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  • 1
    Electronic Resource
    Electronic Resource
    Free lateral vibration of an axially creeping beam-column under initial axial compression (1977)
    Springer
    Meccanica 12 (1977), S. 151-158 
    Details
    ISSN: 1572-9648
    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: Summary The free lateral vibration of a nonlinear viscoelastic beam column subjected to an initial compressive axial load is considered. The costitutive law is formulated with a linear elastic term and with power functions of stress in the transient and steady creep terms, and is of the nonlinear generalized Kelvin type. By assuming that the stress caused by the oscillation is of much smaller magnitude than the initial stress, the problem is linearized. The problem is analyzed for five special viscoelastic models using small deformation theory, and numerical results are discussed for a stainless steel alloy.
    Notes: Sommario Si considerano le vibrazioni libere laterali di un'asta viscoelastica non lineare soggetta inizialmente ad un carico assiale di compressione. La legge costitutiva si compone di un termine elastico lineare e di termini non lineari nello sforzo sia per lo scorrimento viscoso transitorio sia per quello stazionario; essa è del tipo Kelvin generalizzato non lineare. Si linearizza il problema assumendo che gli sforzi causati dall'oscillazione siano molto più piccoli degli sforzi iniziali. Si studia il problema per cinque particolari modelli viscoelastici usando la teoria valida per le piccole deformazioni, e si discutono risultati numerici validi per un acciaio inossidabile.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02179929
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  • 2
    Electronic Resource
    Electronic Resource
    Wave front stress relaxation in viscoelastic materials with random temperature distributions (1975)
    Springer
    Acta mechanica 22 (1975), S. 11-30 
    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 Für die statistischen Eigenschaften der Spannung an der Wellenfront eines plötzlich belasteten halbunendlichen Stabes aus viskoelastischem Werkstoff mit Potenzgesetz werden analytische und numerische Lösungen angegeben. Temperatur und daher temperaturempfindliche Werkstoffparameter werden zufallsabhängig angenommen. Eine kritische Zeit, bei der die Mittelwertsfunktionen die deterministischen Lösungen schneiden und die Varianzen ein Maximum annehmen, wird festgestellt.
    Notes: Summary Analytical and numerical solutions are presented for the statistical properties of the stress at the wave front in a suddenly loaded semi-infinite rod of a viscoelastic material with a stress power constitutive law. The temperature and accordingly the temperature sensitive material parameters are assumed to be random. A critical time is observed, where the mean solutions cross the deterministic solutions and the variance is a maximum.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01170617
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  • 3
    Electronic Resource
    Electronic Resource
    On the thermodynamics of nonlinear single integral representations for thermoviscoelastic materials with applications to one-dimensional wave propagation (1977)
    Springer
    Acta mechanica 25 (1977), S. 187-206 
    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 Mit Hilfe der Thermodynamik werden einfache Integrale enthaltende Werkstoffbeziehungen für das nichtlineare thermoviskoelastische Verhalten unter beliebigen Spannungs- und Temperaturverläufen entwickelt und die thermomechanisch gekoppelte Energiegleichung wird angegeben. Im Detail werden der thermodynamisch-einfache Werkstoff, die modifizierte Überlagerung und das isotrope Spannungs-Potenzgesetz diskutiert. Damit thermische Störungen sich mit endlicher Geschwindigkeit ausbreiten, wird ein modifiziertes Fouriersches Wärmeleitgesetz verwendet. Unter Verwendung des nichtlinearen thermoviskoelastischen Spannungs-Potenzgesetzes, der linearisierten Energiegleichung und des modifizierten Wärmeleitgesetzes werden Lösungen der eindimensionalen Wellenfrontausbreitung erhalten.
    Notes: Summary Thermodynamic theory is used to develop single integral constitutive relations for the nonlinear thermoviscoelastic response to arbitrary stress and temperature histories; the thermomechanically coupled energy equation is also obtained. The thermorheologically simple material, modified superposition and the isotropic stress power law are discussed in detail. A modified Fourier heat conduction law is employed to ensure that the propagation of thermal disturbances takes place at a finite velocity. Using the nonlinear thermoviscoelastic stress power law along with the linearized energy equation and modified Fourier law, one-dimensional wave front solutions are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01376991
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  • 4
    Electronic Resource
    Electronic Resource
    Longitudinal waves in nonlinear viscoelastic rods under initial axial stress (1970)
    Springer
    Acta mechanica 10 (1970), S. 277-300 
    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 Es wird die Ausbreitung von Longitudinalwellen in einem halbunendlichen Stab betrachtet. Das Material ist nichtlinear viskoelastisch und befindet sich unter konstanter axialer Anfangsspannung, d. h., der Stab erleidet eine axiale Kriechdeformation. Der Deformationsgradient wird infinitesimal klein angenommen, die Deformation selbst kann aber endlich sein. Die Materialgleichung enthält eine Spannungs-Potenzfunktion im elastischen Teil sowie instationäre und stationäre Kriechanteile. Die Welle wird durch eine Stufenfunktion in der Geschwindigkeit oder Spannung an einem Ende des Stabes erzeugt. Die Anfangsspannung wird groß gegenüber der stoßartig aufgebrachten Spannung angenommen. Zur Lösung wird eine Störungsmethode verwendet. Für fünf nichtlinear viskoelastische Modelle werden geschlossene Lösungen für die Störspannungen erhalten. Numerische Beispiele werden angegeben und diskutiert.
    Notes: Summary Longitudianal wave propagation in a semi-infinite rod is considered, where the medium is nonlinear viscoelastic and under constant initial axial stress, i.e., the rod is undergoing axial creep deformation. The deformation gradient is assumed to be infinitesimal, but the deformation itself may be finite. The constitutive law is taken with stress power functions in the elastic, transient creep and steady creep terms. A wave is generated by a step input in velocity or stress at one end of the rod. It is assumed that the initial stress is much greater than the increment of stress generated by the impact and a perturbation technique is employed. Closed form perturbation stress solutions are obtained for five nonlinear viscoelastic models. Numerical examples are given and discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01175884
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  • 5
    Electronic Resource
    Electronic Resource
    Some results on the one-dimensional coupled nonlinear thermoviscoelastic wave propagation problem with second sound (1980)
    Springer
    Acta mechanica 37 (1980), S. 111-129 
    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 Eindimensionale Spannungs- und Temperaturfelder in einem plötzlich belasteten und/oder erwärmten, halbunendlichen Stab aus nichtlinearem, viskoplastischen Material werden mit Hilfe der gekoppelten thermodynamischen Theorie untersucht. Der Wärmetransport gehorcht dem modifizierten Fourierschem Wärmeleitungsgesetz und erfolgt daher eher durch Wellenausbreitung als durch Diffusion. Die Aufbringung thermischer oder mechanischer Störungen am Ende des Stabs läßt zwei Wellenfronten entstehen, mit welchen die Störungen fortschreiten. Feldlösungen für Spannungen und Temperatur werden durch numerische Integration längs der fünf Charakteristiken der beschreibenden Gleichungen erhalten und die Resultate für einige lineare und nichtlineare viskoelastische Modelle angegeben.
    Notes: Summary One-dimensional stress and temperature fields in a suddenly loaded and/or heated semi-infinite rod of nonlinear thermoviscoelastic material are studied using coupled thermomechanical theory. The transport of heat is governed by the modified Fourier heat conduction law, and thus proceeds by wave propagation rather than by diffusion. The application of thermal and mechanical disturbances at the end of the rod gives rise to two wave fronts along which these disturbances propagate. Field solutions for the stress and temperature are obtained by numerical integration along the five characteristics of the governing equations, and results are presented for several linear and nonlinear viscoelastic models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01441248
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  • 6
    Electronic Resource
    Electronic Resource
    Stress intensification in a viscoelastic plate on a Winkler foundation and under a large thermal gradient (1988)
    Springer
    Acta mechanica 72 (1988), S. 189-203 
    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
    Notes: Summary A thin viscoelastic plate on a Winkler foundation is subjected to vertical loads. Its response is strongly affected by the presence of a vertical temperature gradient which causes a very pronounced change in the viscosity coefficient through the plate thickness. While eventually the entire load will be transferred to the underlying foundation, during the time dependent deformation process it is possible that some bending stresses will actually increase rather than decrease as would normally be expected with this relaxation process. The rationale for this behavior lies in the competition between the two physical processes of a) the load transfer to the foundation causing an overall relief of the bending moment and thus the bending stress and b) the rapid relaxation of bending stress in the hot lower portion of the plate causing the colder upper portion to carry a larger share of that portion of the bending moment still carried by the plate. The simple case of a clamped circular plate of a metallic material and subjected to a uniform load is used to illustrate this behavior. Certain simplifications are made to allow an analytic solution; these simplifications do not alter the basic behavior. In the present case, these simplifications are the neglect of Poisson's ratio effects and the assumption of a linear “equivalent” viscoelastic material behavior. This latter point is discussed in an appendix. Numerical solutions containing more general behavior indicate that the basic behavior is still well modeled even with these assumptions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01178307
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