Identification of a Lumped Element Modeled Ring Shaped Structure Via Peak Pickıng Method

Abstract

This paper presents an application of a well-known modal system identification method (i.e., Peak Picking Method) on ring shaped structures with imbalances in terms of natural frequency and damping ratio mismatches, in-silico. To the best of our knowledge, the application of this method to ring shaped structures is novel in the literature. The system is modeled at secondary vibration pattern (n=2) via zero dimension lumped element modeling approach. Hence the model has two orthogonal modes (i.e., 2-DOF) with coupling terms of natural frequency and time constant mismatch azimuth angles in-between. Natural frequencies and damping ratios in modal coordinates are estimated using Peak Picking Method based on Real and Imaginary parts of Direct and Cross Frequency Response Functions (FRFs). For this purpose, sine-sweep force signals are applied to the model and displacement values of the both modes are collected. Additionally, eigenvalue decomposition method is utilized to obtain the system characteristic as well as to derive system parameters and coupling terms in generalized coordinates. This identification approach is applied to model with varying quality factors (ranging between 2,5001,000,000), natural frequencies (ranging between 500-3501 Hz) with numerous natural frequency differences of 0.2 Hz, 1 Hz, and 5 Hz, and different natural frequency azimuth mismatch angle values of pi/6 and pi/12 while keeping the time constant azimuth mismatch angle value at pi/8 for performance evaluations. Results show that Peak Picking Method can accurately estimate the natural frequencies in all scenarios, on the other hand damping ratio estimations present higher errors in lower quality factors. Also, both azimuth mismatch angle estimations always converge to the highest value given, which is a shortcoming of this method.