Forces acting on stationary and moving solid obstacles in plane wave sound fields
Aerodynamic forces acting on oscillating cylinders in plane wave sound fields
Sutherland, L. C.↗
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The propagation of plane waves in a thermally stratified atmosphere
The behavior of a plane wave reflecting from a finite impedance surface with a realistic atmospheric temperature profile is investigated. An approximate solution has been implemented on a digital computer and this solution is presented graphically for a number of cases at low incidence angles.
Van Moorhem, W. K.↗
Saturation and the limit of jet mixing enhancement by single frequency plane wave excitation: Experiment and theory
The limitations of single frequency plane wave excitation in mixing enhancement are investigated for a circular jet. Measurements made in an 8.8 cm diameter jet are compared with a theoretical model. The measurements are made to quantify mixing at excitation amplitudes up to 2 percent of the jet exit velocity. The initial boundary layer state, the exit mean and fluctuating velocity profiles and spectra are documented for all cases considered. The amplitude of the fundamental wave is recorded along the jet axis for various levels of excitation. As the amplitude of excitation is increased the jet spreading rate is increased, but beyond a saturation amplitude further increases have no effect on the spreading. The experimental results are compared with theoretical estimates. In the theory the flow is split into the mean flow, large scale motions, and fine scale turbulence. Shape assumptions for the mean flow, and fine scale turbulence along with the shape for the large scale motions obtained from a linear stability theory provide the closure. The experimental results compare reasonably well with predictions.
Raman, Ganesh↗
Saturation and the limit of jet mixing enhancement by single frequency plane wave excitation - Experiment and theory
The limitations of single frequency plane wave excitation in mixing enhancement are investigated for a circular jet. Measurements made in an 8.8 cm diameter jet are compared with a theoretical model. The measurements are made to quantify mixing at excitation amplitudes up to 2 percent of the jet exit velocity. The initial boundary layer state, the exit mean and fluctuating velocity profiles and spectra are documented for all cases considered. The amplitude of the fundamental wave is recorded along the jet axis for various levels of excitation. As the amplitude of excitation is increased the jet spreading rate is increased, but beyond a saturation amplitude further increases have no effect on the spreading. The experimental results are compared with theoretical estimates. In the theory the flow is split into the mean flow, large scale motions, and fine scale turbulence. Shape assumptions for the mean flow, and fine scale turbulence along with the shape for the large scale motions obtained from a linear stability theory provide the closure. The experimental results compare reasonably well with predictions.
Raman, Ganesh↗
On the propagation of plane waves above an impedance surface
The propagation of grazing incidence plane waves along a finite impedance boundary is investigated. A solution of the semi-infinite problem, where a harmonic motion, parallel to the boundary, is imposed along a line perpendicular to the boundary, is obtained. This solution consists of quasiplane waves, waves moving parallel to the boundary with amplitude and phase variations perpendicular to the boundary. Several approximations to the full solution are considered.
Zhong, F. H.↗
The use of the plane wave fluid-structure interaction loading approximation in NASTRAN
The Plane Wave Approximation (PWA) is widely used in finite element analysis to implement the loading generated by an underwater shock wave. The method required to implement the PWA in NASTRAN is presented along with example problems. A theoretical background is provided and the limitations of the PWA are discussed.
Dawson, R. L.↗
A high frequency analysis of electromagnetic plane wave scattering by perfectly-conducting semi-infinite parallel plate and rectangular waveguides with absorber coated inner walls
An approximate but sufficiently accurate high frequency solution which combines the uniform geometrical theory of diffraction (UTD) and the aperture integration (AI) method is developed for analyzing the problem of electromagnetic (EM) plane wave scattering by an open-ended, perfectly-conducting, semi-infinite hollow rectangular waveguide (or duct) with a thin, uniform layer of lossy or absorbing material on its inner wall, and with a planar termination inside. In addition, a high frequency solution for the EM scattering by a two dimensional (2-D), semi-infinite parallel plate waveguide with a absorber coating on the inner walls is also developed as a first step before analyzing the open-ended semi-infinite three dimensional (3-D) rectangular waveguide geometry. The total field scattered by the semi-infinite waveguide consists firstly of the fields scattered from the edges of the aperture at the open-end, and secondly of the fields which are coupled into the waveguide from the open-end and then reflected back from the interior termination to radiate out of the open-end. The first contribution to the scattered field can be found directly via the UTD ray method. The second contribution is found via the AI method which employs rays to describe the fields in the aperture that arrive there after reflecting from the interior termination. It is assumed that the direction of the incident plane wave and the direction of observation lie well inside the forward half space tht exists outside the half space containing the semi-infinite waveguide geometry. Also, the medium exterior to the waveguide is assumed to be free space.
Noh, H. M.↗
Reflection of plane waves from the flat boundary of a micropolar elastic half-space.
Reflection of plane waves from stress free flat surface of micropolar elastic half space, presenting reflection laws and amplitude ratios
Eringen, A. C.↗
Acoustic plane waves normally incident on a clamped panel in a rectangular duct
The theory of acoustic plane wave normally incident on a clamped panel in a rectangular duct is developed. The coupling theory between the elastic vibrations of the panel (plate) and the acoustic wave propagation in infinite space and in the rectangular duct is considered. The partial differential equation which governs the vibration of the panel (plate) is modified by adding to its stiffness (spring) forces and damping forces, and the fundamental resonance frequency and the attenuation factor are discussed. The noise reduction expression based on the theory is found to agree well with the corresponding experimental data of a sample aluminum panel in the mass controlled region, the damping controlled region, and the stiffness controlled region. All the frequency positions of the upward and downward resonance spikes in the sample experimental data are identified theoretically as resulting from four cross interacting major resonance phenomena: the cavity resonance, the acoustic resonance, the plate resonance, and the wooden back panel resonance.
Unz, H.↗
The scattering of obliquely incident plane waves from a corrugated conducting surface
A physical optics solution is presented for the scattering of plane waves from a perfectly conducting corrugated surface in the case of waves incident from an arbitrary direction and for an observer far from the surface. This solution is used to compute the radar cross section of the surface in the case of backscatter from irregular (i.e., stochastic) corrugations. An interesting feature of the solution is the occurrence of singularities in the scattered fields. These singularities appear to be a manifestation of focusing by the surface at its 'stationary' points. Whether or not the singularities occur in the solution depends on the manner in which one restricts the analysis to the far-field.
Surface waves↗
Theoretical calculation of plane wave speeds for alkali metals under pressure.
Theoretical calculations of the variation with pressure of small amplitude plane wave speeds are performed for sodium and potassium at zero temperature. The results obtained for wave speeds associated with volume dependent second-order elastic coefficients show better agreement with experimental data than for wave speeds associated with shear dependent coefficients. This result is believed to be due to omission of the band structure correction to the strain energy density.
Eftis, J.↗
Propagation of plane waves in a variable area duct carrying a compressible subsonic flow
A complete numerical solution is obtained for plane wave propagation in a variable-area duct which carries a mean compressible flow. The equation solved is a matrix formulation of the equations first derived by Tsien in 1952. Sample calculations are presented for four particular flow configurations: (1) a duct-nozzle-duct combination with the acoustic wave traveling with the flow, (2) a duct-nozzle-duct combination with the acoustic wave traveling against the flow, (3) an inlet-nozzle-duct configuration with the acoustic wave traveling against the flow, and (4) a duct-nozzle-exit configuration with the acoustic wave traveling with the flow. For each of these cases, the variation of energy flux with frequency is shown for particular geometry and flow condition.
Davis, S. S.↗
Attenuation of plane wave and higher order mode sound propagation in lined ducts
Perturbation method to obtain analytical expressions for attenuation of plane wave sound propagation in lined ducts
Doak, P. E.↗
Errors incurred in a plane-wave-type expansion of a Gaussian beam
The multipole expansion obtained by Morita et al. (1968) of the Gaussian laser beam used to levitate an aerosol particle in order that its complete phase matrix may be measured is compared with that of Tsai and Pogorzelski (1975) in order to demonstrate the effect of the incorrect expansion used by Morita. Errors incurred by the use of an equation in which one side satisfies the scalar wave equation while the other side does not and can be reduced to a plane wave amplitude are calculated as functions of the inverse of the wave number times the beam waist, the wave number times the radial spherical coordinate and the angular spherical coordinate. Errors on the order of a few percent, considered undetectable are obtained in the squared-field amplitudes due to the expansion, however, they are found to become significant (several tens of percent) when the angle is zero. It is concluded that the expansion of Morita should only be used in the regions where the spherical angle is less than 0.01 and its product with the wave number and the radial spherical coordinate is less than unity.
Kattawar, G. W.↗
Pulsed plane wave analytic solutions for generic shapes and the validation of Maxwell's equations solvers
Generic shapes are subjected to pulsed plane waves of arbitrary shape. The resulting scattered electromagnetic fields are determined analytically. These fields are then computed efficiently at field locations for which numerically determined EM fields are required. Of particular interest are the pulsed waveform shapes typically utilized by radar systems. The results can be used to validate the accuracy of finite difference time domain Maxwell's equations solvers. A two-dimensional solver which is second- and fourth-order accurate in space and fourth-order accurate in time is examined. Dielectric media properties are modeled by a ramping technique which simplifies the associated gridding of body shapes. The attributes of the ramping technique are evaluated by comparison with the analytic solutions.
Yarrow, Maurice↗
Analytically reduced form for the class of integrals containing multicenter products of 1s hydrogenic orbitals, Coulomb or Yukawa potentials, and plane waves
The class of integrals containing the product of N 1s hydrogenic orbitals and M Coulomb or Yukawa potentials with m plane waves is investigated analytically. The results obtained by Straton (1989) are extended and generalized. It is shown that the dimensionality of the entire class can be reduced from 3m to M+N-1.
Straton, Jack C.↗
Scattering from a moving spherical particle by two crossed coherent plane waves
The Mie scattering properties of a homogeneous, isotropic spherical particle, moving at a constant velocity and illuminated by two intersecting coherent plane waves having the same polarization direction, have been analyzed based upon an exact solution to Maxwell's equations. The solutions are in a form suitable for the calculation of the time varying scattered signal integrated across a detector aperture of variable size that is centered on either the forward or backward scattering direction. This problem is of importance in defining the scattered signal in a cross beam laser Doppler velocimeter (LDV). Results obtained from calculating the integrated scattered signal indicate a strong dependence upon the following physical parameters: particle size, index of refraction, cross beam angle, and collection solid angle.
Chu, W. P.↗
Gravitational scattering of zero-rest-mass plane waves
The Feyman-diagram technique is used to calculate the differential cross sections for the scattering of zero-rest-mass plane waves of spin 0, 1, and 2 by linearized Schwarzschild and Kerr geometries in the long-wavelength weak-field limit. It is found that the polarization of right (or left) circularly polarized electromagnetic waves is unaffected by the scattering process (i.e., helicity is conserved) and that the two helicity (polarization) states of the photon are scattered differently by the Kerr geometry. This coupling between the photon helicity and the angular momentum of the scatterer also leads to a partial polarization of unpolarized incident light. For gravitational waves, on the other hand, there is neither helicity conservation nor helicity-dependent scattering; the angular momentum of the scatterer has no polarizing effect on incident unpolarized gravitational waves.
De Logi, W. K.↗