Initial–Boundary Value Problems for the Beam VibrationEquation with Allowance for Its Rotational Motionunder Bending

Initial value problems with various boundary conditions at the ends are studied for the beam vibration equation taking into account the beam rotational motion under bending. An energy inequality is established, which implies the uniqueness of the solution of the four initial–boundary value problems posed. In the case of hinged ends, theorems on the existence and stability of the solution of the problem in the classes of regular and generalized solutions are proved.

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