Time Domain Modeling and Simulation of Nonlinear Slender Viscoelastic Beams Associating Cosserat Theory and a Fractional Derivative Model

Abstract

A broad class of engineering systems can be satisfactory modeled under the assumptions of small deformations and linear material properties. However, many mechanical systems used in modern applications, like structural elements typical of aerospace and petroleum industries, have been characterized by increased slenderness and high static and dynamic loads. In such situations, it becomes indispensable to consider the nonlinear geometric effects and/or material nonlinear behavior. At the same time, in many cases involving dynamic loads, there comes the need for attenuation of vibration levels. In this context, this paper describes the development and validation of numerical models of viscoelastic slender beam-like structures undergoing large displacements. The numerical approach is based on the combination of the nonlinear Cosserat beam theory and a viscoelastic model based on Fractional Derivatives. Such combination enables to derive nonlinear equations of motion that, upon finite element discretization, can be used for predicting the dynamic behavior of the structure in the time domain, accounting for geometric nonlinearity and viscoelastic damping. The modeling methodology is illustrated and validated by numerical simulations, the results of which are compared to others available in the literature.

Modeling and Visual Servoing of Single and Cooperative Continuum Robots

“…The resulted shape highlights the high impact of the loading pattern, which corresponds to the number and type of the constraints between the tendons and backbones. Dynamic modeling of Cosserat rods considers the system in response to an external loading in the form of distributed loading or boundary conditions at the end [73]- [80]. Many of the previous works focused on modeling continuum objects (such as hair [76], or a piece of fabric [81], [82]), mainly pursued by mathematicians, graphists, and computer engineers.…”

“…Lagrangian-based dynamics of CRs have been formulated mainly using two main approaches, one based on Cosserat rod theory [73], [198], and the other according to the constant-curvature assumption [31]. While the former provides continuous exact modeling, the latter, indeed, is a discrete approach using the classic massspring model.…”

Modeling the creep behavior of GRFP truss structures with Positional Finite Element Method

“…Furthermore, some recent studies about viscoelasticity present developments related to the use of fractional derivatives to obtain simpler rheological models and with a more precise representation of the complex behavior of real materials, such as composite materials, polymeric materials, biological tissues, among others (Bahraini et al, 2013;Pérez Zerpa et al, 2015;Ciniello et al, 2017;Borges et al, 2017).…”