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  • 1
    Electronic Resource
    Electronic Resource
    On the boundary conditions for ultrasonic transmission by partially closed cracks (1991)
    Springer
    Journal of nondestructive evaluation 10 (1991), S. 139-149 
    Details
    ISSN: 1573-4862
    Keywords: Closed cracks ; ultrasonics ; reflection and transmission ; coefficients ; effective boundary conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract The probability of detecting crack-like defects using ultrasonic techniques can be severely reduced if the crack is closed by a static background pressure. In this paper, we model the contacting faces of a partially closed crack by an array of circular spot-welds randomly distributed over an infinite plane. We give an exact derivation of the reflection and transmission coefficients for a plane elastic wave at such a boundary in terms of the mean interfacial stresses. The latter are estimated in the limit when the contact radius is much smaller than the wavelength and the contacts are sparsely distributed. This calculation is then related to a distributed spring model of the interface. The latter replaces the real interface by an effective homogeneous linear boundary condition which relates the crack opening displacement to the boundary stresses by effective stiffnesses. These unknown parameters are chosen to ensure that the model condition predicts the exact values of the mean interfacial stresses and the reflection and transmission coefficients in the limit already described. Our results are consistent with and complement those of Baik and Thompson(1) who introduced the distributed spring model in this and a number of other contexts. Our analysis provides a systematic assessment of the range of validity of the model and suggests ways in which the present estimates may be improved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00567096
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A comparison of exact first order and spring boundary conditions for scattering by thin layers (1992)
    Springer
    Journal of nondestructive evaluation 11 (1992), S. 175-184 
    Details
    ISSN: 1573-4862
    Keywords: Elastic waves ; thin layers ; spring boundary conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract In scattering problems for time-harmonic elastic waves, thin elastic layers are often of interest, e.g., in laminates. Various ways of substituting such layers by some effective boundary conditions have been proposed, and these are briefly reviewed. A rational way of obtaining boundary conditions that are exact to first order in the layer thickness is then described. For a thin spherical layer numerical comparisons are performed between these “exact” first order boundary conditions, the commonly used spring boundary conditions and the exact solution, and it is shown that the “exact” boundary conditions are far superior to the spring boundary conditions in most situations. A drawback with the “exact” boundary conditions is that they are quite complicated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00566408
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Surface waves on the periodic boundary of an elastic half space (1982)
    Springer
    Flow, turbulence and combustion 39 (1982), S. 129-142 
    Details
    ISSN: 1573-1987
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The existence of free surface waves on the periodic boundary of an elastic half space is established. These waves are a generalization of Rayleigh waves, and they can propagate both along and — at low frequencies and small profile heights — normal to the ridges of the periodic surface (periodic in one direction and constant in the other). It is shown how the wave number depends on the height and shape of the periodic surface, the frequency, and the direction of propagation. To give a further insight into behaviour of the surface waves some computations of surface displacements are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00457015
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    Paper (German National Licenses)
    Fulltext
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