Transient modeling of ultrasonic guided waves in circular viscoelastic waveguides for inverse material characterization

Abstract

In this contribution, we present an efficient approach for the transient and time-causal modeling of guided waves in viscoelastic cylindrical waveguides in the context of ultrasonic material characterization. We use the scaled boundary finite element method (SBFEM) for efficient computation of the phase velocity dispersion. Regarding the viscoelastic behavior of the materials under consideration, we propose a decomposition approach that considers the real-valued frequency dependence of the (visco-)elastic moduli and, separately, of their attenuation. The modal expansion approach is utilized to take the transmitting and receiving transducers into account and to propagate the excited waveguide modes through a waveguide of finite length. The effectiveness of the proposed simulation model is shown by comparison with a standard transient FEM simulation as well as simulation results based on the exact solution of the complex-valued viscoelastic guided wave problem. Two material models are discussed, namely the fractional Zener model and the anti-Zener model; we re-interpret the latter in terms of the Rayleigh damping model. Measurements are taken on a polypropylene sample and the proposed transient simulation model is used for inverse material characterization. The extracted material properties may then be used in computer-aided design of ultrasonic systems.

An Ultrasonic Laminated Transducer for Viscoelastic Media Detection

“…Through P-wave transmission testing, the wave velocity and attenuation factor were obtained, and then the high-frequency complex modulus was calculated. A transient model of guided waves in a viscoelastic cylinder was established by Bause et al [12], and the scale boundary finite element method was applied to calculate the phase velocity dispersion effectively. Aksoy [13] proposed a method based on the combination of acoustic wave transmission and broadband spectroscopy to realize the measurement of the phase velocity and attenuation coefficient of ultrasonic waves.…”

Ultrasonic transmission measurements in the characterization of viscoelasticity utilizing polymeric waveguides

“…Validation of this novel combination of modal expansion approach and SBFEM based on a real-valued (i.e. elastic) material model can be done by using a time domain finite element simulation, see [46] for details on the FEM model. As time domain simulations in FEM often only allow considering the Rayleigh damping model, a validation of the viscoelastic case is not straightforward, see also [46,47] for details on a validation of modal expansion in the context of Rayleigh damping.…”

“…This approximation does not have any influence on the experiments, because of the high damping characteristics of the polymers under consideration. damped signal including Rayleigh damping behavior, where in FEM we used the Rayleigh damping model and the Anti-Zener model for SBFEM and modal expansion, see [46,47].…”

Investigation of Viscoelastic Guided Wave Properties in Anisotropic Laminated Composites Using a Legendre Orthogonal Polynomials Expansion–Assisted Viscoelastodynamic Model

“…Based on the spectral finite–element method, Marzani [ 12 ] investigated the transient responses of attenuative guided waves in damped cylinders, and Luo et al [ 13 ] studied the propagation of guided waves in layered viscoelastic film materials. By establishing boundary finite–element–based models considering the anti–Zener and fractional Zener viscoelastic models, Bause et al [ 14 ] simulated the transient responses of guided waves in viscoelastic waveguides. Hayashi et al [ 15 ] established a semi–analytical finite–element (SAFE) method to obtain the phase– and group–velocity dispersion curves for bars with arbitrary cross–sections.…”