Sabih I. Hayek

Propagation of sound above a porous half‐space

An exact solution for the field due to a point source above a homogeneous and isotropic porous ground has been derived in terms of a single branch line integral and a pole residue. The expected properties of the porous ground lead to a less complex solution than that usual to geophysics or underwater acoustics. The method of steepest descents modified by subtraction of the pole enables the derivation of an approximate solution for an externally reacting boundary. The precise nature of the further approximations that follow the assumption of a locally reacting (or impedance) boundary is made explicit and the role of the surface wave pole is clarified. Finally, the existing solutions for a locally reacting boundary are compared, and with one exception they are shown to be identical.

Acoustic propagation over an impedance plane

A new solution is obtained for the acoustic pressure field generated by a point source and scattered by a locally reacting impedance covered plane. The new solution is obtained in the form of an asymptotic series which has been shown to agree well with other studies. One of the most important features of this solution is that higher‐order terms can be calculated from preceding terms in the series by the use of recursion formulas. Comparing data predicted from this solution with that from a numerical integration of the exact expression shows the asymptotic series to be extremely accurate, even for relatively low values of the parameter kR. Not surprisingly, the plane‐wave solution often shows major deviations from the exact integral solution.

Mathematical modeling of absorbent highway noise barriers

Abstract Analytical modeling methods of complex noise barriers are presented in this paper. The models are developed by use of the geometrical theory of diffraction which allows for modeling of simple and complex shaped noise barriers. These models involve diffraction coefficients that include the influence of frequency, grazing angle, surface impedance and the source and receiver positions. The diffraction coefficients for complex shaped barriers are constructed from those for simple shapes by use of geometrical optics and physical acoustics. The influence of the ground on barrier diffraction is included through complex reflection coefficients for point sources off impedance covered planes. For highway noise barrier applications, the barrier noise reduction efficiency is calculated for a line of incoherent point sources. Scale model tests were conducted on barriers of various shapes. These include barriers shaped as thin walls, wedges, trapezoids with vertical or sloped walls and double thin walls. These barriers were tested with hard or absorbent surfaces erected over hard or absorbent ground.

Complex natural frequencies of vibrating submerged spheroidal shells

Abstract The differential equations governing the free axisymmetric extensional vibrations of an elastic prolate spheroidal shell submerged in an infinite acoustic medium are obtained in prolate spheroidal coordinates using Hamiltons principle. Solutions are obtained by a perturbation technique which converges well for shells of small eccentricity. Numerical results are presented for the fundamental mode, frequency and acoustic impedance of steel shells in water for ratios of major to minor axis up to 1.23 over a wide range of shell length to thickness ratios.

Acoustic radiation from an insonified elastic plate with a line discontinuity

This paper deals with the development of analytic models for the prediction of the acoustic radiated field from an infinite elastic plate with a single line force and line moment impedance discontinuity due to an incident plane acoustic wave. The solution is in the form of a Fourier integral with a kernel having ten poles. The integral is evaluated by three methods. The first uses the steepest descent path (SDP) method, leading to a solution that decays as 1/(k0r)1/2. The second method used conformal transformations and the modified saddle point (MSP) method, where all ten poles of the integrand are factored out. This second method yields a solution that has complementary error functions and an asymptotic series in (k0r). The third method employs a transformation of the integrand to effect an efficient and fastly convergent numerical integration algorithm. In general, the MSP asymptotic series solution and the numerical integration yielded numerically identical results. However, while the SDP solution pre...

Acoustic radiation from point excited rib‐reinforced plate

An analytic solution for the acoustic radiation from a rib‐reinforced infinite elastic plate which is excited by a point force located on the rib was obtained. The solution exhibits a new coincidence angle, where the radiated pressure peaks, which depends on the relative stiffness and mass of the attached beam. An expression for the radiated power was also obtained which shows the general reduction of radiated power explicitly as a function of the mass and stiffness of the attached beam. Approximate formulas for the complex interaction between the beam and the plate were developed for frequencies above and below the coincidence frequency. Approximate expressions for the radiated power were obtained from simplified physical models.

Diffraction of a point source by two impedance covered half‐planes

An analytical solution is given to predict the propagation of noise from a point source to a point receiver over an infinite plane consisting of two half‐planes, each covered by a different impedance. The solution is found by the use of function theoretic methods, and is evaluated asymptotically by the method of pole subtraction. It includes a reflected wave, three diffracted (ground) waves, and a surface wave due to each impedance in addition to a direct wave. The reflection coefficient form is different from the plane‐wave reflection and it is influenced by the sphericity of the wavefront at the receiver range. However, it reduces to the plane‐wave reflection coefficient once the point source position approaches infinity representing an incoming plane wave. Out of the two reflecting waves, only one contributes depending on the position of the receiver. The two surface waves correspond to the two impedance half‐planes, generally only one contributes depending on the location of the receiver. If the recei...

Diffraction by a hard–soft barrier

An analytical solution for the diffraction by a half‐plane is given for a plane‐wave incidence and a point source. One surface of the half‐plane has a hard impedance (rigid) and the other has a soft impedance (pressure release). The solution is obtained by function theoretic methods and has a simple form in marked contrast to those obtained by the Wiener–Hopf technique. A null in the diffracted field was shown to exist as a function of the source location. In general, the diffracted field tended to resemble that of a soft–soft half‐plane in the half‐space adjacent to the soft face and resembles that of a hard–hard half‐plane in the other half‐space.

Transmission of Acoustic Waves through Submerged Orthotropic Spherical Shells

The problem of transmission of acoustic waves through submerged orthotropic spherical shells was considered. The sound radiation in an infinite acoustic fluid is induced by a rigid spherical transducer, concentric within an orthotropic spherical shell having an axisymmetric surface‐velocity distribution. The space between the spherical transducer and the orthotropic spherical shell is full of the same acoustic fluid as that outside of the shell. The equations of motion for orthotropic shells, as well as for the fluid inside and outside, were derived. These equations are then solved by satisfying the continuity conditions on all solid‐fluid interfaces. Four representative transducer surface‐velocity distributions were considered. The solution for the farfield acoustic pressure was obtained for an orthotropic and for an isotropic shell.

Acoustic radiation from an impulsively excited elastic plate

The acoustic radiated pressure time signature of a submerged elastic plate which is impulsively loaded is predicted analytically by use of integral transforms on time and space. The first arrival of the acoustic pulse at an observer point in the medium was shown to correspond to the acoustic time of arrival for the normal distance from the observer to the plate. After the first arrival, the time signature oscillates with decreasing amplitude with the passage of time. The period of oscillation was shown to increase with time and the decay rate was shown to decay inversely with elapsed time. [Work supported by NAVSEA.]