Publications

Instantaneous Frequency and Damping from Transient Ring-Down Data

Kuether, Robert J.; Brake, Matthew R.

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 and can be applied with a variety of boundary conditions. Non-stationary 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 work uses the short-time Fourier transform to estimate the instantaneous frequency and damping ratio from either measured or simulated transient ring-down data. By combining the discrete Fourier transform with an expanding or contracting window function that moves along the time axis, the resulting spectrum is used to estimate the instantaneous frequencies, damping and complex Fourier coefficients. This method is demonstrated on a multi-degree-of-freedom beam with a cubic spring attachment, and investigates the amplitudefrequency dependence in connection to the undamped nonlinear normal modes. A second example shows the results from experiment ring-down response on a beam with a lap joint, and reveals how the system behaves as energy dissipates.