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  • 1
    Electronic Resource
    Electronic Resource
    Self-similar solutions of some nonlinear equations (1970)
    Springer
    Flow, turbulence and combustion 22 (1970), S. 449-461 
    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 method of group invariance under an infinitesimal transformation is applied to a class of nonlinear partial differential equations. Besides yielding a large number of known forms of self-similar solutions, the method also gives new types of solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00400548
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  • 2
    Electronic Resource
    Electronic Resource
    Linear dispersive shear waves in two-layer elastic medium (1973)
    Springer
    Flow, turbulence and combustion 27 (1973), S. 451-462 
    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 In linear isotropic elasticity, cases exist where pure shear waves are possible even in bounded media; these have a nondispersive mode with propagation speed equal to that in an infinite medium. For these cases, consideration of a two-layer medium shows the existence of dispersion which vanishes only with equality of the propagation speeds. The present study uses the method of asymptotic expansions; a uniformly valid approximation is obtained to describe the speed and dispersive nature of these waves. The elegance of this approach is brought out by derivation of the basic result of this study viz., Jeffrey equation to describe the farfield structure of these waves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00382507
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  • 3
    Electronic Resource
    Electronic Resource
    Longitudinal waves in two-layered solid circular cylinder (1976)
    Springer
    Acta mechanica 24 (1976), S. 13-24 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Zusammenfassung Die Methode der asymptotischen Entwicklung wird zur Aufstellung einer Theorie der Wellenfortpflanzung in einem festen Zylinder aus zwei Schichten von verschiedenem elastischem Material verwendet. Die Wellengeschwindigkeit wird vom Verhältnis der Summe der Produkte von Flächen und effektiven Moduln und der Summe der Produkte von Flächen und Dichten bestimmt. Allerdings gehen die effektiven Moduln für gleiche Poisson-Zahlen in die Elastizitätsmoduln über. Die nächste, die Streuwellenbewegung beschreibende Näherung wird ferner von der Differenz der Wellengeschwindigkeiten in den beiden Schichten beeinflußt. Diese Wellengeschwindigkeit ist das Verhältnis des effektiven Moduls zur Dichte. Es zeigt sich, daß in der formalen Lösung Säkularglieder auftreten. Für den Fall einer Wanderwelle wird eine gleichförmig geltende Lösung dieser Ordnung angegeben.
    Notes: Summary The method of asymptotic expansions is used to construct a theory of wave-propagation along a solid cylinder made up of two layers of different elastic materials. Wave speed is determined by the ratio of the sum of the area times the effective moduli to that of the area times the densities. However, the effective modulus reduces to Youngs' modulus only if Poisson ratios are equal. The higher approximation, describing dispersive wave-motion, is further affected by the difference in wave-speeds for the two layers. This wave-speed is the ratio of effective modulus to density. The formal expansion is seen to give rise to secular terms. A uniformly valid approximation is given to this order, for the case of a travelling wave.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01175754
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  • 4
    Electronic Resource
    Electronic Resource
    Torsional waves in an infinite elastic rod of elliptical cross section (1972)
    Springer
    Acta mechanica 13 (1972), S. 117-132 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Zusammenfassung Eine Störungsrechnung zur Beschreibung der Form des Fernfeldes von Torsionswellen in einem linear-elastischen Stab von elliptischem Querschnitt, mit den Halbachsena undb, wird entwickelt. Die Näherung niedrigster Ordnung, die sich mit bekannten Resultaten vergleichen läßt, führt zu einer in Achsrichtung mit der Geschwindigkeitc = [2ab/(a 2+b 2)](μ/ϱ)1/2 fortlaufenden Welle. Eine Näherung höherer Ordnung, die für große Zeiten gültig ist, wird erhalten; eine Darstellung ihrer Lösung durch ein Airy-Integral zeigt den Dispersionscharakter der Welle.
    Notes: Summary A perturbation method is developed to describe the far-field structure of torsional waves in a linearly elastic rod of elliptical cross section with semi-axes of lengthsa andb. The highest order problem, comparable to what is known, leads to a wave propagating along the axis with a speedc = [2ab/(a 2+b 2)](μ/ϱ)1/2. A higher order approximation is obtained, uniformly valid for large time; a representation of its solution in terms of Airy integral brings out the dispersive nature of the wave.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01179661
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  • 5
    Electronic Resource
    Electronic Resource
    Asymptotic solution for the hartmann problem through circular tube (1965)
    Springer
    Flow, turbulence and combustion 11 (1965), S. 145-160 
    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: Summary Asymptotic solutions valid for sufficiently large Hartmann numbers M are presented in this paper. It is found that the velocity profiles are elliptic paraboloids of revolution whose major axis are parallel to the direction of the imposed magnetic field. Also the velocity profiles along the diameter parallel to the imposed field are like those of Hartmann for parallel plates and perpendicular to the field these are almost of parabolic character.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00384021
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    Paper (German National Licenses)
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