Amplitude Modulation of a Forced System by Parameter Variation

Classical (primary) parametric amplification is reviewed. This phenomenon is known to occur for a parametric variation with a frequency of twice that of a harmonic input in the neighborhood of a system’s characteristic frequency. A higher-order phenomenon that is identified as secondary parametric amplification (or attenuation), is discussed in detail and solutions related to Mathieu’s equation are presented. Its occurrence is characterized by a frequency of the parametric variation that is of the order of 2α/n (where n = 1, 2, 3, …, and α is the undamped characteristic frequency of the system) and a harmonic input of a much lower frequency. The amplification (or attenuation) resulting from the secondary parametric amplification phenomenon is manifested in an overmodulated response that must be low-pass filtered to recover the desired low frequency response.