On coupled thermoelastic vibration of geometrically nonlinear thin plates satisfying generalized mechanical and thermal conditions on the boundary and on the surface

Hans-Ullrich Wenk

Aplikace matematiky (1982)

  • Volume: 27, Issue: 6, page 393-416
  • ISSN: 0862-7940

Abstract

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The vibration problem in two variables is derived from the spatial situation (a plate as a three-dimensional body) on the basis of geometrically nonlinear plate theory (using Kármán's hypothesis) and coupled linear thermoelasticity. That leads to coupled strongly nonlinear two-dimensional equilibrium and heat conducting equations (under classical mechanical and thermal boundary conditions). For the generalized problem with subgradient conditions on the boundary and in the domain (including also classical conditions), existence and dependence of the weak variational solution on the given data is proved.

How to cite

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Wenk, Hans-Ullrich. "On coupled thermoelastic vibration of geometrically nonlinear thin plates satisfying generalized mechanical and thermal conditions on the boundary and on the surface." Aplikace matematiky 27.6 (1982): 393-416. <http://eudml.org/doc/15261>.

@article{Wenk1982,
abstract = {The vibration problem in two variables is derived from the spatial situation (a plate as a three-dimensional body) on the basis of geometrically nonlinear plate theory (using Kármán's hypothesis) and coupled linear thermoelasticity. That leads to coupled strongly nonlinear two-dimensional equilibrium and heat conducting equations (under classical mechanical and thermal boundary conditions). For the generalized problem with subgradient conditions on the boundary and in the domain (including also classical conditions), existence and dependence of the weak variational solution on the given data is proved.},
author = {Wenk, Hans-Ullrich},
journal = {Aplikace matematiky},
keywords = {nonlinear dynamical; kinematical; linear constitutive thermoelastic; coupled heat conduction equations; spatial problem; Kirchhoff’s and von Kármán’s hypothesis; twodimensional equations; generalized problem with subgradient conditions on boundary; existence of solution; continuous dependence on given data; nonlinear dynamical; kinematical; linear constitutive thermoelastic; coupled heat conduction equations; spatial problem; Kirchhoff’s and von Kármán’s hypothesis; twodimensional equations; generalized problem with subgradient conditions on boundary; existence of solution; continuous dependence on given data},
language = {eng},
number = {6},
pages = {393-416},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On coupled thermoelastic vibration of geometrically nonlinear thin plates satisfying generalized mechanical and thermal conditions on the boundary and on the surface},
url = {http://eudml.org/doc/15261},
volume = {27},
year = {1982},
}

TY - JOUR
AU - Wenk, Hans-Ullrich
TI - On coupled thermoelastic vibration of geometrically nonlinear thin plates satisfying generalized mechanical and thermal conditions on the boundary and on the surface
JO - Aplikace matematiky
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 27
IS - 6
SP - 393
EP - 416
AB - The vibration problem in two variables is derived from the spatial situation (a plate as a three-dimensional body) on the basis of geometrically nonlinear plate theory (using Kármán's hypothesis) and coupled linear thermoelasticity. That leads to coupled strongly nonlinear two-dimensional equilibrium and heat conducting equations (under classical mechanical and thermal boundary conditions). For the generalized problem with subgradient conditions on the boundary and in the domain (including also classical conditions), existence and dependence of the weak variational solution on the given data is proved.
LA - eng
KW - nonlinear dynamical; kinematical; linear constitutive thermoelastic; coupled heat conduction equations; spatial problem; Kirchhoff’s and von Kármán’s hypothesis; twodimensional equations; generalized problem with subgradient conditions on boundary; existence of solution; continuous dependence on given data; nonlinear dynamical; kinematical; linear constitutive thermoelastic; coupled heat conduction equations; spatial problem; Kirchhoff’s and von Kármán’s hypothesis; twodimensional equations; generalized problem with subgradient conditions on boundary; existence of solution; continuous dependence on given data
UR - http://eudml.org/doc/15261
ER -

References

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  8. I. Hlaváček J. Naumann, Inhomogeneous Boundary Value Problems for the von Kármán's Equations, I, Apl. Matem., 19 (1974), 253 - 269. (1974) Zbl0313.35064MR0377307
  9. I. Hlaváček J. Naumann, Inhomogeneous Boundary Value Problems for the von Kármán's Equations, II, Apl. Matem., 20 (1975), 280-297. (1975) Zbl0317.35041MR0377308
  10. I. Hlaváček J. Nečas, On Inequalities of Korn's Type, I: Boundary value problems for elliptic systems of partial differential equations, II: Applications to linear elasticity, Arch. Rat. Mech. Anal., 36 (1970), 305-334. (1970) Zbl0193.39001MR0252844
  11. R. Hünlich J. Naumann, On General Boundary Value Problems and Duality in Linear Elasticity, I, Apl. Matem., 23 (1978). (1978) Zbl0401.73025MR0489538
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  13. J. Naumann, On Some Unilateral Boundary Value Problems for the von Kármán's Equations, part I: The coercive case, Apl. Matem., 20 (1975), 96-125. (1975) Zbl0311.73029MR0437916
  14. J. Naumann, On Some Unilateral Boundary Value Problems in Non-linear Plate Theory, Beiträge zur Analysis, 10 (1977), 119-134. (1977) Zbl0369.35020MR0489204
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  20. H.-U. Wenk, Functional-analytical Investigations on Unilateral Problems in Plate Theory, (in German). Thesis A, Humboldt-Univ., Berlin 1978. (1978) 

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