Modelagem numérico-computacional de vigas sanduiches viscoelásticas sujeitas a grandes deslocamentos na presença de Incertezas paramétricas

Abstract

This work is dedicated to numerical-computational modeling of viscoelastically damped sandwich beam structures and subject to non-linearity by large displacements. To evaluate the nonlinear effects, the strain field was modeled according to the classical theory of Von Karman and the nonlinear response of the system obtained by combining the Galerkin method and the Harmonic Balance method. In order to represent the effects of damping on the Galerkin base, it was necessary to solve the complex eigenvalue problem, and in this case, an iterative method was proposed so that the undamped natural frequencies converged to the damped frequencies. The costly computational effort during the calculation of the complex eigenvalues was reduced thanks to the model reduction method proposed in this work. In order to take into account the uncertainties arising from geometric and physical factors, a non-linear stochastic model based on the discretization of random Karhunen-Loève fields was also evaluated. To verify the accuracy of the deterministic and stochastic numerical-computational model for the nonlinear sandwich beam, an experimental procedure was also carried out inside a thermal camera with strict temperature control. Through the various examples of simulations and experimental tests, the results show that the methodologies proposed in this work were able to represent the influence of operational and environmental conditions on dynamic responses in viscoelastic systems with geometric nonlinearity. It was verified both numerically and experimentally that the non-linear response of the system is influenced by factors such as the excitation force and the operating temperature of the viscoelastic material.