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.
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.
References
HOFF N. J.,Damping of the Vibrations of a Coiled Spring due to Creep, in «Creep in Structures» (IUTAM-Stanford) (ed. by N. J. Hoff), New York, Academic Press Inc., pp. 355–373, 1962.
COZZARELLI F. A., WU J. J., TANG S.,Lateral Vibration of a Non-Linear Viscoelastic Beam under Initial Axial Tension, J. Sound Vib.,13, 147, 1970.
RABOTNOV Yu. N., SHESTERIKOV S. A.,Stability of Rods and Plates under Creep Conditions, PMM, vol. 21, Issue 3, 1957.
RABOTNOV Yu: N., SHESTERIKOV S.A.,Creep Stability of Columns and Plates, J. Mech. Phys. Solids, 6, 1957.
JAHSMAN W. E., FIELD F. A.,Dynamic Creep Instability of Initially Straight, Centrally Loaded Columns, J. Appl. Mech., 84, 73, 1962.
JAHSMAN W.E.,Creep Stability of a Column, in «Creep in Structures» (IUTAM-Gothenburg) (ed. by Jan Hult), Berlin-Heidelberg, Springer-Verlag, pp. 360–370, 1970.
DISTEFANO J. N., SACKMAN J. L.,Stability of a Non-Linear Viscoelastic Column, Z. Angew. Math. Mech., 47, 349, 1967.
DISTEFANO J. N., SACKMAN J. L.,On the Stability of an Initially Imperfect Nonlinearly Viscoelastic Column, Int. J. Solids Structures, 4, 341, 1968.
SHAW R. P., COZZARELLI F. A.,Stress Relaxation at Wave Fronts in One-Dimensional Media Described by Nonlinear Viscoelastic Models, Int. J. Non-Linear Mech., 5, 171, 1970.
DISTEFANO J. N.,Sulla stabilità in regime visco-elastico a comportamento lineare, Acc. dei Lincei, Rendiconti, Ser. VIII, XXVII, 56, 1959.
GAROFALO F.,Fundamentals of Creep and Creep-Rupture in Metals, London, Mac Millan, 1965.
GAROFALO F., RICHMOND C., DOMIS W. F., VON GEMMINGEN F.,Strain-Time, Rate-Stress and Rate-Temperature Relations During Large Deformations in Creep, Proc. Joint Int. Conf. Creep, Inst. Mech. Eng., 1963.
ODQVIST F. K. G., HULT J.,Kriechfestigkeit Metallischer Werkstoffe, Berlin, Springer-Verlag, 1962.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cozzarelli, F.A., Tittemore, G. Free lateral vibration of an axially creeping beam-column under initial axial compression. Meccanica 12, 151–158 (1977). https://doi.org/10.1007/BF02179929
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02179929