Geodesic
On one solution of the vibration problem of mechanical systems with moving boundaries
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 30 (2024) no. 1, pp. 40-49

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An analytical method of solving the wave equation describing the oscillations of systems with moving boundaries is considered. By changing the variables that stop the boundaries and leave the equation invariant, the original boundary value problem is reduced to a system of functional-difference equations, which can be solved using direct and inverse methods. An inverse method is described that makes it possible to approximate quite diverse laws of boundary motion by laws obtained from solving the inverse problem. New particular solutions are obtained for a fairly wide range of laws of boundary motion. A direct asymptotic method for the approximate solution of a functional equation is considered. An estimate of the errors of the approximate method was made depending on the speed of the boundary movement.
Keywords: wave equation, boundary value problems, oscillations of systems with moving boundaries, laws of boundary motion, functional equations.
Mots-clés : change of variables 
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     title = {On one solution of the vibration problem of mechanical systems with moving boundaries},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
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V. L. Litvinov; K. V. Litvinova. On one solution of the vibration problem of mechanical systems with moving boundaries. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 30 (2024) no. 1, pp. 40-49. http://geodesic.mathdoc.fr/item/VSGU_2024_30_1_a3/