A damping apparatus comprises an actuator consisting of an oscillating element for transforming an electric oscillation into a mechanical oscillation and an amplifying mechanism for amplifying the resulting mechanical oscillation as interposed between two structures at least one of which is a source of vibration so that the mechanical oscillation output of the actuator is superimposed on the vibration to be controlled. As such, it may include a sensor disposed in the path of propagation of the vibration to be attenuated and a control device which, in response to the output signal from said sensor, applies an electric oscillation associated with the vibration to be attenuated. A sensor transforms the mechanical vibration to be attenuated into an electric oscillation and, in response to this output electric oscillation, the control device applies an electric signal associated with the vibration to be attenuated to the oscillating element. This oscillating element transforms the applied electric signal into a mechanical oscillation having a very small amplitude. This small-amplitude mechanical oscillation is amplified by the amplifying mechanism and an amplified mechanical oscillation is made available from the actuator. This output mechanical oscillation from the actuator interposed between two structures is superimposed on the target vibration in its path of propagatin to produce the desired damping effect.