Research On Nonlinear Statics And Dynamics For The Moderate Thickness Rectangular Plates Including The Coupled Effect Of Elastic Foundation

The moderate thickness rectangular plate on elastic foundation is considered as the subject investigated in this dissertation. The nonlinear static behaviors, the nonlinear vibration behaviors, the bifurcation and chaos motions of the moderate thickness rectangular plate with or without crack are investigated systematically under considering the coupled effect of the foundation. And the nonlinear static and dynamic behaviors of the discontinuities moderate thickness rectangular plate with dowels on elastic foundation are studied. The investigation results have more profound theoretical significances and important engineering application values. The main results contain as follows:Based on Reissner moderate thickness plate theory and using energy variation principle, a coefficient γ_d reflecting the sedimentation degree of the foundation is proposed. Then, the calculation formula of foundation modulus denoted by γ_d is derived. The nonlinear control equations for the moderate thickness rectangular plate on elastic foundation are derived with considering the coupled effect of the foundation and nonlinear effect of the plate which can effectively reflect that the elastic foundation works well with the moderate thickness plate. The suitable expressions of trial functions satisfied all boundary conditions are sought. By means of Galerkin method, the nonlinear bending problems for the moderate thickness rectangular plate on elastic foundation with freely supported boundary are investigated. In additional, by choosing the beam eigenfunctions as the form of solution, and using Galerkin method and harmonic balance method, the nonlinear equations of motion are solved. In the numerical computations, the effects of the structure parameters of the plate and the parameters of foundation on the nonlinear bending behaviors and the nonlinear free vibration behaviors, for the moderate thickness rectangular plate on elastic foundation with freely supported boundary, are discussed and compared with previous data.The moderate thickness rectangular plate with dowels on elastic foundation is investigated. The discontinuities of the plates are connected by dowels. The load transferred on dowels is modeled as vertical springs. The stiffness of vertical springs is depended on the dowel properties and the dowel-plate interaction. By using energy variation principle, the nonlinear control equations of the moderate thickness plate with discontinuities on two-parameter foundation are derived including the coupledeffect of the foundation. The suitable expressions of trial functions satisfied all boundary conditions of the problem are sought. By means of Galerkin method and harmonic balance method, the nonlinear equations are solved. In the numerical computations, the effects of the parameters of dowels, the structure parameters of the plate as well as the parameters of foundation on the nonlinear bending and free vibration behaviors of moderate thickness rectangular plate with discontinuities on elastic foundation, are considered and compared with previous data.By using the energy variation principle, the nonlinear control equations for moderate thickness plate with transverse surface penetrating crack and freely supported boundary on elastic foundation are derived. The physical features in crack are modeled as equal line-springs. The suitable expressions of trial function satisfied all boundary conditions and crack's continuous conditions are sought. By using the Galerkin method and harmonic balance method, the problems are solved. In the numerical calculations, the influences of the different location and depth of crack, the structure parameters of the plate as well as the parameters of foundation on the nonlinear bending behaviors and the nonlinear free vibration behaviors of the freely supported moderate thickness rectangular plate on elastic foundation are considered.By employing the modern methods in nonlinear dynamics and introducing new variables, the complex nonlinear dynamic system of the moderate thickness rectangular plate with or without crack on elastic foundation are investigated qualitatively. The time history, phase plane portrait, Poincare map, bifurcation diagram and so on, for the nonlinear system are determined and the plenty and complex nonlinear dynamical behaviors are revealed. In the numerical calculations, the effects of the external excitation, the different location and depth of crack as well as the parameters of foundation on the bifurcation and chaos motions of the moderate thickness rectangular plate on elastic foundation are considered in detail.