Linear theory of gravitational wave propagation in a magnetized, relativistic Vlasov plasma

2010 ◽  
Vol 82 (12) ◽  
Author(s):  
Mats Forsberg ◽  
Gert Brodin
Keyword(s):  
Wave Propagation ◽  
Gravitational Wave ◽  
Linear Theory ◽  
Vlasov Plasma

Wave Propagation in the Linear Theory of Elastic Shells

1976 ◽  
Vol 43 (2) ◽  
pp. 281-285 ◽  
Author(s):  
H. Cohen
Keyword(s):  
Wave Propagation ◽  
Circular Cylinder ◽  
Linear Theory ◽  
Wave Mode ◽  
Mode Shapes ◽  
Elastic Shells ◽  
Special Cases ◽  
Cosserat Surface ◽  
Singular Wave ◽  
The Right

The problem of wave propagation in elastic shells within the framework of a linear theory of a Cosserat surface is treated using the method of singular wave curves. The equations for determining the speeds of propagation and their associated wave mode shapes are obtained in a form involving the speeds of propagation in Cosserat plates and the curvature of the shell. A number of special cases in which the speeds and mode shapes simplify are considered. In particular, these special cases are shown to include as examples, certain systems of waves in elastic shells whose middle surfaces are the surface of revolution, the circular cylinder, the sphere, and the right helicoid.

scholarly journals Gaussian processes reconstruction of modified gravitational wave propagation

2020 ◽  
Vol 101 (6) ◽  
Author(s):  
Enis Belgacem ◽  
Stefano Foffa ◽  
Michele Maggiore ◽  
Tao Yang
Keyword(s):  
Wave Propagation ◽  
Gravitational Wave ◽  
Gaussian Processes

Surface waves on water of non-uniform depth

1958 ◽  
Vol 4 (6) ◽  
pp. 607-614 ◽  
Author(s):  
Joseph B. Keller
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Linear Theory ◽  
Gravity Waves ◽  
Geometrical Optics ◽  
Surface Wave Propagation ◽  
Special Cases

Gravity waves occur on the surface of a liquid such as water, and the manner in which they propagate depends upon its depth. Although this dependence is described in principle by the equations of the ‘exact linear theory’ of surface waves, these equations have not been solved except in some special cases. Therefore, oceanographers have been unable to use the theory to describe surface wave propagation in water whose depth varies in a general way. Instead they have employed a simplified geometrical optics theory for this purpose (see, for example, Sverdrup & Munk (1944)). It has been used very successfully, and consequently various attempts, only partially successful, have been made to deduce it from the exact linear theory. It is the purpose of this article to present a derivation which appears to be satisfactory and which also yields corrections to the geometrical optics theory.

WAVE PROPAGATION ON AN ELASTIC BEAM TRAVELING IN A TUBE: LINEAR THEORY OF AERODYNAMIC LOADING

2001 ◽  
Vol 09 (03) ◽  
pp. 1227-1236 ◽  
Author(s):  
N. SUGIMOTO ◽  
K. KUGO
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Linear Theory ◽  
Elastic Beam ◽  
Flexural Wave ◽  
Wave Approximation ◽  
Aerodynamic Loading ◽  
Long Wave ◽  
Characteristic Wavelength ◽  
Long Wave Approximation

Linear theory is developed of flexural wave motions of an elastic beam of circular cross-section traveling along its axial direction at a constant speed in an air-filled, circular tube placed coaxially. The beam is constrained to deflect in a plane and is subjected to a restoring force in proportion to the magnitude of deflection. Both beam and tube are assumed to be long enough for end effects to be ignored. Taking account of aerodynamic loading on the lateral surface of the beam, wave propagation is examined under a long-wave approximation that a characteristic wavelength of flexural waves is much longer than the tube's radius. Using the lossless, acoustic wave equation for the velocity potential of the air, and the classical, flexural wave equation for the deflection of the beam, an asymptotic-expansion method is applied based on the long-wave approximation. A linear wave equation for the deflection is derived and its dispersion relation is examined by comparing with the exact one derived previously without any long-wave approximation. Higher-order effects of the axial curvature of the beam and the compressibility of air on the aerodynamic loading are also discussed.

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