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AUTHOR(S): Ludmila Alexeyeva, Asiyat Dadayeva, Nursaule Ainakeyeva
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TITLE General Function Method in Periodic Boundary Value Problems on Thermoelastic Star Graphs |
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ABSTRACT Boundary value problems of thermoelasticity on graphs can be used to study various thermoelastic network structures under the action of various external forces and thermal heating or cooling. This makes it relevant to formulate and solve such problems on graphs of various structures. In this paper, using the method of generalized functions, a technique for calculating the thermoelastic state of star-type rods and rod structures is developed. Generalized solutions of non-stationary and stationary boundary value problems of thermoelasticity are constructed for various boundary conditions at the ends of the star graph and the generalized Kirchhoff condition at its common node. Regular integral representations of solutions to boundary value problems in analytical form are obtained. The obtained solutions allow modeling sources of forces and heat of various types, including using singular generalized functions. The developed technique allows solving a wide class of boundary value problems with local and coupled boundary conditions at the ends of graph edges and various transmission conditions at the nodes of not only a star graph, but also graphs of linear and mixed structure. |
KEYWORDS thermoelasticity, rod, boundary conditions, transmission condition, fundamental and generalized solutions, Fourier transform, resolving boundary equations, thermal conductivity, star graph |
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Cite this paper Ludmila Alexeyeva, Asiyat Dadayeva, Nursaule Ainakeyeva. (2025) General Function Method in Periodic Boundary Value Problems on Thermoelastic Star Graphs. International Journal of Mechanical Engineering, 10, 6-14 |
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