On reducing uncertainty on the Elliptical Plane modal identification method

Abstract

The Elliptical Plane has been recently introduced as a modal identification method that uses an alternative plot of the receptance. The method uses the dissipated energy per cycle of vibration as a starting point. For lightly damped systems with conveniently spaced modes, it produces quite accurate results, especially when compared to the well-known method of the inverse. When represented in the Elliptical Plane, the shape of the receptance is elliptical near resonant frequencies. The modal damping factor can be determined from the angle of the ellipse’s major axis with the horizontal axis, whereas the real and imaginary parts of the modal constants can be determined from numerical curve-fitting (as in the method of the circle - Nyquist plot). However, the lack of points that can be used near the resonance (due to limitations in the frequency resolution, and effects from other modes near each resonance) and the fact that measurements are polluted by noise, bring uncertainty to the numerical curve-fitting. This paper aims at providing the first steps on the improvement of the quality of the modal identification of the receptance in the Elliptical Plane. The method and results are discussed with a multiple degree-of-freedom numerical example.