Estimating Experimental Dispersion Curves from Steady-State Frequency Response Measurements

TL;DR

This paper introduces a data-driven method to estimate dispersion curves from steady-state frequency response measurements, offering advantages over transient techniques in accuracy and noise susceptibility.

Contribution

It proposes a novel approach using vector-fitting on experimental FRFs to estimate dispersion curves, reducing the need for transient experiments and high sampling rates.

Findings

Maximum 4% error in group velocity estimation over 40 kHz

Out-of-plane FRFs provide accurate dispersion estimates

Method outperforms transient experiment-based estimates

Abstract

Dispersion curves characterize the frequency dependence of the phase and the group velocities of propagating elastic waves. Many analytical and numerical techniques produce dispersion curves from physics-based models. However, it is often challenging to accurately model engineering structures with intricate geometric features and inhomogeneous material properties. For such cases, this paper proposes a novel method to estimate group velocities from experimental data-driven models. Experimental frequency response functions (FRFs) are used to develop data-driven models, {which are then used to estimate dispersion curves}. The advantages of this approach over other traditionally used transient techniques stem from the need to conduct only steady-state experiments. In comparison, transient experiments often need a higher-sampling rate for wave-propagation applications and are more susceptible to noise. The vector-fitting (VF) algorithm is adopted to develop data-driven models from experimental in-plane and out-of-plane FRFs of a one-dimensional structure. The quality of the corresponding data-driven estimates is evaluated using an analytical Timoshenko beam as a baseline. The data-driven model (using the out-of-plane FRFs) estimates the anti-symmetric ($A_0$) group velocity with a maximum error of $4\%$ over a 40~kHz frequency band. In contrast, group velocities estimated from transient experiments resulted in a maximum error of $6\%$ over the same frequency band.