Problem on vibration of a bar with nonlinearsecond-order boundary damping

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.

dynamic boundary conditions, nonlinear damping, pseudohyperbolic equation, generalized solution, Rayleigh’s model.