Poles tracking of weakly nonlinear structures using a Bayesian smoothing method

Abstract

This paper describes a method for the identication and the tracking of poles of a weakly nonlinear structure from its free responses. This method is based on a model of multi-channel damped sines whose parameters evolve over time. Their variations are approximated in discrete time by a nonlinear state space model. States are recursively estimated by a new method which couples a two-pass Bayesian estimator with an Expectation-Maximization (EM) algorithm. An iterative procedure between them allows an accurate and robust tracking of poles. As a result, equivalent modal parameters such as frequency and damping are obtained as a function of amplitudes. The method is applied on numerical and experimental cases and show promising results.

Challenging an experimental nonlinear modal analysis method with a new strongly friction-damped structure

“…To the best of the authors' knowledge, experiments exhibiting such a large increase in the damping ratio with subsequent decrease are scarce. Stephan et al reported an increase with subsequent decrease in the modal damping ratio for large vibration amplitudes (from about 5.6 % to about 4 %) [14].…”

“…A different approach for nonlinear modal testing, suited for both conservative and non-conservative nonlinearities is adopted from modal hammer testing. By analyzing the free decay, amplitude-dependent modal properties are extracted for the vibration levels covered by the free decay [12][13][14]. This approach assumes weak nonlinearity such that modes remain uncoupled, even when several modes are simultaneously excited through impulse forcing.…”

“…With free-decay approaches, amplitude-dependent modal damping ratios of up to 8 % were determined experimentally, where damping was caused by dry friction [12,14,16,17]. Virtual experiments suggest that high damping ratios can be extracted with force appropriation using PLL [10], but this has not yet been experimentally verified.…”

“…Alternative test rigs replicate a specific joint or contact situation, for example under-platform damper test rigs (e.g. [26][27][28]) or bolted joint such as the Brake-Reuß-beam [29], the joint resonator [30,31] or the H testbench [14]. Since the authors are not aware of a suitable test rig that covers the full range from full-stick to mainly sliding, we suggest a new design of a cantilevered beam under the influence of dry friction.…”

Nonlinear modal testing of damped structures: Velocity feedback vs. phase resonance

“…Nonlinear modal testing refers to obtaining amplitude-dependent modal properties from experimental data. Several researches have proposed to extract modal properties from free decay measurements, either using hammer excitation [9][10][11] or force appropriation with subsequent removal of the excitation [12][13][14]. The signal length of a free decay is inherently limited and depends on the damping.…”