Mechanics Properties Study Of The Beam And Plate On The Viscoelastic Foundations

The model of Winkle beam and plate laid on elastic foundation is popular in the field of civil engineering for a long period. While it is well known foundations with mechanic properties of elastic-viscoelasity are common and models for elastic-viscoelasity have a great diversity, improvement of solutions of these models is important for development of engineering practice and theory.In this paper, the solutions of the beam and plate laid on elastic foundation are transferred into Laplace space by Laplace transform according to elastic-viscoelastic theory, then the analytic solutions of the beam and plate on viscoelastic foundation are get by inverse Laplace transform; some inverse Laplace transform cannot be transformed easily as the complexity of the boundary conditions, so the numerical inverse Laplace transform method is used, and the solutions of the two simply supported sides and two free sides plate and the two simply supported sides and two fixed sides plate on viscoelastic foundation are deduced.The basic knowledge, the corresponding principle and the calculation method of the elastic—viscoelastic foundation are introduced. Through the analytic solutions of the beam and plate laid on elastic foundation, the corresponding equations of Laplace space are deduced following the corresponding principle by Laplace transform. At the same time, the solutions about the viscoelastic foundation are deduced by the methods in this paper, and examples are presented to illustrate the correctness of the method and the results.As the solutions of the beams and plates on the viscoelastic foundations with different boundary conditions are not perfect in engineering, the results in this paper puts forward the study to viscoelastic foundation theory, and they have important guide meanings to the designs and constructions of plates on freeway, airport aircraft parking area, wharf freight shed, slab-foundations.