THE METHOD OF VARIATION OF ARBITRARY CONSTANTS IN THE CASE OF A SYSTEM OF LINEAR DIFFERENTIAL EQUATIONS OF DIFFERENT ORDERS
Kanguzhin B.E. Auzerkhan G.S. Tastanov M.G.
30 September 2021al-Farabi Kazakh State National University
KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2021#111Issue 316 - 27 pp.
The paper considers structures consisting of rods connected in one node.Longitudinal and transverse vibrations of such a structure are described by systems of linear differential equations on star graphs.The noted system of equations consists of three linear differential equations of different orders.Two equations correspond to two transverse vibrations, and the third equation describes the longitudinal vibrations of the bar.Moreover, the system of three linear differential equations in the general case does not decompose. In this work, a fundamental system of solutions of a homogeneous system is constructed when the conjugation conditions are satisfied at the point of connection of the rods. Also, by the method of variation of arbitrary constants, a particular solution of an inhomogeneous system is constructed, which is subject to the conjugation conditions at the point of connection of the rods. In subsequent works, the authors intend to investigate the natural frequencies of longitudinal and transverse vibrations of a structure consisting of many rods.
boundary conditions , boundary problem , boundary value problems , canonical problems , fundamental system of solutions of a homogeneous system , private solution , public solution , star graph , wronskian determinant
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Al-Farabi Kazakh National University, Almaty, Kazakhstan
Akhmet Baitursynov Kostanay regional university, Kostanay, Kazakhstan
Al-Farabi Kazakh National University
Akhmet Baitursynov Kostanay regional university
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