Variational principles for a double Rayleigh beam system undergoing vibrations and connected by a nonlinear Winkler–Pasternak elastic layer

Abstract Variational principles and variationally consistent boundary conditions are derived for a system of double Rayleigh beams undergoing vibrations subject to axial loads. The elastic layer connecting the modelled as three-parameter nonlinear Winkler–Pasternak with Winkler having linear components Pasternak only component. forced freely vibrating beam using semi-inverse approach. Hamilton’s principle is given quotients vibration frequency buckling load. Natural geometric which leads set coupled due presence beams.