Vibrations of a Composite Beam Under Thermal and Mechanical Loadings

Warmińska, Anna; Manoach, Emil; Warmiński, Jerzy

doi:10.1016/j.proeng.2016.05.123

Cited by 12 publications

(13 citation statements)

References 9 publications

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“…1. The partial differential equations of fully coupled, axissymmetric vibration of a nonlinear thermo-elastic plate is presented in [7] and has the form…”

Section: Plate Modelmentioning

confidence: 99%

“…It has been shown that among periodic also chaotic oscillations may arise and a small temperature variation may transit the system to regular motion. The bifurcation analysis based on a reduced beam model but for a nonuniform temperature distribution has been presented in [7]. The analysis performed for beams has been extended in [7] for plates.…”

Section: Introductionmentioning

confidence: 99%

“…The bifurcation analysis based on a reduced beam model but for a nonuniform temperature distribution has been presented in [7]. The analysis performed for beams has been extended in [7] for plates. The preliminary results for circular plate model for elevated temperature and two variants external excitation frequencies have been presented.…”

Section: Introductionmentioning

confidence: 99%

“…The preliminary results for circular plate model for elevated temperature and two variants external excitation frequencies have been presented. In this paper we reduce the thermo-mechanical model of the circular plate described by PDEs presented in paper [7]. The preliminary results are obtained for clamped boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of a Circular Mindlin Plate under Mechanical Loading and Elevated Temperature

2016

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Abstract. Dynamics of a nonlinear circular Midlin plate is studied in the paper. The mathematical model represented by partial differential equations includes nonlinear geometrical terms resulted from large displacements. The plate is subjected to mechanical and thermal loadings. The dynamics of a coupled thermo-mechanical problem is reduced from partial to ordinary differential equations. Considering the first mode reduction and uniformly distributed temperature just a single nonlinear differential equation is obtained. The bifurcation analysis shows that elevated temperature shifts the rezonanse curve and new solutions arise. Depending on initial conditions this may lead to buckling phenomenon and then relatively small oscillations around this state, symmetric periodic oscillations of large amplitude, or irregular oscillations.

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“…1. The partial differential equations of fully coupled, axissymmetric vibration of a nonlinear thermo-elastic plate is presented in [7] and has the form…”

Section: Plate Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamics of a Circular Mindlin Plate under Mechanical Loading and Elevated Temperature

2016

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“…Furthermore, above the certain threshold, the increased temperature has led to bucking phenomenon and small oscillations around a new post-⋆ e-mail: a.warminska@pollub.pl ⋆⋆ e-mail: e.manoach@imbm.bas.bg ⋆⋆⋆ e-mail: j.warminski@pollub.pl buckled state or large chaotic oscillations around the neutral position. The thermo-elastic Timoshenko beam model has been extended for a nonuniform distribution of the temperature [6]. The reduced model allowed bifurcation analysis for nonuniform heat distribution.…”

Section: Introductionmentioning

confidence: 99%

A Reduced Model of a Thermo-Elastic Nonlinear Circular Plate

2018

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Abstract. Nonlinear vibrations of a circular plate subjected to mechanical and thermal loadings are presented in the paper. A model of the plate is based on the extended Mindlin theory, taking into account nonlinear geometrical terms and acting heat uniformly distributed along the plate span. The dynamics of a coupled thermo-mechanical problem is reduced from a set of partial differential equations to ordinary differential equations. Considering oscillations around the first natural frequency just one mode reduction is proposed. The analysis shows that elevated temperature shifts the resonance curve and new post-buckling oscillations arise. Depending on initial conditions for the post-buckling state various scenarios of bifurcations take place and transient irregular oscillations may occur. The proposed one degree of freedom model shows a good agreement with response of the model based on three or five-modes reduction.

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