Discrete Representation of the Fourier Integral Transform

2020 ◽  
Author(s):  
Leonid P. Yaroslavsky
Keyword(s):  
Integral Transform ◽  
Fourier Integral ◽  
Discrete Representation ◽  
Fourier Integral Transform

Effects of Interleaves on Fracture of Laminated Composites: Part I—Analysis

1990 ◽  
Vol 57 (1) ◽  
pp. 168-174 ◽  
Author(s):  
A. K. Kaw ◽  
J. G. Goree
Keyword(s):  
Composite Laminates ◽  
Integral Transform ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Elastic Media ◽  
Two Dimensional ◽  
Shear Moduli ◽  
Fourier Integral Transform ◽  
Shaped Crack ◽  
Symmetric Crack

The influence of placing interleaves between fiber-reinforced plies in multilayered composite laminates is investigated. The geometry of the composite is idealized as a two-dimensional, isotropic, linearly elastic media consisting of a damaged layer bonded between two half-planes and separated by thin interleaves of low extensional and shear moduli. The damage in the layer is taken in the form of a symmetric crack perpendicular to the interface. The case of an H-shaped crack in the form of a broken layer with delamination along the interface is also analyzed. Fourier integral transform techniques are used to develop the solutions in terms of singular integral equations.

Transient Response of a Periodically Supported Cylindrical Shell Immersed in a Fluid Medium

1965 ◽  
Vol 32 (3) ◽  
pp. 562-568 ◽  
Author(s):  
Harry Herman ◽  
J. M. Klosner
Keyword(s):  
Cylindrical Shell ◽  
Integral Transform ◽  
Circular Cylindrical Shell ◽  
Fourier Integral ◽  
Cylindrical Wave ◽  
Acoustic Medium ◽  
Steel Shell ◽  
Fluid Medium ◽  
Wave Approximation ◽  
Fourier Integral Transform

The dynamic response of a periodically simply supported, infinitely long, circular cylindrical shell to a pressure suddenly applied through the surrounding acoustic medium is investigated. The incident particle velocity is zero, and the pressure is assumed to have a harmonic spatial variation parallel to the shell axis. The exact solution is obtained by use of a Fourier integral transform, and the resulting inversion integral is evaluated by numerical and asymptotic integration. Two solutions to the same problem are obtained by using a plane and cylindrical wave approximation for the radiated field. The range of their applicability is investigated. For a steel shell in water ccs2=0.08815 it is found that, when the supports are placed three shell diameters apart, the use of the cylindrical wave approximation results in a 5-percent underestimation of the maximum deflection, while when the supports are placed one sixth of a shell diameter apart, the approximations are invalid.

The fourier integral transform on nilpotent lie groups

1983 ◽  
Vol 8 (6) ◽  
pp. 667-691 ◽  
Author(s):  
Nghiěn XU[acaron]n Hai
Keyword(s):  
Lie Groups ◽  
Integral Transform ◽  
Fourier Integral ◽  
Nilpotent Lie Groups ◽  
Fourier Integral Transform

On the theory of the diffraction of a plane wave by a large perfectly conducting circular cylinder

1961 ◽  
Vol 264 (1317) ◽  
pp. 235-245 ◽  
Keyword(s):  
Circular Cylinder ◽  
Plane Wave ◽  
Boundary Value Problem ◽  
Cross Section ◽  
Integral Transform ◽  
Forward Direction ◽  
Fourier Integral ◽  
Straightforward Application ◽  
Total Scattering Cross Section ◽  
Fourier Integral Transform

The solution is obtained by a method somewhat different from those previously given by other authors. The method is in principle a straightforward application of Fourier integral transform analysis to a boundary-value problem, and is shown to lead rather naturally to the various field representations suitable for different regions, including that at infinity in the forward direction which gives the total scattering cross-section. No new results are obtained in the present paper, but mention is made of other problems which have subsequently been successfully attacked on the basis of the method given.

Interaction between an Embedded Crack and an Interface Crack in Nonhomogeneous Coating System

2005 ◽  
Vol 492-493 ◽  
pp. 397-402
Author(s):  
E.E. Theotokoglou ◽  
Glaucio H. Paulino
Keyword(s):  
Coordinate System ◽  
Half Plane ◽  
Stress Condition ◽  
Integral Transform ◽  
Local Coordinate System ◽  
Fourier Integral ◽  
Plane Stress Condition ◽  
Transform Method ◽  
Fourier Integral Transform ◽  
Embedded Crack

A general methodology is constructed for the fundamental solution of a crack in the homogeneous half-plane interacting with a crack at the interface between the homogeneous elastic half-plane and the nonhomogeneous elastic coating in which the shear modulus varies exponentially with one coordinate. The problem is solved under plane strain or generalized plane stress condition using the Fourier integral transform method. The stress field in the homogeneous half plane is evaluated by the superposition of two states of stresses, one is associated with a local coordinate system in the infinite fractured plate, while the other in the infinite half plane defined in a structural coordinate system.

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