Author(s)

J. T. Katsikadelis & N. G. Babouskos

Abstract

In this paper the buckling of viscoelastic plates is studied. The constitutive equations of the viscoelastic material are expressed in differential form using fractional derivatives. The proposed analysis is illustrated with the fractional Kelvin-Voigt and fractional Standard solid models. Plates of arbitrary shape with any type of boundary conditions under interior and edge conservative membrane loads are considered. The principle of the analog equation is applied to convert the original equation into a plate equation (biharmonic) under a fictitious load. Subsequent application of the BEM enables the spatial discretization resulting thus an initial value problem for the values of the fictitious load, which is a system of linear Fractional Differential Equations (FDEs) with respect to time. Using a property of the Mittag-Leffler function a dynamic criterion is established and the eigenvalue problem for the evolution equations is converted into an eigenvalue problem of linear algebra, which permits the evaluation of the buckling loads of the viscoelastic plate. Several plate problems are studied and interesting conclusions on the effect of viscoelasticity on bucking of thin plates are drawn. Keywords: thin plates, viscoelastic, fractional derivative models, buckling, boundary element method, analog equation method. 1 Introduction The buckling of viscoelastic structures modelled with integral or integer order differential constitutive equations has been investigated by several authors [1–3]. There are papers dealing with the stability of viscoelastic beams [4–7] and viscoelastic plates under conservative loads [8–10] using such models. In the last

Keywords

thin plates, viscoelastic, fractional derivative models, buckling, boundary element method, analog equation method