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  • 1
    Electronic Resource
    Electronic Resource
    A note on thermal stresses in hollow cylinders (1959)
    Springer
    Archive of applied mechanics 27 (1959), S. 227-241 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Conclusions The extensions of Trostel's solutions derived in this paper may be employed tor general ν over wide conditions with a resulting error less than 3%, the stress values being too small in magnitude by this amount. The error decreases as the variation of physical properties of the media decreases or as ν → 1/2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00538344
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  • 2
    Electronic Resource
    Electronic Resource
    On the steady thermoelastic problems with elastic characteristics depending on temperature (1960)
    Springer
    Archive of applied mechanics 29 (1960), S. 260-261 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Conclusion We therefore conclude that the approximate solution B gives in a single operation, the “Grundlösung” and about 70% of the first correction term of the exact solution A.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00536708
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  • 3
    Electronic Resource
    Electronic Resource
    The steady-state thermal stress field in an isotropic sphere with temperature dependent properties (1962)
    Springer
    Archive of applied mechanics 31 (1962), S. 241-249 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Conclusion For many purposes, the infinite series can be neglected in equations (29) and (30) for the stress field in a hollow sphere and in equations (47) and (48) for a solid sphere. The error estimate from equation (42) or equation (46) may be used as a criterion for deciding whether or not this is permissible. Finally, the method outlined in preceeding discussion is applicable to any one-dimensional thermoelastic problem with only very mild requirements on the variation of Young's Modulus as specified by equation (39). As would be suspected, the use of the procedure for higher dimensional problems entails the specific assumption that second order variations in Young's Modulus are negligibly small if any degree of calculational simplicity is to be retained. Still, this does not require small variations of first order.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00536721
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  • 4
    Electronic Resource
    Electronic Resource
    On the response of thin elastic plates by means of green's functions (1979)
    Springer
    Archive of applied mechanics 48 (1979), S. 279-288 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Für verschiedene Belastungsfälle wird mit Hilfe von Green-Funktionen eine exakte Lösung für das Verhalten einer dünnen elastischen Platte angegeben, die längs eines Randes fest eingespannt, l:angs der anderen Ränder frei aufgelagert ist. Die Ergebnisse für Durchbiegungen und Momente werden für verschiedene Belastungsfälle mit denen nach einer Näherungsmethode von Timoshenko und nach dem Verfahren der finiten Elemente erhaltenen verglichen. Es zeigt sich, daß die Ergebnisse nach Timoshenko sowie nach der Methode der finiten Elemente gut mit der hier gegebenen exakten Lösung übereinstimmen.
    Notes: Summary By means of Green's functions, an exact solution has been found for the thin elastic rectangular plate, built-in along one edge and simply supported along the other edges, for various static loading conditions. The results for deflections and moments have been compared with an approximate method by Timoshenko and the finite element method for different loading cases. It has been shown that results given by Timoshenko and finite element methods agree well with the exact solution, presented in this work.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00586068
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  • 5
    Electronic Resource
    Electronic Resource
    A contribution to the stability of circular plates (1977)
    Springer
    Archive of applied mechanics 46 (1977), S. 383-388 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Für dünne Kreisplatten, die in beliebiger Weise örtlich und zeitlich belastet werden, wird das dynamische Verhalten und die Stabilität untersucht. Die Lösung wird in geschlossener Form mit Hilfe von Green-schen Funktionen angegeben, die nach den entsprechenden Eigenfunktionen entwickelt werden. Für den Fall einer auf dem Umfang bewegten Last reduziert sich die Stabilitätsbestimmung auf die Untersuchung von zwei zeitabhängigen Funktionen. Diese Funktionen zeigen, daß im Fall einer konstanten Last, die mit konstanter Geschwindigkeit wandert für einen gewissen Bereich von Eigenfrequenzen Instabilität auftreten kann.
    Notes: Summary The dynamical response of thin circular plates and their stability, resulting from the action of an arbitrary load which is a spacetime function, has been examined. The solution is obtained in closed form by means of Green's function and its expansion in terms of corresponding eigenfunctions. In the case of a load moving on the periphery the stability criterion is reduced to the examination of two time-dependent functions. These functions show that, for a constant load moving with constant angular velocity and for a given range of eigenfrequencies, the motion is unstable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00535289
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  • 6
    Electronic Resource
    Electronic Resource
    Dynamic responses of orthotropic plates under moving masses (1988)
    Springer
    Archive of applied mechanics 58 (1988), S. 9-14 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: übersicht Behandelt wird die Bewegung von Massenpunkten auf rechteckigen Leichtbau-Platten aus orthotropem Werkstoff, die für Raumfahrtkonstruktionen vorgesehen sind. ZunÄchst wird die Bewegungsgleichung orthotroper Platten mit singulÄren Ausdrücken in den Raum- und Zeitkoordinaten angegeben. Die Antwort wird als Doppelsumme einer zweifachen Reihenentwicklung dargestellt und die Bewegungsgleichung mit Hilfe der Greenschen Funktion in eine Integro-Differentialgleichung für die Modalamplituden transformiert. Die Greensche Funktion ist so gewÄhlt, da\ sie die Anfangs- und Randbedingungen sowie die übergangsbedingungen unter der bewegten Masse erfüllt. Die Lösung durch Reihenentwicklung zeigt gute Konvergenz. Der Einflu\ der Orthotropie auf die Eigenfrequenzen und die dynamischen Antworten wird veranschaulicht.
    Notes: Summary The problem considered is that of heavy masses moving on lightweight rectangular plates of orthotropic materials, slated for use in space structures. The dynamic equation of motion for orthotropic plates which contains singularities in both space and time variables is first presented. The response is expressed as a summation of double series of eigenfunctions. The equation of motion is transformed into an integro-differential equation for modal amplitudes using the Green's function. The Green's function is chosen to satisfy the initial conditions, the boundary conditions, and the transient conditions due to the moving masses. The solution series exhibits a good convergence. The effect of orthotropicity on natural frequencies and dynamic responses is demonstrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00537195
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  • 7
    Electronic Resource
    Electronic Resource
    A contribution to the Kryloff-Bogoliuboff theory in nonlinear mechanics (1973)
    Springer
    Archive of applied mechanics 42 (1973), S. 371-380 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Es wird eine Erweiterung für die von Kryloff und Bogoliuboff angegebene Methode der Theorie nichtlinearer Schwingungen beschrieben. Das Verfahren ist vorwiegend für die Resonanzanalyse bei stationären oder instationären Bewegungen geeignet. Subharmonische und superharmonische Bewegungen lassen sich in voller Allgemeinheit damit berechnen. Das Verfahren wird am Beispiel einer Gleichung demonstriert, die die Bewegungen eines harmonisch erregten nichtlinearen Schwingers beschreibt. Höhere Näherungen werden abgeleitet, und die Stabilität der Lösungen wird untersucht. Ein Vergleich mit exakten Lösungen zeigt, daß das angegebene Verfahren gut brauchbar für die Berechnung der Bewegungen nichtlinearer Systeme mit harmonischen Erregungen ist.
    Notes: Summary An extension of the Kryloff-Bogoliuboff method in the theory of nonlinear oscillation has been developed. The method is intended primarily for the resonant analysis of systems exhibiting transient as well as steady motion, and describes subharmonic and superharmonic responses in complete generality. The method is applied to the equation describing the motion of a harmonically driven nonlinear oscillator. Higher approximation is obtained and the stability of the solution has been examined. The results of this method, when compared with exact solutions, show that this technique affords a more workable means for studying the responses of the nonlinear system harmonic forces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00535763
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  • 8
    Electronic Resource
    Electronic Resource
    A rapidly converging technique for vibration analysis of plates with a discrete mass distribution (1968)
    Springer
    Archive of applied mechanics 37 (1968), S. 189-195 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Es wird eine auf dem Galerkin-Verfahren basierende Methode zur Berechnung der Eigenfrequenzen rechteckiger Platten mit diskreten Einzel-Massen angegeben. Es werden einfach aufgelagerte und eingespannte rechteckige Platten untersucht, jedoch ergeben sich keine Schwierigkeiten bei der Anwendung derselben Methode auf Platten anderer Formen mit anderen Randbedingungen. Für einen Sonderfall werden die Ergebnisse der Berechnungen mit exakten Lösungen verglichen, wobei eine ausgezeichnete Übereinstimmung festgestellt werden kann.
    Notes: Summary A technique based on the Galerkin approach has been developed for determination of the natural frequencies of rectangular plates with discrete masses added. The technique is applied to the rectangular plates with simply supported and clamped boundary conditions, but no difficulty exists in applying the same method to the plates of various forms with different boundary conditions. The results of this technique applied to one particular case are compared to a solution obtained by an exact method; the comparison shows the two methods to be in excellent agreement.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00532608
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  • 9
    Electronic Resource
    Electronic Resource
    On a theory concerning the dynamical behavior of structures carrying moving masses (1974)
    Springer
    Archive of applied mechanics 43 (1974), S. 295-305 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Es werden zwei neue Methoden zum Bestimmen des Verhaltens von Strukturen mit bewegten Massen behandelt. Die erste Methode trägt analytischen Charakter und kann als eine Modifikation der asymptotischen Methode der Theorie nichtlinearer Schwingungen betrachtet werden. Die zweite Methode basiert auf einer exakten numerischen Integration. Sie ist allgemein genug, um das beschreibende System gewöhnlicher Differentialgleichungen exakt zu lösen. Ein Vergleich der Ergebnisse zeigt, daß ausgezeichnete Übereinstimmung erreicht wird. Die Auswertungen zeigen, daß die Einwirkung des Struktur-Verhaltens auf die bewegte Massc berücksichtigt werden muß.
    Notes: Summary Two new methods are presented in order to determine the behavior of a structure carrying moving masses. The first method is analytic in nature and represents a modified asymptotic method in the theory of nonlinear phenomena. The second method is an exact numerical technique general enough to be used for solving exactly a set of differential equations with singular coefficients. The results show that the analytical method is in excellent agreement with the exact one obtained by means of a numerical technique. Furthermore, it is shown that the effect of the response of the structure to the moving mass has to be properly considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00537218
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  • 10
    Electronic Resource
    Electronic Resource
    On a new theory of the dynamic behavior of the structures carrying moving masses (1985)
    Springer
    Archive of applied mechanics 55 (1985), S. 176-185 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht In dieser Arbeit wird eine exakte Lösung für das Verhalten von Strukturen unter bewegten Massen gegeben. Die Lösung wird durch eine Reihenentwicklung in Eigenfunktionen ermittelt, wobei die Eigenfunktionen mit Hilfe von Stieltjes Integralen exakt bestimmt werden. Die Reihen konvergieren schnell; die Ergebnisse stimmen ausgezeichnet mit bekannten numerischen Lösungen überein.
    Notes: Summary This paper represents an exact solution for a problem which has been of interest in Structural Engineering for many years. The solution is “exact” in the engineering sense; it converges very rapidly. The solution is given by means of an expansion of the eigenfunctions in a series. The eigenfunctions satisfying the boundary and transient conditions for masses moving over a structure have been determined exactly by performing the integration in the Stieltjes sense. The method is simple, short and elegant and is based on operational calculus. It yields the results in perfect agreement with an accurate numerical solution previously given in the literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00536412
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