ANALYSIS OF VISCOELASTIC RECTANGULAR PLATES.

A solution of a viscoelastic rectangular plate of Burgers material is presented. The rheological Burgers model is capable of expressing in a simple manner, linear reversible as well as irreversible long-term deformations. The physical equation for this model was obtained by combining the expressions of deformation dependence of the Maxwell and Kelvin-Voigt solids extended to a multidimensional region. The resultant system of differential equations of strain components and stress components was simplified by the introduction of a proportion between the elastic and viscous transverse compressibility factors. This system of partial differential equations was solved for the stress components sigma //x, sigma //y, sigma //x//y. Using the derived stress components, an integro-differential plate equation was derived for the Burgers material. The integro-differential equation of the deflection surface was solved as Volterra's equation of the second kind by the method of successive approximations. An estimate of the error of the solution was also taken for the j-th approximation.