Dynamics of magneto electro elastic curved beams: Quantification of parametric uncertainties

Abstract

The objective of this paper is the evaluation of uncertainty propagation associated to several parameters in the dynamics of magneto-electro-elastic (MEE) curved beams. These MEE structures can be employed as imbedded parts in high performance technological systems to control motions and/or attenuate vibrations, for energy harvesting, etc. Although a lot of research connected with these structures was done for dynamics and statics, it is remarkable the scarcity of articles analyzing random dynamics of MEE structure, provided that many models have uncertainties associated to their parameters: loads and/or material properties, among others. A theory for MEE curved beams is derived and assumed as the deterministic model. The response is calculated by means of a finite element formulation. The probabilistic model is constructed appealing to the finite element formulation of the deterministic approach, by adopting random variables for the uncertain parameters selected. The probability density functions of the random variables are derived with the Maximum Entropy Principle. The Monte Carlo method is used to perform simulations with independent realizations. Studies are carried out in order to evaluate the influence of Magneto-elastic and/or piezoelectric coupling in the dynamics of MEE curved beams in both contexts: the deterministic and the stochastic.