Evaluation of the damping ratio for a base-excited system by the modulations of responses

Abstract The present article gives a method for evaluating or identifying the linear viscous damping ratio of single-degree-of-freedom systems, which are excited from its base. Unlike most of the existing methods that are based on transient responses and the assumption of small damping, the present method does not require the system to have a small damping. The novel method is derived using the input-forcing function as the reference signal, and the corresponding system responds as the modulator. However, in order to get the phase-lag signal without measuring the amplitudes of input and response, a second reference signal has been proposed in the present report. That is, the input-forcing function with 90 ∘ shift in its phase is taken as the second reference. The two modulated signals are then independently split into two parts. The part, which is time-invariant, is the one containing the system damping. It has been shown by the numerical simulations that the given method identifies the damping ratio with a good accuracy if the excitation frequency is tuned to the phase-sensitive region. Finally, the experimental study in the present report also further substantiates the applicability and validity of the method.