Analytical study on the motion of a system with varying damping subject to harmonic force

To show the possibility of a new kind of a moment shaker, the motion of a system composed of a rigid plate, constant springs and time-varying dampers has been considered when the plate is subjected to harmonic force. The vertical displacement at the center of the plate and the rotational displacement of the plate were obtained by numerical integration of the equations of motion. The major frequency components of these responses were found through fast Fourier transform and the condition under which the plate oscillates with almost a single frequency and a large amplitude was found. The existence of the frequency components of the vertical and rotational displacements of the plate has been proved analytically. Approximate expressions for the amplitude of the vertical and rotational displacements have been derived for a special case.