Algebraic identification of the first two natural frequencies of flexible-beam-like structures

The residual vibrations of highly resonant flexible structures can be usually composed of sinusoidal signals. The identification of the frequencies, amplitudes and/or phases of these sinusoidal signals may be of interest for health monitoring or to update controller parameters in active vibration control systems. This work considers a previously developed algebraic estimator of the frequencies, amplitudes and phases of two sinusoidal signals in order to identify the first two natural frequencies of flexible-beam-like structures. The influence of the unconsidered vibration modes on the estimation accuracy is studied by simulating a residual vibration formed by four sinusoidal components. It has been shown that the velocity and accuracy in the estimation of the first two natural frequencies depend on the distance between frequencies and the amplitudes of the first three vibration components. Finally, the beam parameters are related to the estimation performance.