are performed for two ships. The wave-drift damping moment is found to become positive in the present examples. When the rotation axis is moved far away from the body, the slow motion becomes effectively unidirectional, and results of the translational case are recovered.

Hydrodynamic manoeuvring aspects of planing craft

Abstract: To get a better insight in hydrodynamic forces and moments acting on a planing hull during a manoeuvre in the horizontal plane oscillation runs have been performed. During these tests the model was fully constrained and forced into a manoeuvring motion (pure sway, pure yaw and yaw with drift). Forces and moments were measured in six degrees of freedom. Draught, trim angle, forward speed and swayand yaw velocity have been varied systematically. Based on the measured forces and moments a mathematical model has been formulated by performing regression analysis with the varied coefficients as input variables. Subsequently, the mathematical model has been implemented in a simulation program, which has been developed earlier to describe the motional behaviour of a planing hull in six degrees of freedom. A number of simulation runs has been performed to observe the behaviour of a planing hull. Hydrodynamic terms as added mass appear to depend on forward speed.

A numerical simulation of hydrodynamic forces of ground-effect problem using Lagrange's equation of motion

Abstract: SUMMARY On the basis of the potential flow theory, Lagrange’s equation of motion is used to study the unsteady ground-effect problem. The forces and moments acting on the moving body are solved in terms of the derivatives of added masses in which the generalized Taylor’s formulae are applied. The singular integral equations used to solve the surface source intensities and their derivatives are regularized by the Gauss flux theorem and are therefore amenable to the direct use of the Gaussian quadrature formula. In illustration, the condition of a prolate spheroid moving in the fore-and-aft direction at constant speed past a flat ground with a protrusion is considered. The hydrodynamic forces and moments acting on the moving spheroid are investigated systematically by varying the size of the protrusion and the cruising height of the spheroid. © 1998 John Wiley & Sons, Ltd.

On the added mass of rippled discs

Abstract: The problem of three-dimensional potential flow past a thin rigid screen is reduced to a hypersingular boundary integral equation This equation is then projected onto a flat reference screen, which is taken to be a circular disc Solutions are obtained for screens that are axisymmetric perturbations from the disc, so that the screen is rippled concentrically The added mass is calculated for axisymmetric flow past such screens, correct to second order