Parameter Estimation via Instantaneous Frequency and Damping from Transient Ring-Down Data

Abstract

Broadband impact excitation in structural dynamics is a common technique used to detect and characterize nonlinearities in mechanical systems since it excites many frequencies of a structure at once. Nonstationary time signals from transient ring-down measurements require time-frequency analysis tools to observe variations in frequency and energy dissipation as the response evolves. This chapter uses the Short-Time Fourier Transform (STFT) to estimate the instantaneous parameters from measured or simulated data. By combining the discrete Fourier transform with an expanding or contracting window function that moves along the time axis, the resulting spectra are used to estimate the instantaneous frequencies, damping ratios, and complex Fourier coefficients. Other methods such as Hilbert transforms in conjunction with the Zeroed Early Fast Fourier Transform (ZEFFT) or wavelet based approaches are also able to be applied in similar manners as the STFT. From any of these methods, the amplitude-frequency dependence in the damped response is able to be extracted in order to determine the parameters for a joint model.