Simultaneous Estimation of Multiple Backbone Curves Using Smooth Coordinate Tracking

We present a novel algorithm for accurately estimating frequency-amplitude backbone curves of weakly damped mechanical systems with weak stiffness-based nonlinearities. Our smooth-coordinate-decomposition-based algorithm decomposes multivariate decay responses into sets of single-degree-of-freedom responses and rejected noisy coordinates. By applying local and global techniques on orthogonal smooth coordinate pairs, our algorithm estimates each mode’s instantaneous frequency and amplitude, allowing for simultaneous estimation of multiple backbone curves for all excited modes.