Time-harmonic Pressure Research Articles

THE INFLUENCE OF SHAPE ON THE RAYLEIGH CONDUCTIVITY OF A WALL APERTURE IN THE PRESENCE OF GRAZING FLOW

A numerical investigation of the influence of grazing flow on the Rayleigh conductivityKRof an aperture in a thin rigid wall is made. The Mach number is sufficiently small for the local motion near the aperture to be regarded as incompressible, and the Reynolds number is taken to be large enough for the aperture shear layer to be modelled by a vortex sheet. The vortex sheet is assumed to be linearly perturbed from its equilibrium position by a small amplitude, time-harmonic pressure, andKRis determined from the ratio of the resulting aperture volume flux to the applied pressure. The frequency dependence ofKRis computed for a variety of aperture shapes for both one-sided and two-sided flows. For apertures of equal maximum streamwise dimension in one-sided flow, the Strouhal number range within which perturbation energy is extracted from the mean flow [whereIm(KR)>0] is found to be effectively independent of the aperture shape. The frequency of the first “operating stage” of self-sustained (unforced) oscillations of the aperture shear layer lies approximately in the center of this range, and is the minimum frequency at which narrow band sound is generated by nominally steady flow over the aperture. The numerical predictions are shown to satisfy the reverse flow reciprocal theorem, according to whichKRis unchanged when the mean flow directions on both sides of the wall are reversed (when vortex shedding occurs from the “opposite” edge of the aperture).

Generation of internal waves by moving non-stationary disturbances in a real stratified ocean

The plane problem on the generation of linear internal waves by a moving area of time-harmonic surface pressures in a continuously-stratified ocean of constant depth is considered. An analytical relation has been derived for forced internal waves off the site of their generation in the form of an internal wave field superposition corresponding to individual vertical modes. The possible wave regimes are determined. For the Brunt-Vaisala frequency distribution in the North Atlantic, the generation conditions and amplitudes of diverse radiated waves are numerically determined.

Electrokinetic dissipation induced by seismic waves

When a fluid electrolyte moves relative to a solid, an electric field is generated that migrates ions and thus dissipates energy. This “electrokinetic” dissipation is theoretically compared to the viscous shear dissipation for fluid flow generated by a fixed time harmonic pressure gradient in a planar quartz duct. It is shown that, regardless of frequency, it is safe to ignore the electrokinetic losses when the electrolyte molarity is on the order of 0.1 M or greater. For low molarity electrolytes [Formula: see text], however, the electrokinetic losses do become significant compared to the viscous losses for flow in sufficiently tight pores. The ratio of electrokinetic dissipation [Formula: see text] to viscous dissipation [Formula: see text] is always a maximum when the electrokinetic radius (the duct haft‐width divided by the Debye length) is ≈1.5. The maximum value of [Formula: see text] does not exceed 0.5 for the NaCl, KCl, and quartz systems considered. The generated electric field pushes on the excess ions in the duct in a direction opposite to the applied pressure gradient, thus giving rise to an apparent viscosity enhancement. This enhancement is ⩽45 percent for the systems considered here, and can be directly obtained from the [Formula: see text] ratio. Indeed, the central effect of a large [Formula: see text] ratio is that the amount of relative fluid flow is reduced, and thus, the amount of wave attenuation is reduced.

Time harmonic acoustic radiation from a submerged elastic shell defined by nonconcentric circular cylinders

A time harmonic pressure is applied to the interior of an elastic body bounded by nonconcentric circular cylinders and immersed in an acoustic fluid. The resulting acoustic radiation is determined as an expansion in the nonconcentricity distance, in the same manner as done earlier [R. P. Shaw and G. R. Tai, J. Acoust. Soc. Am. 56, 1437–1443 (1974)] for an acoustic body. Full equations of elasticity are used since the boundary integral equation method employed reduces these to the consideration of surfaces anyway as would be the case for shell theory. Again, nearest neighbor modes (j−1 and j+1) are introduced in the first order solution for a forcing internal pressure in the jth mode. [Work supported by Structural Mechanics Division, ONR.]

Time harmonic acoustic radiation from nonconcentric circular cylinders

A time harmonic pressure is applied at the inner boundary of an acoustic fluid body, composed of two parallel, nonconcentric circular cylinders, which is itself embedded in another infinite acoustic fluid. The resulting radiation is determined as an expansion in terms of the nonconcentricity. For an applied internal pressure in a j th spatial mode, each order of this expansion introduces a “nearest neighbor” mode, e.g., the first order requires a (j + i)th and a (j − i)th mode. The solution procedure is based on an expansion of the Helmholtz integral equation formulation.

Forced Motions of an Encased Cylinder of Decreasing Thickness

A hollow cylinder is encased in a thin elastic shell and subjected to a time harmonic pressure at the inner surface of the cylinder. Plane strain and axial symmetry are assumed. The material of the cylinder is incompressible in bulk and both elastic and viscoelastic behavior in shear are considered. The inner radius of the cylinder increases monotonically with time. The influence of loss of mass and stiffness on the forced motion of the system is considered. The oscillatory motion consists of the superposition of a maintained vibration and a transient term. The maintained vibration takes into account the loss of mass and stiffness in a quasistatic manner. For an encased viscoelastic cylinder, the transient term is damped rapidly. A bounded resonance effect occurs when the instantaneous frequency of the system passes through the value of the external forcing frequency.

The Vibration of an Internally Damped Sandwich Plate Radiating Into a Fluid Medium

An analysis is given for the vibration of a long sandwich plate with linear internal damping properties. The plate is subjected to a time-harmonic pressure loading of constant amplitude and is considered vibrating both in vacuo and in an environment consisting of vacuum on one side and a fluid medium on the other. Numerical results are presented for both a conventional and a highly damped sandwich plate. The conventional (aluminum honeycomb) sandwich plate produces only a small amount of damping, but when the honeycomb core is replaced by a highly dissipative thermoplastic, the maximum deflection and stress at resonance are reduced theoretically by about two orders of magnitude.