Abstract
The purpose of this paper is to study nonlinear oscillations of a heated plate subjected to dynamic loading. The response of moderately thick circular plate at elevated temperatures subjected to harmonic loading is analysed. A mathematical model of the plate is derived applying the geometrically nonlinear Reisner-Mindlin plate theory. A reduced model of the plate motion is created and the harmonic balance method is applied to the reduced model taking into account the first vibration mode. The numerical simulations are performed for the plate subjected to uniformly distributed harmonic loading and different temperatures. The model represented by a set of partial differential equations is reduced to one degree of freedom system by Galerkin orthogonalization method based on the first vibration mode. The obtained reduced nonlinear one degree of freedom model with cubic nonlinearity is studied by the harmonic balance method. The influence of the amplitude of the loading and the elevated temperature on the frequency response functions is studied.
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Acknowledgments
This work has been accomplished with the financial support of the Bulgarian Ministry of Education and Science, Grant No. D01-221/03.12.2018 for NCDSC—part of the Bulgarian National Roadmap on RIs. The second author has been financed within the framework of the project “Lublin University of Technology-Regional Excellence Initiative”, funded by the Polish Ministry of Science and Higher Education (Contract No. 030/RID/2018/19).
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Doneva, S., Warminski, J., Manoach, E. (2021). Dynamics of Circular Plates Under Temperature and Mechanical Loadings. In: Awrejcewicz, J. (eds) Perspectives in Dynamical Systems II: Mathematical and Numerical Approaches. DSTA 2019. Springer Proceedings in Mathematics & Statistics, vol 363. Springer, Cham. https://doi.org/10.1007/978-3-030-77310-6_19
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DOI: https://doi.org/10.1007/978-3-030-77310-6_19
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