Nonlinear Dynamic Analysis For Moderate Thickness Rectangular Plates With Four Free Edges Resting On Viscoelastic Foundation

The structure of viscoelastic foundation plates were widely used in engineering. The question of nonlinear free vibration analysis for moderate thickness rectangular plates with four free edges resting on viscoelastic foundation has been widespread concerned in academic and engineering fields,but due to the complexity of the foundation model and boundary conditions handling problems,has not been resolved satisfactorily. Based on the theory of Reissner moderate thickness plate, considering the effects of foundation viscous force for nonlinear vibration of plate, the Hamilton energy variational principle was used to establish the nonlinear dynamic equations of the moderate thickness rectangular plates with four free edges resting on viscoelastic foundation considering the coupling effect of the foundation in order to solve the question of free rectangular middle thick plate with biparametric viscoelastic foundation; the vibration method of pb-2 Rayleigh-Ritz analysis the vibration problems of moderate thickness rectangular plates with four free edges resting on a biparametric viscoelastic foundation was used in order to solve the question of free rectangular middle thick plate with biparametric viscoelastic foundation, the influence and change laws of the vibration characteristics of the plates caused by the size parameters,transverse shear factor, reaction modulus of foundation are discussed in the paper. The article also apply Rayleigh-Ritz method and iteration method, some analysis and research were made about the dynamic characteristics of the moderate thickness rectangular plates under harmonic loads and vehicle loads, the influence of the geometric parameters of plates,foundation elastic modulus and foundation viscous forces for moderate thickness rectangular plates with four free edges resting on viscoelastic foundation were investigated, the development and innovation were conducted for the traditional research methods of moderate thickness rectangular plates on viscoelastic foundation. Research on the dynamics characteristics of the two-parameter viscoelastic foundation plates, help people to have a better understanding on the dynamics characteristics of the pavement plates, also to provide guidance and reference for the engineering practice.First of all, based on the Reissner-Mindlin theory, Hamilton energy principle was used to study the nonlinear vibration properties of the moderate thickness rectangular plates with four free edges resting on a two-parameter viscoelastic foundation. Considering the effect of transverse shear for the plates, shear factor of the plates was introduced to motion control equation of the moderate thickness rectangular plates. The influence of the geometrical parameters of the moderate thickness rectangular plate, the foundation reaction modulus and viscous forces of the foundation for the free vibration frequency of the moderate thickness rectangular plates with four free edges resting on viscoelastic foundation.Besides, the forced vibration response of the moderate thickness rectangular plates with four free edges resting on viscoelastic foundation under the harmonic loads were researched. Discusses the effect of the aspect ratio,the thickness -span ratio, the foundation reaction modulus, foundation tensile coefficient, amplitude and frequency of the excitation force and other factors of the rectangular plates under harmonic loads on the plates of the amplitude-frequency response curves.Finally, based on the Reissner moderate thickness plates theory, introducting of a quarter vehicle model and using Hamilton’s energy variational principle, considering the coupling effect of foundation, geometric nonlinear effects transverse shear deformation effect and other factors,derive the nonlinear motion equations of the three coupled system of vehicles-pavement-the foundation, and use the Galerkin method to solve the approximate of equations. Under total unsprung mass and unsprung mass,through numerical examples analyze the dynamic response of pavement systems excluding vehicle excitation in both cases.