A Bayesian Framework for Selecting Fractional Viscoelastic Models in Unconstrained-Layer Damped Beams

Abstract This work presents a Bayesian framework for the identification and selection of fractional viscoelastic constitutive models for layered beams with unconstrained damping treatments. The physical problem is described by one-dimensional homogenized beam models, in which the viscoelastic layer is represented through a frequency-dependent complex modulus. Both the classical thin-layer formulation and a shear-corrected thick-layer model are considered through a unified effective flexural stiffness. The resulting frequency-domain boundary value problem is solved by the Generalized Integral Transform Technique (GITT), leading to a semi-analytical expression for the beam-tip receptance. This formulation provides an efficient forward model for repeated evaluations in inverse analysis. Several fractional viscoelastic models, including Kelvin--Voigt, Maxwell and Zener formulations, are investigated as competing model classes. Bayesian parameter estimation is performed using Transitional Markov Chain Monte Carlo (TMCMC), which provides posterior samples of the constitutive parameters and estimates of the model evidence. The evidence is then used for Bayesian model class selection, naturally balancing data-fitting capability and model complexity. In addition, global sensitivity analysis is employed to assess the influence and practical identifiability of the uncertain parameters on the frequency-response predictions. The proposed methodology combines a mesh-free semi-analytical structural solver with a probabilistic framework for uncertainty quantification, parameter estimation, and model comparison. The results demonstrate that the GITT-based forward model is suitable for Bayesian inverse analysis of viscoelastic layered beams, enabling the systematic evaluation of competing fractional constitutive descriptions from frequency-response data. The model comparison shows that layer thickness determines which constitutive model is favored by the data, suggesting geometry as an integral part of constitutive-model identifiability.