Journal of Theoretical
and Applied Mechanics

50, 3, pp. 743-753, Warsaw 2012

Nonlinear dynamic analysis of viscoelastic membranes described with fractional differential models

John T. Katsikadelis
The dynamic response of an initially flat viscoelastic membrane is investigated. The viscoelastic model is described with fractional order derivatives. The membrane is subjected to surface transverse and inplane dynamic loads. The governing equations are three coupled second order nonlinear partial FDEs (fractional differential equations) of hyperbolic type in terms of the displacement components. These equations are solved using the BEM for fractional partial differential equations developed recently by Katsikadelis. Without excluding other viscoelastic models, the herein employed material is the Kelvin-Voigt model with a fractional order derivative. Numerical examples are presented which not only demonstrate the efficiency of the solution procedure, but also give a better insight into this complicated but very interesting response of structural viscoelastic membranes. It is worth noting that in case of resonance, phenomena similar to those of the Duffing equation are observed.
Keywords: viscoelastic membranes; nonlinear vibrations; nonlinear fractional differential equations; analog equation method; boundary elements