Classical Solution of a Mixed Problem of Vibrations of a Nonlinear Timoshenko Beam

This paper is devoted to the study of a mixed problem in a half-strip for a hyperbolic second-order system of partial differential equations, which can be used to model vibrations of finite Timoshenko beams. The solution to the problem is constructed in an implicit analytical form as a solution to a system of some integro-differential equations. The solvability of these equations, as well as the dependence on the initial data and the smoothness of their solutions, is studied. For the problem in question, the uniqueness of the solution is proved and the conditions under which its classical solution exists are established.