Identification of Nano-Beams Rigidity Coefficient: A Numerical Analysis Using the Landweber Method

Elisa Ferreira Medeiros; Adriano De Cezaro; Fabiana Travessini De Cezaro

Elisa Ferreira Medeiros Instituto Federal de Educação, Ciência e Tecnologia Sul-rio-grandense, Pelotas, RS http://orcid.org/0000-0002-5356-8244
Adriano De Cezaro Instituto de Matemática, Estatística e Física, Universidade Federal do Rio Grande, FURG http://orcid.org/0000-0001-8431-9120
Fabiana Travessini De Cezaro Instituto de Matemática, Estatística e Física, Universidade Federal do Rio Grande, FURG http://orcid.org/0000-0001-9401-5315

Keywords: micro/nano-beams, inverse problem, fractal media, Landweber's method

Abstract

Due to their supporting function, beams are one of the main elements in structural projects. With the intense technological development in the field of nanotechnology, beams at micro- and nanoscales have become objects of intense study and research interest, see for example [8]. In this approach, we analyze numerically the inverse problem of identifying the stiffness coefficient in micro-nano-beams as a function that implicitly depends on the fractal media map for the continuum from strain measurements. Such a problem is unstable with respect to noise in strain measurements, which is inherent in practical problems. We introduce the equations that compose Landweber's iterative regularization method as a strategy to obtain a stable and convergent approximate solution with respect to the noise level in the measurements. We show some scenarios with simulated data for identifying the stiffness coefficient for different noise levels in measurements and for different coefficient of transformation of fractal medium. The results found numerically show that Landweber's method is a regularization strategy for the problem of identifying the stiffness coefficient in micro/nano-beams.

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