Nonlocal viscoelastic Euler-Bernoulli beam model: a Bayesian approach for parameter estimation using the delayed rejection adaptive metropolis algorithm

Abstract

The present work presents a model for nonlocal and viscoelastic Euler-Bernoulli beams and aspects of its calibration are addressed. The nonlocal feature of the model is described by the nonlocal elasticity theory proposed by Eringen and its viscoelastic behaviour is modelled by means of internal variables. Parametric analyses are performed to determine the impact of the nonlocal and viscoelastic parameters on the modal properties of the system. Inverse analyses are performed under the Bayesian framework and samples of the posterior density function are obtained by means of the Delayed Rejection Adaptive Metropolis (DRAM). The inverse analyses consider a nonlocal viscoelastic beam model with one internal variable and they address three aspects, namely: the impact of a misspecification of the beam diameter, the impact of modelling the beam diameter as an unknown but uninteresting model parameter and the model calibration when synthetic experimental data comes from a model containing two internal variables. The model parameters were chosen such that the system resembles a Single-Walled Carbon Nanotube (SWCNT).

Keywords:

• Nonlocal viscoelasticity
• internal variables
• parametric analysis
• Bayesian inference
• delayed rejection adaptive metropolis

2010 Mathematics Subject Classifications:

• 62F15
• 62D05
• 74Dxx

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - (CAPES/Brasil) under Finance Code 001, by Fundação Carlos Chagas Filho de Amparo á Pesquisa do Estado do Rio de Janeiro (FAPERJ) and by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under grant number 304773/2017-4 and 210.360/2019.