Abstract. We consider several problem statements for the optimal controlled excitation of oscillations of a hinged beam. Oscillations occur under the influence of several external periodic forces. In the simplest statement, it is assumed that the structure of the beam is homogeneous. In a more complex formulation, inhomogeneities (defects) on the beam are allowed. The goal of controlling the oscillations of the beam is to provide a predetermined shape and a predetermined pointwise phase of oscillations in a given frequency range. The task is to determine the number of forces and their characteristics (application, amplitude and phase of oscillations), which provide the desired form of oscillation with a given accuracy. With the help of analytical mathematical methods, the problems in question are reduced to simpler multiextremal problems of minimizing basic functionals, which are numerically solved using the multifunctional package AORDA PSG.

Keywords: vibrations, waveform, optimal actuation.