V. V. Varadan

Scattering of an obliquely incident acoustic wave by an infinite cylinder

Expressions are derived for the scattered farfield pressure which results from the illumination of an infinite aluminum cylinder by a plane acoustic wave, whose propagation direction makes an arbitrary angle, α, with the normal to the cylinder axis. Computations are made at angles between α=0 ° and the Rayleigh critical angle, α=31.3 °. Changes in the scattered field are related to shifts in the paths of geometric and elastic surface waves from circumferential at α=0 °, to helical, to axial Rayleigh surface waves generated at the Rayleigh critical angle.

Model of a bilaminar actuator for active acoustic control systems

To increase levels of sound attenuation, it is often necessary to utilize active acoustic control methods. A complete active acoustic control system typically consists of sensing devices, an electronic control circuit, and an actuating device. Each component is designed to cause destructive interference of the impressed acoustic pressure field. A piezocomposite actuator is presented for active underwater attenuation control of an impressed acoustic field. The actuator is composed of bilaminate plates for absorption of both the reflection and the transmission of normally incident acoustic waves independent of the backing impedance. An electromechanical model of the bilaminate piezocomposite design with an analytical discussion is presented. An illustrated numerical example and discussion of system implications are included.

Sound scattering by rigid and elastic infinite elliptical cylinders in water

Numerical results are presented here to the problem of scattering of acoustic waves from infinite elastic elliptic cylinders under water. The T‐matrix (or null field) method has been used to evaluate the scattered field coefficients. Comparisons have been drawn between the form functions of a rigid (acoustically hard) cylinder and an elastic cylinder of similar geometry. The smooth periodic form function of the rigid cylinder is analyzed on the basis of the existence of Franz waves (creeping waves), while the sharp peaks in the elastic cylinder case have been interpreted as due to resonance effects of the submerged cylinder. Though, in general, it is possible to distinguish between the two kinds of targets from the scattering pattern (polar plots at fixed frequencies), it is observed that at ka = 5.0, one cannot distinguish between a rigid cylinder and an elastic cylinder.

Comparison of sound scattering by rigid and elastic obstacles in water

Acoustic wave scattering by prolate and oblate spheroids and finite cylinders immersed in water is compared when rigid body and elastic boundary conditions, respectively, are satisfied at the fluid–scatterer interface. The frequency dependence of the scattered farfield is obtained for various angles of incidence for both types of boundary conditions using the null field or T‐matrix approach. From our computations it is concluded that only for restricted materials properties of the scatterer, scattering geometry and scatterer shape, the scattering characteristics of an elastic obstacle, and a rigid obstacle of the same shape are comparable up to wavelengths comparable to the size of the obstacle.

Scattering of elastic waves by a fluid inclusion

The scattering of harmonic elastic waves by a bounded fluid inclusion in an infinite elastic continuum is considered. The formalism is an extension of the T‐matrix method developed for solid inclusions and cavities in elastic media and elastic solid inclusions in fluid media. The problem that is considered here is somewhat more complicated and shares some similarities with the case of an elastic cavity. For the fluid inclusion, however, the scattering amplitudes display resonance peaks due to interior resonances of the fluid. The convergence of the truncated series is dependent on the largest wavenumber which in the cases studied here is that in the fluid inclusion. Numerical results are presented for a prolate spheroidal inclusion.

Analysis and computation of the acoustic scattering by an elastic prolate spheroid obtained from the T‐matrix formulation

The T‐matrix formulation is used to compute the form function of an elastic prolate spheroid. The method allows acoustic scattering computations to be made for finite bodies at frequencies into the resonance region, and the lowest order resonance observed is, as expected, due to the excitation of a Rayleigh surface wave.

T‐matrix approach to study the vibration frequencies of elastic bodies in fluids

The T matrix or null field method is used as a computational scheme for analyzing the scattering frequencies of a homogeneous elastic body in a fluid. These frequencies have a unique distribution, in the complex plane, for each body. We solve a scalar transcendental equation to find the scattering frequencies for a sphere. These frequencies are used as starting points in a matrix approach to find the scattering frequencies for a prolate spheriod. Lists and figures of the most important scattering frequencies for a sphere and a prolate spheroid are given.

Acoustic wave scattering by elastic cylindrical shells in water

Frequency dependence of acoustic wave scattering by an infinite cylindrical shell of arbitrary cross section is analyzed using the T‐matrix approach. Numerical results are obtained for plane wave incidence normal to the axis of the shell but arbitrary with respect to the noncircular cross section for a range of frequencies. Results obtained for shells of circular and elliptical cross sections are compared with experimental results.

Large area sensors for active acoustic control systems

The design and development of a composite piezoelectric polymer (PVDF) sensor for use in an active acoustic control system are presented. Large area PVDF plates are encapsulated in a polymer matrix to detect both the incident and reflected signals in an underwater pulse tube at low frequencies. These signals are amplified, phase shifted, and then used to drive an absorbing transducer to negate reflections. The results of this system are compared with earlier data [X.‐Q. Bao, V. K. Varadan, and V. V. Varadan, J. Acoust. Soc. Am. Suppl. 1 84, S49 (1988)] that utilized piezoceramic spherical hydrophones. [Work supported by the Research Center for the Engineering of Electronic and Acoustic Materials.]

Finite element eigenfunction method (FEEM) for elastic (SH) wave scattering

A finite element eigenfunction method (FEEM) is presented for elastic (SH) wave scattering by cylinders of arbitrary cross section. The problem has been analyzed by enclosing the scatterer within an imaginary circular cylinder. The scattered field outside the circular cylinder is expanded in the usual cylindrical harmonics. The nearfield solution inside the circular cylinder is also assumed to be expanded by a series of eigenfunctions. The eigenfunctions for the nearfield are generated through the standard finite element technique by imposing suitable conditions on the circle. Then both the coefficients of the scattered field and those of the nearfield are found by means of a least‐square fit for the continuity conditions across the circle. The solution obtained thereby is considered complete in the sense that both the scattered and the nearfields are solved simultaneously. The validity of this method has been verified by comparing results with calculations from exact analysis and the T‐matrix method for ...