Increasing dimensions of ground based telescopes and adaptive optics needs for these instruments require wide deformable mirrors with a high number of actuators to compensate the effects of the atmospheric turbulence on the wave fronts. The new dimensions and characteristics of these deformable mirrors lead to the apparition of structural vibrations, which may reduce the rejection band width of the adaptive optics control loop. The aim of this paper is the study of the dynamic behavior of a 1-meter prototype of E-ELT's deformable mirror in order to identify its eigenmodes and to propose some ways to control its vibrations. We first present the first eigenmodes of the structure determined by both finite element analysis and experimental modal analysis. Then we present the frequency response of the prototype to a tilt excitation to estimate the effects of its vibrations on the adaptive optics loop. Finally we suggest a method to control the dynamics of the deformable mirror.