Open AccessProblem on vibration of a bar with nonlinearsecond-order boundary damping
Author(s) -
Alexander B. Beylin,
Л. С. Пулькина
Publication year - 2015
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2015-21-3-9-20
Subject(s) - galerkin method , a priori and a posteriori , boundary value problem , vibration , nonlinear system , boundary (topology) , bar (unit) , mathematics , order (exchange) , mathematical analysis , construct (python library) , calculus (dental) , computer science , physics , acoustics , finance , meteorology , economics , medicine , philosophy , dentistry , epistemology , quantum mechanics , programming language
In this paper, we study the initial-boundary problem with nonlinear dynam- ical boundary condition for the pseudohyperbolic equation. This problem repre- sents a mathematical model of longitudinal vibration in a thick short bar with dynamic nonlinear second-order boundary damping. The existence and unique- ness of a generalized solution are proved. The proof is based on a priori estimates and Galerkin procedure. This approach allows to construct approximation in the suitable for practical application form.