Vibration Of Fluid Research Articles

Symmetrization of the contained compressible‐fluid vibration eigenproblem

AbstractThis paper studies the symmetrization of the problem of coupled vibrations of an acoustic fluid enclosed in an elastic container. The container structure is discretized by a displacement finite element formulation and the acoustic fluid by a displacement‐potential formulation. The vibrations of this physically conservative coupled system are governed by an unsymmetric algebraic eigenvalue problem. Eight equivalent symmetric forms of this problem are exhibited. The fluid‐pressure formulation leads to a similar unsymmetric eigenproblem, which in turn can be converted to another eight equivalent symmetric forms.

Transition surfaces for short-wave vibrations of an ellipsoidal shell in a fluid

The problem of resonance short-wave vibrations of a closed ellipsoidal elastic shell of revolution in a fluid is examined. An asymptotic solution (with respect to a large frequency parameter) is constructed for the Helmholtz equation for the acoustic pressure mode matched to the solutions of the system of equations of relative shell displacement. Is is shown that the radiation of a vibrating shell is governed by the location of the transition surfaces (TS) in the fluid and the transition lines on the shell that separate the non-wave zone with intensive pressure damping in the neighbourhood of the shell from the remote slowly damping radiation field. Regularities are investigated for the motion of the TS as the vibration frequency, circumferential wave number, and degree of curvature (prolateness) of the shell change. Estimates are given of the applicability of the asymptotic approach. It is known that the vibrations of shells of revolution of non-constant curvature in a vacuum occur with the formation of transition lines in certain frequency bands, where the nature of the state of shell stress and strain changes /1/. It is natural to expact that this property is conserved even for shell vibrations in a fluid, where TS also originate in the fluid because of the connectedness between the shell and fluid vibration modes. Interest in studying TS in fluids gave rise to a tendency to construct a solution of the problem that is valid both in the fluid layer surrounding the shell and in the far field. If radiation is not taken into account, then a problem is obtained that is similar to problems on shell vibrations in an incompressible fluid, whose solution for the pressure in the medium does not change its nature with distance from the shell. This problem is solved effectively by approximate analytical methods (see /2/, say). However, such a problem leaves open questions about the amplitudes of the resonant vibrations modes of the “shell-fluid” system, their damping because of energy radiation, and on the radiation field itself. Knowledge of the location of the TS as the connecting link between the near and far pressure fields in the fluid is the key to the solution of these questions within the framework of approximate methods.

Vibration of a liquid with a free surface in a spinning spherical tank

The problem of forced fluid vibrations in a partially filled spinning spherical tank is solved numerically by using the finite element method. The governing equations include Coriolis acceleration and spatially homogeneous vorticity. An exponential instability is detected in the present simulation for fill ratios below 0·5 and centrifugal acceleration to thrust ratios less than 1·7. This fictitious instability appears in the model as a result of the homogeneous vortex assumption since the free slosh equations are neutrally stable in the Liapunov sense.

Influence of eccentric valves on the vibration of fluid conveying pipes

The dynamic stability of motion of fluid conveying pipes has been the subject of numerous studies. Theoretical interest was stimulated by the non-conservativeness of these systems. Design requirements for pipelines and nuclear related systems provided the additional impetus. Recently, the assessment of the probable influence that large, rigid valves frequently encountered on piping systems might have on the behavior of the overall system was required. In spite of the above mentioned wealth of literature, a great paucity of information was found on the influence of lumped masses. Consideration of rotatory inertia is apparently non-available. The motivation and contents of the present study stem from these facts. A variational formulation is followed by a Galerkin approximation that is applied to simply supported and cantilever pipes. Lumped translational and rotatory inertia are introduced. The results are reported for values of dimensionless parameters selected in a representative manner. Substantial modifications on the magnitudes of the frequencies are shown. The influence of the eccentricity is found of greater importance than that of the mass for constant eccentricity factor. The character of the equilibrium configurations associated with vanishing frequencies is a function highly dependent on the mass and eccentricity of the valve. The need for ensuing research on coupled out-of-plane bending and twisting of the pipe system is also established.

Fluid self-centering vibration and shock mount

A vibration eliminating mount for supporting a load is disclosed herein having a three point suspension wherein each of the three points includes a pair of angularly disposed brackets secured to the load and the support respectively. Carried between opposing parallel surfaces on the brackets is a fluid vibration eliminating assembly movably separating the pair of brackets. The assembly is carried in a dish or pan which is fixedly secured to at least one of the brackets and provision is made for accommodating a fluid valve for suitably pressurizing the assembly.

Visual characteristics of inhomogeneous acoustic waves

Experimentally obtained visualizations of propagating inhomogeneous acoustic waves driven by zero-order antisymmetric Lamb waves (flexural waves) in water are presented. The inhomogeneous waves are visualized by optical holographic interferometry. A series of photographs show the evolution in time of instantaneous acoustic pressure distributions associated with propagating inhomogeneous waves. The photographs reveal characteristic features of flexurally driven inhomogeneous waves such as transversely attenuated wavefronts oriented perpendicularly to the plate boundary and a phase propagation velocity along the boundary approximately equal to the plate wave velocity (250 meters/second). Effects due to the dispersive nature of the flexural plate waves are also noted in the photographic series. Features distinguishing these subsonic, inhomogeneous surface waves (also called trapped or evanescent waves) from the leaky, lateral or head wave and also from incompressible fluid motions associated with low frequency vibrations of fluid loaded plates are identified. The relevance of inhomogeneous acoustic waves driven by subsonic flexural waves to practical sound-structure interaction problems is discussed.

Axial Vibrations of Fluid Filled Pipe

Pipelines carry fluids important to modern civilization. Many cross seismically active regions where they may be subjected to damage from earthquake induced ground shaking. The pipe motion may be in the lateral or axial directions, or both. The current note is an attempt to answer the question of fluid pipe interaction when the only mechanism for coupling is the fluid viscosity. As such, the results are not applicable to situations where frequent bens or changes in cross section give rise to coupling mechanisms related to motion normal to the surface.

Essays on the History of Rocketry and Astronautics: Proceedings of the Third through the Sixth History Symposia of the International Academy of Astronautics

This two volume publication presents the proceedings of the third through sixth history symposia of the International Academy of Astronautics. Thirty-nine papers are divided into four categories: (1) Early Solid Propellant Rocketry; (2) Rocketry and Astronautics: Concepts, Theory, and Analyses after 1880; (3) The Development of Liquid and Solid Propellant Rockets from 1880 to 1945; and (4) Rocketry and Astronautics after 1945. Categories 1 and 2 will be found in volume 1 and the remainder in volume 2. Among other diciplines, Rocketry and Astronautics encompasses the physical and engineering sciences including fluid mechanics, thermodynamics, vibration theory, structural mechanics, and celestial mechanics. Papers presented in these two volumes range from those of empirical experimenters who used the time-honored cut and try methods to scientists wielding theoretical principles. The work traces the coupling of the physical and engineering sciences, industrial advances, and state support that produced the awesome progress in rocketry and astronautics for the most part within living memory. The proceedings of the four symposia present in these two volumes contain information on the work of leading investigators and their associates carried out in the first two-thirds of the twentieth century.

A displacement method for the analysis of vibrations of coupled fluid‐structure systems

AbstractA variational principle in terms of displacements in the fluid and the structure with a penalty for irrotationality of displacement in the fluid is developed for the analysis of harmonic vibrations of ideal compressible fluid and elastic structure systems. Its Discretization by the finite element method leads to an algebraic eigenvalue problem with a positive definite symmetric banded matrix. Numerical examples obtained for pure acoustic cases and coupled cases show the efficiency of the method.

Three-dimensional finite-element acoustic analysis of solid rocket motor cavities

This paper briefly discusses the state-of-the-art of combustion stability analysis of solid propellant rocket motors and the fact that an accurate, unperturbed, acoustical frequency-modal analysis is an initial requirement in the stability analysis. The formulation of a general three-dimensional finite-element structural vibration analysis model is presented in condensed fashion and it is shown how this formulation can be simply modified to yield a fluid vibration analysis model. The resulting model is applied to a simple example problem for the purpose of demonstrating the feasibility of utilizing an existing structural analysis code for a direct threedimensional acoustic analysis.

Edge scattering of aerodynamic sound by a lightly loaded elastic half-plane

We investigate the acoustic field radiated when a compact turbulent eddy lies close to a semi-infinite wave-bearing surface, but many acoustic wavelengths from its edge. The Lighthill acoustic analogy is used to reduce the problem to the simpler one of the diffraction of a plane sound wave by a semi-infinite elastic plate. This is solved exactly in terms of a contour integral by means of the Wiener-Hopf technique. An explicit solution for the far sound field is then developed for the limiting case when a non-dimensional fluid loading parameter ϵ tends to zero. Particular attention is paid to the subsonic surface wave modes which couple the fluid and plate vibrations. At low frequencies the bulk of the elastic wave energy induced in the plate by the adjacent turbulent eddy propagates without attenuation in a subsonic surface wave mode. Interaction with the edge of the plate induces an indirect scattered field whose intensity exhibits the dependence on cos 2 ½ θ (the line θ = 0 defines the semi-infinite surface) typical of the acoustic field of an edge scattering half-plane. The acoustic power of the eddy is increased over its free space value by a factor ϵ 2 ( Ma s ) -1 , where Ma s = c p/ c represents the ratio of the natural speed of plate waves in vacuo to the speed of sound. In typical aeronautical applications e can be as large as 18 dB at characteristic eddy frequencies of 100 Hz.

Oscillometry on various stape protheses. Experimental examination of human temporal bone preparations

In human temporal bone specimens the vibrations of the labyrinthine fluid were measured by a piezoelectric system after application of various techniques of otosclerosis surgery. Compared with the amplitude in the case of a normal stapes, the surgical techniques according to Zangemeister, Shea and Schuknect resulted in considerable transmission losses in the high frequency range, while transmission of low frequencies to the inner ear was almost equivalent to normal transmission via the stapes. For frequencies of more than 3,000 Hertz the damping influence of the fibrous tissue implanted into the oval window was verified. The results of surgery according to Zangemeister, Shea and Schuknechtdid not differ significantly in the low and medium frequency range. Only a Robinson prosthesis implanted like a Teflon piston caused an impairment of transmission, while the method of fitting this prosthesis onto fibrous tissue was equilvalent to the other techniques.

Effect of vibration on the rate of mass transfer

The rate of mass transfer at vibrating electrodes was measured using an electrochemical technique. The system chosen was stress-free polycrystalline electrolytic copper in CuSO4/H2SO4 solution. The concentration of the electrolyte was 0·05 mol dm−3 CuSO4 and 1·5 mol dm−3 H2SO4. Electrodes (160mm ×25 mm ×3 mm) were subjected to vertical vibrations and the limiting current density was determined at a section not subjected to end effects. The electrodes were especially designed so that the results would be unaffected by the turbulence generated at the leading vibrating edge. This enabled the investigation of the effect of parallel fluid vibrations without interference from the other factors.

Vibrations in Fluid

Sound, Structures and Their Interaction. By Miguel C. Junger and David Feit. Pp. x + 470. (The MIT: Cambridge, Massachusetts and London, October 1972.) $27.50.

Local Potentials Recorded from the Tunnel of Corti

Microelectrodes are inserted into the cells and fluid spaces of the organ of Corti under direct visual control monitored by closed-circuit television. Local dc resting potentials, tissue-electrode impedance, and ac potentials resulting from fluid vibrations applied by two methods are simultaneously recorded. Vibrations are applied either directly to the stapes or to the basilar membrane in the area of electrode insertion. The ac response recorded from the polarized cells and spaces of the organ of Corti are different depending upon whether the ac is locally or remotely generated. The magnitude and distribution of dc resting potentials are greatly dependent upon the local physiological condition of the exposed organ of Corti. Of most importance are an intact capillary system in the local area and good general physiological condition of the animal. Location of electrode tip is determined visually followed by microscopic examination of surface preparations.

A New Fluid Picture of the Electromagnetic Fields in Potential-Representation Using the Rapidity Vectors

The form of existence of the classical electromagnetic field caused by electric charge is studied in terms of a Lorentz-invariant density Oq; of the 4-potential and its rapidity vector V. This leads to a new fluid picture of the field which can reveal the simple mechanism underlying the fundamental electromagnetic phenomena. The fluid plays the role of the so­ called ether or the medium of the classical electromagnetic wave corresponding to the accel­ eration field. The free electromagnetic field ln empty space or the pure radiation may be visualized as the propagation of coupled vibration of positive and negative fluids ±Oq;frce similar to the above fluid. This wave travels through empty space, since the sum of ±o<Pfrce reduces to zero or 'vacuum', and the wave is composed of the vibration around the balanced state of 'vacuum'.

Ear structure and function in modern mammals.

The acoustic portions of the mammalian ear display greater morphological diversity in peripheral than in central portions. In many mammals the pinna is of negligible auditory significance. The tympano-ossicular system of all mammals sensitive to air-borne sounds must transform air vibrations to fluid vibrations in the inner ear by matching the acoustical impedances. Within the cochlea the energy of the fluid vibrations is transduced into nerve impulses. In highly specialized mammals the morphology of these transformer and transducer mechanisms is adapted for the reception of extreme frequencies. Echolocating bats and whales possess different, but effective, specializations for the reception of ultrasonic frequencies. Moles and kangaroo rats, on the other hand, have specialized ear structures for the reception of low frequencies.

A note on slow vibrations in a viscous fluid

An approximate expression is obtained for the force on an arbitrary body executing slow vibrations in a viscous fluid.

Evaluation of the proper vibrations of a fluid in a fixed vessel by the variational method

THE problem of evaluating the proper vibrations of a heavy ideal incompressible fluid in a fixed vessel leads to the solution in eigenvalues of a boundary value problem for the Laplace equation in the given three-dimensional region and is of some theoretical interest. We propose here a method of evaluating the proper vibrations of an ideal fluid for a wide class of regions.

Three problems on the vibrations of a viscous fluid

Three problems on the vibrations of a viscous fluid