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1
Content available Thermally induced vibration of a cantilever beam with periodically varying intensity of a heat source
Kidawa-Kukla J.
Journal of Applied Mathematics and Computational Mechanics
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2013
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Vol. 12, nr 4
59--65
EN
In this paper an exact solution to the problem of the thermally induced vibration of a cantilever beam is presented. It is assumed that on a part of the beam the surface acts as a periodically time-varying heat source. The changing of the beam temperature produces thermal stresses, which cause displacements of the beam. The vibration of the beam is governed by the Bernoulli-Euler equation which includes the variable thermal moment. The heat equation and the vibration problem are solved by using the Green’s function method. The symbolic software Mathematica has been used to obtain the solution of the problem in an analytical form.
2
Content available remote Thermally induced vibration of an annular plate subjected to the oscillating heat stream
Kidawa-Kukla J.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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Vol. 11, nr 4
65-74
EN
A solution of the problem of the thermally induced transverse vibration of an annular plate is presented. One assumes that the plate temperature changes by periodic oscillation of the heat stream in a ring region on one side of the plate. The axisymmetric temperature distribution in the plate is determined by the conductivity equation and corresponding initial and boundary conditions. The heat conduction problem in the plate and the problem of transverse vibration of the plate is solved by using the Green's function method.
3
Content available remote Thermally induced vibration of an annular plate
Kidawa-Kukla J.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2011
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Vol. 10, nr 2
107-116
EN
The exact solution to a problem of the thermally induced vibration of a homogeneous annular plate is presented. The considered plate is subjected to the activity of a point heat source, which moves with a constant angular velocity on the plate surface along a trajectory. The thermal moment is derived on the basis of a temperature field in the plate. The solution to the vibration problem is obtained by using Green's function method.
4
Content available remote Application of the Green's function method to the problem of thermally induced vibration of a circular plate
Kidawa-Kukla J.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2010
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Vol. 9, nr 1
53-60
EN
The thermally induced vibration of a homogeneous thin circular plate is considered. The plate is subjected to the activity of the point heat source which moves with constant angular velocity on the plate surface along a concentric circular trajectory. The thermal moment is derived on the basis of temperature field in the plate. The solution of the vibration problem is obtained by using the Green's function method.
5
Content available remote Temperature distribution in an annular plate with a moving discrete heat generation source
Kidawa-Kukla J.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2009
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Vol. 8, nr 1
77-84
EN
The problem of heat conduction in an annular plate is considered. The plate is subjected to the activity of the point heat source which moves with constant angular velocity on the plate surface along a concentric circular trajectory. The solution of the problem is obtained by using the Green's function.
6
Content available remote Temperature distribution in a circular plate heated by a moving heat source
Kidawa-Kukla J.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2008
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Vol. 7, nr 1
71-76
EN
This paper concerns the heat conduction problem in a circular thin plate subjected to the activity of a heat source which changes its place on the plate surface with time. The heat source moves along an circular trajectory round centre of the plate with constant angular velocity. The solution of the problem is obtained in an analytical form by using the Green's function method.
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