A selective damping apparatus includes at least one sensor for detecting, and producing signals indicative of at least the frequency and amplitude of vibrations of a first structural component (a “resonant structure”) having one or more resonant frequencies. At least one vibration generator is provided for generating damping vibrations for application to the resonant structure, as well as a controller for controlling the operation of the vibration generator in delayed response to the signals produced by the at least one sensor. The at least one sensor and at least one vibration generator are adapted to cooperate with a second structural component (a “non-resonant structure”) that is relatively insensitive to the resonant frequencies of the resonant structure. The nonresonant structure is connected or coupled to the resonant structure either directly or indirectly, via one or more intermediate structural components.