Geodesic
Problem on vibration of a bar with nonlinear second-order boundary damping
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3 (2015), pp. 9-20

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In this paper, we study the initial-boundary problem with nonlinear dynamical boundary condition for the pseudohyperbolic equation. This problem represents a mathematical model of longitudinal vibration in a thick short bar with dynamic nonlinear second-order boundary damping. The existence and uniqueness 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.
Keywords: dynamic boundary conditions, nonlinear damping, pseudohyperbolic equation, generalized solution, Rayleigh’s model. 
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     author = {A. B. Beylin and L. S. Pulkina},
     title = {Problem on vibration of a bar with nonlinear second-order boundary damping},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {9--20},
     publisher = {mathdoc},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2015_3_a0/}
}
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A. B. Beylin; L. S. Pulkina. Problem on vibration of a bar with nonlinear second-order boundary damping. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3 (2015), pp. 9-20. http://geodesic.mathdoc.fr/item/VSGU_2015_3_a0/