An approximate treatment of high-frequency scattering

1957 ◽  
Vol 53 (3) ◽  
pp. 691-701 ◽  
Author(s):  
D. S. Jones ◽  
G. B. Whitham
Keyword(s):  
Approximate Method ◽  
Energy Flux ◽  
Incident Wave ◽  
High Frequency ◽  
Harmonic Wave ◽  
Incident Beam ◽  
Scattered Wave ◽  
The Body ◽  
Scattering Coefficient ◽  
Wave Number

In some recent work Kodis* considers the scattering of a plane harmonic wave by a circular cylinder and uses variational methods to deduce an asymptotic formula for the scattering coefficient in the case of high-frequency waves. The scattering coefficient, σ, is denned as the total energy flux outward from the cylinder in the scattered wave divided by the energy flux in the beam of the incident wave which falls on the cylinder. In the limit, of geometrical optics, the scattered wave is made up of a wave reflected from the forward half of the cylinder with energy flux equal to that in the incident beam, and a wave behind the cylinder cancelling the incident wave there to form the shadow. Thus σ → 2 as ka → ∞, k being the wave number of the incident wave and a the radius of the cylinder. The next term in the asymptotic expansion for σ is proportional to . It has been determined already from the exact series expression for the field by White (6), Wu and Rubinow (7) and Kear (3). But Kodis gives an approximate method which also supplies this result and, since the coefficient is in good agreement with the values obtained from the exact solution, concludes that his approximate procedure could also be used for more general obstacles. In the present paper, we propose an alternative approximate method which is related to the one given by Kodis but is very much simpler. Also we go on to obtain the correction terms for general obstacles in detail. Various writers (see, for example, Keller (4) and van de Hulst(8)) have suggested previously that the correction is still proportional to , where a is some length defined by the body shape. However, the determination of a and of the numerical coefficient has been limited to two-dimensional obstacles.

Wave Forcing and Wave Scattering From a Vertical Surface-Piercing Cylinder

2005 ◽  
Author(s):  
Chris Swan ◽  
Stephen Masterton ◽  
Rizwan Sheikh ◽  
Alessandra Cavalletti
Keyword(s):  
High Frequency ◽  
Harmonic Wave ◽  
Laboratory Data ◽  
Perturbation Expansion ◽  
Vertical Cylinder ◽  
Scattered Wave ◽  
Vertical Surface ◽  
The Body ◽  
Wave Forces ◽  
High Frequency Waves

This paper concerns the nonlinear, higher-harmonic, wave-forces acting on a vertical surface-piercing cylinder. New laboratory data is presented which confirms that in the case a vertical cylinder, the diameter of which is large but not sufficiently large that the body lies within the linear diffraction regime, the second- and third-harmonic forces are not well described by existing models. This is particularly apparent when the incident waves are steep and have a relatively small wave period. Indeed, under these conditions the second-, third- and fourth-harmonic forces are shown to be comparable in size. This is clearly at odds with the results of a traditional perturbation expansion. An explanation for this lies in the nature of the scattered wave field, particularly the high-frequency waves identified by Sheikh & Swan [1]. The phasing of these scattered waves are, at least in part, dependent upon the motion of the fluid around the circumference of the cylinder and will not therefore be captured by a series solution based solely on the harmonics of the incident wave motion. The paper considers several test cases, fully exploring the correlation between the nonlinear forcing and the high-frequency scattering. The practical implications of these results are also addressed.

Theory of Short Wave Excitation

1986 ◽  
Vol 30 (03) ◽  
pp. 147-152
Author(s):  
Yong Kwun Chung
Keyword(s):  
Incident Wave ◽  
Characteristic Length ◽  
Finite Depth ◽  
Short Wave ◽  
The Body ◽  
Wave Number ◽  
Floating Body ◽  
Wave Excitation ◽  
Exciting Forces ◽  
Wave Exciting Forces

When the wavelength of the incident wave is short, the total surface potential on a floating body is found to be 2∅ i & O (m-l∅ i) on the lit surface and O (m-l∅ j) on the shadow surface where ~b i is the potential of the incident wave and m the wave number in water of finite depth. The present approximation for wave exciting forces and moments is reasonably good up to X/L ∅ 1 where h is the wavelength and L the characteristic length of the body.

The reflexion of internal/inertial waves from bumpy surfaces

1971 ◽  
Vol 46 (2) ◽  
pp. 273-291 ◽  
Author(s):  
P. G. Baines
Keyword(s):  
Plane Wave ◽  
Energy Flux ◽  
Incident Wave ◽  
Wave Number ◽  
Inertial Waves ◽  
Incident Wavelength ◽  
Reflected Wave ◽  
Incident Plane ◽  
The Difference ◽  
Reflecting Surface

When internal and/or inertial waves reflect from a smooth surface which is not plane, there is in general some energy flux which is ‘back-reflected’ in the opposite direction to that of the incident energy flux (in addition to that ‘transmitted’ in the direction of the reflected rays), provided only that the incident wavelength is sufficiently large in comparison with the length scales of the reflecting surface. The reflected wave motion due to an incident plane wave is governed by a Fredholm integral equation whose kernel depends on the form of the reflecting surface. Some specific examples are discussed, and the special case of the ‘linearized boundary’ is considered in detail. For an incoming plane wave incident on a sinusoidally varying surface of sufficiently small amplitude, in addition to the main reflected wave two new waves are generated whose wave-numbers are the sum and difference respectively of those of the surface perturbations and the incident wave. If the incident wave-number is the smaller, the difference wave is back-reflected.

Reflection and Refraction of a Harmonic SH Wave at the Interface of Two Dissimilar Media With MicroHeterogeneity

2012 ◽  
Vol 79 (6) ◽  
Author(s):  
Burhanettin S. Altan
Keyword(s):  
Incident Wave ◽  
Critical Angle ◽  
Harmonic Wave ◽  
Classical Case ◽  
Wave Number ◽  
Sh Wave ◽  
Sh Waves ◽  
Reflection And Refraction ◽  
Strain Relationship ◽  
The Media

Reflection and refraction of harmonic SH-waves from the interface of two dissimilar media with microheterogeneity is studied. The effect of the microheterogeneity on the overall behavior of the media is taken into account by adding higher order displacement gradients in the stress-strain relationship. It is found that a harmonic wave reflects back with the same angle of the incident wave, like in a classical case. However, it is found that the direction of propagation of the refracted wave is dependent on the wave number. It is also shown that the critical angle for which the incident wave cannot be transmitted to the other half plane is dependent on the wave number.

Inversion of Wave-number Spectrum from Simulated Bistatic High-frequency Radar Data

2011 ◽  
Vol 33 (10) ◽  
pp. 2477-2482
Author(s):  
Huan He ◽  
Heng-yu Ke ◽  
Xian-rong Wan ◽  
Fang-zhi Geng
Keyword(s):  
High Frequency ◽  
Radar Data ◽  
Wave Number ◽  
High Frequency Radar

High Frequency Vibration Analysis of Automotive Body Panels with Damping Materials

2010 ◽  
Vol 36 ◽  
pp. 293-296
Author(s):  
Yoshio Kurosawa ◽  
Takao Yamaguchi
Keyword(s):  
High Frequency ◽  
Large Scale ◽  
The Body ◽  
Viscoelastic Damping ◽  
Fe Model ◽  
Test Results ◽  
Automotive Body ◽  
Modal Damping ◽  
Practical Tool ◽  
Damping Materials

We have developed a technique for estimating vibrations of an automotive body structures with viscoelastic damping materials using large-scale finite element (FE) model, which will enable us to grasp and to reduce high-frequency road noise（200～500Hz）. In the new technique, first order solutions for modal loss factors are derived applying asymptotic method. This method saves calculation time to estimate modal damping as a practical tool in the design stages of the body structures. Frequency responses were calculated using this technique and the results almost agreed with the test results. This technique can show the effect of the viscoelastic damping materials on the automotive body panels, and it enables the more efficient layout of the viscoelastic damping materials. Further, we clarified damping properties of the automotive body structures under coupled vibration between frames and panels with the viscoelastic damping materials.

A dynamic model for far-field acceleration

1982 ◽  
Vol 72 (4) ◽  
pp. 1049-1068
Author(s):  
John Boatwright
Keyword(s):  
Stress Drop ◽  
High Frequency ◽  
Dynamic Stress ◽  
The Body ◽  
Body Waves ◽  
Far Field ◽  
Rupture Velocity ◽  
Frequency Level ◽  
Average Change ◽  
Dynamic Stress Drop

abstract A model for the far-field acceleration radiated by an incoherent rupture is constructed by combining Madariaga's (1977) theory for the high-frequency radiation from crack models of faulting with a simple statistical source model. By extending Madariaga's results to acceleration pulses with finite durations, the peak acceleration of a pulse radiated by a single stop or start of a crack tip is shown to depend on the dynamic stress drop of the subevent, the total change in rupture velocity, and the ratio of the subevent radius to the acceleration pulse width. An incoherent rupture is approximated by a sample from a self-similar distribution of coherent subevents. Assuming the subevents fit together without overlapping, the high-frequency level of the acceleration spectra depends linearly on the rms dynamic stress drop, the average change in rupture velocity, and the square root of the overall rupture area. The high-frequency level is independent, to first order, of the rupture complexity. Following Hanks (1979), simple approximations are derived for the relation between the rms dynamic stress drop and the rms acceleration, averaged over the pulse duration. This relation necessarily depends on the shape of the body-wave spectra. The body waves radiated by 10 small earthquakes near Monticello Dam, South Carolina, are analyzed to test these results. The average change of rupture velocity of Δv = 0.8β associated with the radiation of the acceleration pulses is estimated by comparing the rms acceleration contained in the P waves to that in the S waves. The rms dynamic stress drops of the 10 events, estimated from the rms accelerations, range from 0.4 to 1.9 bars and are strongly correlated with estimates of the apparent stress.

The locust jump. I. The motor programme

1977 ◽  
Vol 66 (1) ◽  
pp. 203-219
Author(s):  
W. J. Heitler ◽  
M. Burrows
Keyword(s):  
High Frequency ◽  
Tactile Stimulation ◽  
The Body ◽  
Flexor Muscle ◽  
Tactile Stimuli ◽  
Extensor Muscles ◽  
Trigger Activity ◽  
Three Stages ◽  
Motor Programme ◽  
Made In

A motor programme is described for defensive kicking in the locust which is also probably the programme for jumping. The method of analysis has been to make intracellular recordings from the somata of identified motornuerones which control the metathoracic tibiae while defensive kicks are made in response to tactile stimuli. Three stages are recognized in the programme. (1) Initial flexion of the tibiae results from the low spike threshold of tibial flexor motorneurones to tactile stimulation of the body. (2) Co-contraction of flexor and extensor muscles followa in which flexor and extensor excitor motoneurones spike at high frequency for 300-600 ms. the tibia flexed while the extensor muscle develops tension isometrically to the level required for a kick or jump. (3) Trigger activity terminates the co-contraction by inhibiting the flexor excitor motorneurones and simultaneously exciting the flexor inhibitors. This causes relaxation of the flexor muscle and allows the tibiae to extend. If the trigger activity does not occur, the jump or kick is aborted, and the tibiae remain flexed.

An Improved Body-Exact Method to Predict Large Amplitude Ship Roll Responses

2018 ◽  
Author(s):  
Rahul Subramanian ◽  
Naga Venkata Rakesh ◽  
Robert F. Beck
Keyword(s):  
Incident Wave ◽  
Large Amplitude ◽  
Nonlinear Models ◽  
Body Position ◽  
Computational Cost ◽  
Offshore Structures ◽  
The Body ◽  
Surface Boundary ◽  
Strip Theory ◽  
New Formulation

Accurate prediction of the roll response is of significant practical relevance not only for ships but also ship type offshore structures such as FPSOs, FLNGs and FSRUs. This paper presents a new body-exact scheme that is introduced into a nonlinear direct time-domain based strip theory formulation to study the roll response of a vessel subjected to moderately large amplitude incident waves. The free surface boundary conditions are transferred onto a representative incident wave surface at each station. The body boundary condition is satisfied on the instantaneous wetted surface of the body below this surface. This new scheme allows capturing nonlinear higher order fluid loads arising from the radiated and wave diffraction components. The Froude-Krylov and hydrostatic loads are computed on the intersection surface of the exact body position and incident wave field. The key advantage of the methodology is that it improves prediction of nonlinear hydrodynamic loads while keeping the additional computational cost small. Physical model tests have been carried out to validate the computational model. Fairly good agreement is seen. Comparisons of the force components with fully linear and body-nonlinear models help in bringing out the improvements due to the new formulation.

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