Axisymmetric Elastic Waves Excited by a Point Source in a Plate

1982 ◽  
Vol 49 (4) ◽  
pp. 821-836 ◽  
Author(s):  
R. L. Weaver ◽  
Yih-Hsing Pao
Keyword(s):  
Point Source ◽  
Stationary Phase ◽  
Elastic Plate ◽  
Elastic Waves ◽  
Normal Modes ◽  
Integral Transforms ◽  
Far Field ◽  
Exact Results ◽  
Ray Theory ◽  
Vertical Step

The response of an infinite elastic plate to dynamic loading is presented by the method of superposition of normal modes, a method particularly appropriate in the intermediate and far field. The method is compared with the method of integral transforms. Explicit expressions are given for the case of loading by a concentrated vertical step force. These expressions are evaluated numerically over a range of distances from 4 to 40 plate thicknesses. The numerical results are compared with qualitative stationary phase analyses and with the exact results of generalized ray theory.

Experimental investigation of aerofoil tonal noise at low Mach number

2021 ◽  
Vol 932 ◽  
Author(s):  
Prateek Jaiswal ◽  
Yann Pasco ◽  
Gyuzel Yakhina ◽  
Stéphane Moreau
Keyword(s):  
Experimental Investigation ◽  
Mach Number ◽  
Three Dimensional ◽  
Normal Modes ◽  
Wall Pressure ◽  
Far Field ◽  
Tonal Noise ◽  
Trailing Edge ◽  
Modal Shape ◽  
Low Mach Number

This paper presents an experimental investigation of aerofoil tones emitted by a controlled-diffusion aerofoil at low Mach number ( $0.05$ ), moderate Reynolds number based on the chord length ( $1.4 \times 10^{5}$ ) and moderate incidence ( $5^{\circ }$ angle of attack). Wall-pressure measurements have been performed along the suction side of the aerofoil to reveal the acoustic source mechanisms. In particular, a feedback loop is found to extend from the aerofoil trailing edge to the regions near the leading edge where the flow encounters a mean favourable pressure gradient, and consists of acoustic disturbances travelling upstream. Simultaneous wall-pressure, velocity and far-field acoustic measurements have been performed to identify the boundary-layer instability responsible for tonal noise generation. Causality correlation between far-field acoustic pressure and wall-normal velocity fluctuations has been performed, which reveals the presence of a Kelvin–Helmholtz-type modal shape within the velocity disturbance field. Tomographic particle image velocimetry measurements have been performed to understand the three-dimensional aspects of this flow instability. These measurements confirm the presence of large two-dimensional rollers that undergo three-dimensional breakdown just upstream of the trailing edge. Finally, modal decomposition of the flow has been carried out using proper orthogonal decomposition, which demonstrates that the normal modes are responsible for aerofoil tonal noise. The higher normal modes are found to undergo regular modulations in the spanwise direction. Based on the observed modal shape, an explanation of aerofoil tonal noise amplitude reduction is given, which has been previously reported in modular or serrated trailing-edge aerofoils.

Response of a Plate Supported by a Fluid Half Space to a Moving Pressure

1970 ◽  
Vol 37 (4) ◽  
pp. 1050-1054 ◽  
Author(s):  
D. H. Y. Yen ◽  
C. C. Chou
Keyword(s):  
Half Space ◽  
Elastic Plate ◽  
Plate Theory ◽  
Fluid Pressure ◽  
Integral Transforms ◽  
Classical Plate Theory ◽  
Plate Deflection

The response of an elastic plate supported by a fluid half space to a steadily moving pressure is studied. The Timoshenko plate theory is used in the study. By the method of integral transforms, solutions for both the plate deflection and the interaction fluid pressure are obtained. The results are then compared in detail with those obtained previously using the classical plate theory.

Multiple scattering of plane harmonic elastic waves in an infinite solid by an arbitrary configuration of obstacles

1969 ◽  
Vol 66 (2) ◽  
pp. 469-480 ◽  
Author(s):  
P. J. Barratt
Keyword(s):  
Scattering Amplitudes ◽  
Integral Equations ◽  
Multiple Scattering ◽  
Elastic Waves ◽  
Iterative Procedure ◽  
Elastic Solid ◽  
Single Scattering ◽  
Far Field ◽  
Rigid Spheres ◽  
Arbitrary Configuration

AbstractThe multiple scattering of plane harmonic P and S waves in an infinite elastic solid by arbitrary configurations of obstacles is considered. Integral equations relating the far-field multiple scattering amplitudes to the corresponding single scattering functions are obtained and asymptotic solutions are found by an iterative procedure. The scattering of a plane harmonic P wave by two identical rigid spheres is investigated.

Etude numérique des modes et fréquences propres d'une cavité à l'aide de la fonction de Green

1979 ◽  
Vol 57 (2) ◽  
pp. 208-217
Author(s):  
Jacques A. Imbeau ◽  
Byron T. Darling
Keyword(s):  
Point Source ◽  
Green’S Function ◽  
Green's Function ◽  
Normal Modes ◽  
Preceding Paper ◽  
Double Precision ◽  
Prolate Spheroidal ◽  
Normal Functions ◽  
Normal Frequency ◽  
High Degree

We apply the methods developed in our preceding paper (J. A. Imbeau and B. T. Darling. Can. J. Phys. 57, 190(1979)) for calculating the Green's function of a cavity to obtain the normal modes and normal frequencies of the cavity. As the frequency of the driving point source approaches that of a normal frequency the response (Green's function) of the cavity becomes infinite, and the form of the Green's function is dominated by the normal mode. There is also a 180° reversal of phase in passing through a resonance. In this way, we are able to calculate the normal frequencies of prolate spheroidal cavities to the full precision employed in the calculations (16 significant digits for double precision of the IBM-370). The Green's functions and the normal functions are also obtainable to a high degree of precision, except in the immediate vicinity of the surface of the cavity where they suffer a well-known discontinuity.

scholarly journals Excitation of normal modes of a thin elastic plate by moving dislocations

Wave Motion ◽  
1999 ◽  
Vol 29 (1) ◽  
pp. 35-46
Author(s):  
Rodrigo Arias ◽  
Fernando Lund
Keyword(s):  
Elastic Plate ◽  
Normal Modes ◽  
Thin Elastic Plate

A topology optimisation for far-field characteristics of elastic waves scattered from periodic structures

2018 ◽  
Vol 2018.13 (0) ◽  
pp. 103
Author(s):  
Kei MATSUSHIMA ◽  
Hiroshi ISAKARI ◽  
Toru TAKAHASHI ◽  
Toshiro MATSUMOTO
Keyword(s):  
Elastic Waves ◽  
Periodic Structures ◽  
Topology Optimisation ◽  
Far Field

Seismic source decomposition

Geophysics ◽  
1983 ◽  
Vol 48 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Paul L. Stoffa ◽  
Anton Ziolkowski
Keyword(s):  
Point Source ◽  
Spectral Characteristics ◽  
Patent Application ◽  
Power Spectra ◽  
Seismic Source ◽  
Three Dimensions ◽  
Far Field ◽  
Air Gun ◽  
Power Spectral ◽  
Directional Characteristics

We exploit the differences that exist between the radiation fields of a point source and an array to design a time‐separated marine seismic source array with desired power spectral and directional characteristics, whose far‐field time signature is known precisely from measurements. The desired power spectral characteristics are created by firing a predetermined series of point source units sequentially, such that their time signatures do not overlap. The effective power spectrum of the whole series of time‐distributed signatures can be made to approximate the sum of the power spectra of the individual signatures and can, therefore, be designed to suit the desired application by the appropriate choice of source units. The desired directional characteristics of the array can be created by arranging the source unit separations such that each source unit reaches the desired spatial position at the prescribed firing instant. The key to the subsequent processing of the recorded data is to measure the pressure wave generated by each point source unit with a hydrophone placed close by, but in the linear radiation field. The position of this hydrophone relative to the source unit must be known accurately in all three dimensions. The depths of the source units and their relative spatial positions at the instants of firing must also all be known. From these measurements the far‐field signature of the sequence in any azimuth can be deduced, and the impulse response of the earth can be recovered by dividing the Fourier frequency spectrum of the recorded reflection data by that of the measured source unit sequence. This process is completely deterministic in nature and depends primarily upon our ability to monitor accurately the far‐field signature of each source unit. Field results from an initial evaluation of this method indicate that this measurement can be readily accomplished. The success of this technique is then ultimately dependent on the signal to noise ratio. [This method is the subject of a patent application.] We stress that, since the signature is known, we are not obliged to make any assumptions about the phase. In particular, we do not need to make the minimum‐phase assumption. We are therefore free to choose our parameters to optimize our desired power spectral and directional characteristics with complete disregard for the conventional requirement that the signature of an air gun source have a high primary‐to‐bubble ratio.

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