Showing papers on "Added mass published in 1972"

Investigation of film‐thickness determination by oscillating quartz resonators with large mass load

Abstract: A one‐dimensional acoustical composite‐resonator model is used to study the behavior of a quartz‐crystal resonator with large mass load. On the basis of this model, it is found that the exact relationship between the frequency shift and the added mass depends on the acoustic impedance of the deposited material. The experimental data for three materials (silver, copper, and lead) with different acoustic impedances are shown to be in good agreement with the theoretical predictions. The validity and limitations of the presently used equations for thickness determination by quartz‐crystal resonators are also discussed.

The Stokes-flow drag on prolate and oblate spheroids during axial translatory accelerations

Abstract: Stokes's linearized equations of motion are used to calculate the flow field generated by a spheroid executing axial translatory oscillations in an infinite, otherwise still, incompressible, viscous fluid. The flow field, expressed in terms of spheroidal wave functions of order one, is used to develop general expressions for the drag on oscillating prolate and oblate spheroids. Formulae for the approximate drag, useful in making calculations, are obtained for small values of an oscillation parameter. These formulae reduce to the Stokes result in the limit when the spheroid becomes a sphere and the steady-state drag for a spheroid as the frequency of oscillation becomes zero. The fluid forces on spheroids of various shapes are compared graphically. The approximate formulae for the drag are integrated over all frequencies to obtain formulae for the drag on spheroids executing general axial translatory accelerations. The fluid resistance on the spheroid is expressed as the sum of an added mass effect, a steady-state drag and an effect due to the history of the motion. A table of added mass, viscous and history coefficients is given.

Fluid finite elements for added mass calculations

Abstract: The equations for the free undamped vibration of a structure in an ideal incompressible fluid medium and their finite element formulation are briefly reviewed. The relevant matrices (stiffness and loading) for two prismatic fluid elements are given explicitly and some numerical results are presented.

Evaluation and verification of computer calculations of wave-induced ship structural loads

Abstract: An analytical method for the determination of conventional merchant ship motions and wave-induced moments in a seaway is developed. Both vertical and lateral plane motions and loads are considered for a ship travelling at any heading in regular waves and in irregular long or short crested seas. Strip theory is used and each ship hull cross-section is assumed to be of Lewis form shape for the purpose of calculating hydrodynamic added mass and damping forces in vertical, lateral and rolling oscillation modes. The coupled equations of motion are linear, and the superposition principle is used for statistical response calculations in irregular seas. All three primary ship hull loadings are determined, i.e. vertical bending, lateral bending and torsional moments, as well as shear forces, at any point along the length, with these responses only representing the low frequency slowly varying wave loads directly induced by the waves. A computer program that carries out the calculations was developed, and is fully documented separately. The results of the method are evaluated by comparison with a large body of model test data. The comparison extends over a wide range of ship speeds, wave angles, wave lengths, and loading conditions, as well as hull forms. The agreement between the calculations and experimental data is generally very good. Thus, a method is available for use in the rational design of the ship hull main girder structure.

Virtual mass of submerged structures

Abstract: A structure submerged in water exhibits different dynamic behavior due to the interaction of the surrounding water than when it vibrates in air. The submerged structure is subjected to additional hydrodynamic pressures and its dynamic characteristics alter when it vibrates in water. Virtual mass concept is increasingly being used in design to account for the influence of surrounding water and this is used indirectly to represent the hydrodynamic pressure. A simple experimental technique for the determination of virtual mass for partially and fully submerged structures is presented herein. The virtual mass depends on the geometry of the structure and its dynamic properties in air. Due to the surrounding water, the natural period of vibration of a structure elongates and the damping increases. Due to the added mass of the surrounding water, the stresses and strains in the structure under dynamic conditions are increased but some relief is provided by the increased damping.

An experimental assessment of the added mass of some plates vibrating in water

Abstract: A reservoir of water is contained by a concrete valley block, a ferrocement wall and a steel plate. Both wall and plate contain an array of pressure transducer sockets (Figures 1 and 2). Using the M.A.M.A.1 equipment pure modes of vibration are excited. Frequency and mode shape are measured with the reservoir empty. When the reservoir is full hydrodynamic pressure is also measured. These hydrodynamic pressures are compared with Chopra's2 two-dimensional, series solution, which includes compressibility of water, and with two- and three-dimensional finite element solutions of Laplace's equation, which do not include compressibility. Chopra's solution is unsatisfactory for modes which contain a vertical node line. The best agreement between experimental and theoretical hydrodynamic pressure is obtained when the latter is obtained from three-dimensional solutions of Laplace's equations, indicating that compressibility does not play a significant rǒle. This conclusion is supported by agreement between experimental frequencies (reservoir full) and those calculated using added mass obtained from the Laplace solution. Similar conclusions were reached from tests on a floating steel plate, suspended in the surface of the reservoir by a soft spring. Here, dynamic pressure measurements were not made, reliance being placed on agreement between calculated and measured frequencies and mode shapes.

Mechanical excitation of offshore tower model

Abstract: A large scale model of a bottom-pivoted, surface-piercing, cylindrical oil-drilling platform was built to obtain experimental data on hydrodynamic coefficients applicable to the structure. The wave force on the structure was simulated by a mechanical device in still water. Thus, the number of variables to calculate the drag and added mass coefficients associated with the structure for use in conjunction with the Morison Equation was reduced. For instance, water particle velocity and acceleration were eliminated from the equation. Test runs were made at different simulated sea conditions. Consistent drag and added mass coefficients were obtained using various data reduction techniques.

A viscoelastic-mass model for muscle

Abstract: This work considers a viscoelastic-mass hypothesis which predicts length-tension, work-load, and force-velocity behavior for muscle-mass systems. The model is considered in detail with respect to its force-velocity and energy-load behavior. The model predicts that maximum shortening velocity (V max ) of a muscle-mass system depends, in a multiplicative manner, on the net initial force exerted by the muscle, the reciprocal of the total inertial mass, the reciprocal of the natural frequency of the system, and a factor (Zeta Factor) which depends entirely upon the damping ratio, ξ, of the system. The equation giving V max as a function of these four factors is similar in form to A.V. Hill's characteristic equation for muscle. The curvature of this theoretical force-velocity relation depends upon two parameters: Initial mass/Isometric mass (M0/M max ) and the value of ξ at zero added mass(after-load). Six sets of normalized force-velocity data from the literature are plotted and graphically compared with curves determined by the model.

Added Mass and Damping of Submerged Bodies Oscillating Near the Surface

Abstract: Oscillatory tests were performed on several geometric shapes in the vicinity of the free surface of an undisturbed fluid. The tests, together with an accompanying literature review, were conducted to determine the influence of geometry, depth, amplitude of motion, and frequency on the fluid added mass and damping coefficients. The results, which are in broad agreement with the theoretical calculations, are used to generate empirical expressions for a range of frequencies, depths, and geometries.

Dynamic Stability of a Cylindrical Shell in an Acoustic Medium

Abstract: A plane‐strain investigation of the dynamic stability of an infinitely long cylindrical shell undergoing breathing oscillations in an infinite inviscid fluid medium is presented. Kinematic nonlinearities of the shell are retained while the fluid is regarded as a linear acoustic medium. A stability criterion which depends strongly upon the acoustic reactance is developed. When the shell is immersed in a fluid, the added mass of the fluid reduces the frequency for parametric resonance. The damping provided by the acoustic resistance proves to be negligible at parametric resonance. The validity of the neglect of kinematic nonlinearities of the fluid is demonstrated by means of an example.

Resonant Response of Offshore Structures

Abstract: A nonlinear deterministic mathematic model is used to investigate the resonant response of a tall offshore structure under the action of periodic deep water waves. The added mass which is attributed to the acceleration of a body in the fluid is taken into consideration. The fundamental period of vibration of a structure is lengthened due to the effect of the added mass. An incremental numerical technique is employed to obtain the solution. The results show that even when damping due to drag is considered, the response of the structure at resonance is greatly amplified.

Calculation of nonlifting potential flow about ship hulls

Abstract: A practical method is described for calculating the non-lifting potential flow about ship hulls. The method utilizes a continuous source density distribution on the surface of a ship, and treats the normal component (or integral equation for the source density distribution), radial component and circumferential component of disturbance velocity as two dimensional problem by assuming the slender body, but treats the longitudinal component as three dimensional problem because of difficulty in applying the slender body assumption. The accuracy of the method is exhibited by means of comparison with the full three dimensional solution by Hess and Smith. As some examples of application, sinkage force, side force and added mass are calculated for Series 60 ship hull.

Five problems on the effect of a solid wall on the added mass of floating cylindrical bodies subject to vertical impact

Abstract: Very few studies have been made of the effect of the channel wall on the added mass of floating cylindrical bodies subject to vertical impact. These include [1–4]. In the present paper we use the direct approach in curvilinear coordinates (under the usual assumptions adopted in hydrodynamic impact theory) to solve the following vertical impact problems: ellipses with semimajor axes horizontal and vertical in confocal vessels; and floating cylinders which are positioned eccentrically in a semicylindrical vessel, near a vertical wall, and near a stationary cylinder. The solutions are valid for any distance between the impacted contour and the channel wall.