A viscoelastic orthotropic Timoshenko beam subjected to general transverse loading

The investigation of lateral vibrations of a simply supported thin beam is the aim of this work. The analytical solution of the problem is derived based on the approximate Timoshenko beam theory for a general continuous loading acting on the upper beam face over the whole beam width and perpendicular to the beam axis. The material of the beam studied is assumed linear orthotropic viscoelastic. The generalized standard viscoelastic solid is chosen for representing of viscoelastic beam behaviour. Final system of partial integro-differential equations is solved by the standard method of integral transforms and resulting relations describing beam deflection, slope of the beam and corresponding stress and strain components are presented. Moreover, the derivation of final functions of beam deflection and slope of the beam for a specific impulse loading is presented and analytical results are compared with results obtained using numerical simulation in 2D (FEM). This confrontation shows very good agreement between results obtained. Furthermore, it was shown that the measure of agreement depends not only on the beam geometry