Stability properties of a class of viscoelastic beams of the hereditary type

Francesco Russo Spena

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1994)

  • Volume: 5, Issue: 1, page 79-87
  • ISSN: 1120-6330

Abstract

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The paper deals with the problem of equilibrium stability of prismatic, homogeneous, intrinsically isotropic, viscoelastic beams subjected to the action of constant compressive axial force in the light of Lyapounov's stability theory. For a class of functional expressions of creeping kernels characteristic of no-aging viscoelastic materials of the hereditary type, solution of the governing integro-differential equations is given. Referring to polymeric materials of the PMMA type, numerical results are obtained showing the influence of the loading duration on system stability.

How to cite

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Russo Spena, Francesco. "Stability properties of a class of viscoelastic beams of the hereditary type." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 5.1 (1994): 79-87. <http://eudml.org/doc/244127>.

@article{RussoSpena1994,
abstract = {The paper deals with the problem of equilibrium stability of prismatic, homogeneous, intrinsically isotropic, viscoelastic beams subjected to the action of constant compressive axial force in the light of Lyapounov's stability theory. For a class of functional expressions of creeping kernels characteristic of no-aging viscoelastic materials of the hereditary type, solution of the governing integro-differential equations is given. Referring to polymeric materials of the PMMA type, numerical results are obtained showing the influence of the loading duration on system stability.},
author = {Russo Spena, Francesco},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Viscoelasticity; Hereditary theory; Creep-stability; constant compressive axial force; Lyapunov's stability theory; creep; integro-differential equations; polymeric materials; kernels},
language = {eng},
month = {3},
number = {1},
pages = {79-87},
publisher = {Accademia Nazionale dei Lincei},
title = {Stability properties of a class of viscoelastic beams of the hereditary type},
url = {http://eudml.org/doc/244127},
volume = {5},
year = {1994},
}

TY - JOUR
AU - Russo Spena, Francesco
TI - Stability properties of a class of viscoelastic beams of the hereditary type
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1994/3//
PB - Accademia Nazionale dei Lincei
VL - 5
IS - 1
SP - 79
EP - 87
AB - The paper deals with the problem of equilibrium stability of prismatic, homogeneous, intrinsically isotropic, viscoelastic beams subjected to the action of constant compressive axial force in the light of Lyapounov's stability theory. For a class of functional expressions of creeping kernels characteristic of no-aging viscoelastic materials of the hereditary type, solution of the governing integro-differential equations is given. Referring to polymeric materials of the PMMA type, numerical results are obtained showing the influence of the loading duration on system stability.
LA - eng
KW - Viscoelasticity; Hereditary theory; Creep-stability; constant compressive axial force; Lyapunov's stability theory; creep; integro-differential equations; polymeric materials; kernels
UR - http://eudml.org/doc/244127
ER -

References

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  1. ROBOTONOV, Y. N. - SHESTERIKOV, A., Creep stability of columns and plates. Jour. Mech. Phys. Solids, vol. 6, 1957, 587-596. Zbl0079.39801MR93181
  2. DOST, S. - GLOCKNER, P. G., On the dynamic stability of viscoelastic perfect columns. Int. Jour. Solids & Struct., vol. 18, 1982, 27-34. Zbl0485.73035
  3. FRANCIOSI, V., Le aste sottili presso-inflesse in regime viscoso. Rend. Acc. Sc. Fis. e Mat., s. 6, vol. XVIII, Napoli1952, 552-565. Zbl0053.31006
  4. D' ONOFRIO, C. - FRANCIOSI, V., Il carico di punta in regime viscoso per travi di sezione variabile. Rend. Acc. Sc. Fis. e Mat., s. 6, vol. XLVI, Napoli1979, 281-293. 
  5. MOLA, F., Stato limite di instabilità. Effetti della viscosità. Progetto delle Strutture in c.a. con il metodo agli Stati limite, CLUP, Milano1986, 311-359. 
  6. LYAPOUNOV, A. M., Problème général de la stabilité du mouvement. Princeton University Press, Princeton1959. Zbl0031.18403
  7. LEITMAN, M. J. - FISHER, G. M., The Linear Theory of Viscoelasticity. Handbuch der Physik, Band VI a/3, 1973. 
  8. VOLTERRA, V., Alcune osservazioni sui fenomeni ereditari. Atti Acc. Lincei Rend, fis., s. 6, vol. 9, 1929, 585-595. JFM55.1151.01
  9. WOINOWSKY KRIEGER, S., The effect of an axial force on the vibration of hinged bars. Trans. ASME J. App. Mech., vol. 17, 1950, 35-36. Zbl0036.13302MR34202
  10. BELLMAN, R., Stability Theory of Differential Equations. McGraw-Hill Book Co., New York, 1953. Zbl0053.24705MR61235

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