The Study On Chaotic Behavior Of Cylindrical Shell And Plate Under Loading Excitation

The thin plate and cylindrical shell, which are the structural elements often used in practical engineering, are being widely applied to aviation, aerospace, military science ship, architecture and etc. The study on their dynamic behavior is a hot topic in solid mechanics. In the 1970s the development upsurge of nonlinear science was raised. The new concepts and methods such as bifurcation and chaos were introduced to the analysis of the structural dynamic behavior, which brought a fresh air into research. Nowadays the chaotic research of thin plate and cylindrical shell mainly focus on perfect, rarely on initial imperfection.However, a certain initial imperfection actually exists in those elements, the study on their nonlinearity have important significance. Based on the above, chaotic motion of imperfect thin rectangular plate and cylindrical shell are investigated on the basis of the theory of large deflection. The results are given as follows:1. Chaotic motion of imperfect cylindrical shell under transverse periodic excitation or under axial pressure and transverse periodic excitation are investigated on the basis of Donnell-Kármán theory of thin shell. The nonlinear dynamic equations of thin cylindrical shell are changed into the square-order and cubic nonlinear differential dynamic system by Galerkin method, and its homoclinic orbit parameter equations are also acquired. The critical conditions of horseshoe-type chaos are obtained by using Melnikov function. The influences of initial imperfection on chaotic motion of system are analysed. The motion behavior of system are described through the bifurcation diagrams, the time-history curve, phase portrait and Poincarémap.2. On the basis of von-Kármán theory of thin plate, chaotic motion of imperfect thin rectangular plate under transverse periodic excitation or under axial pressure and transverse periodic excitation are investigated by using Galerkin method, Melnikov function, the bifurcation diagrams, the time-history curve, phase portrait and Poincarémap.3. The nonlinear dynamic equations of imperfect viscoelastic cylindrical shell and thin rectangular plate under transverse periodic excitation are obtained on the basis of the theory of large deflection ( Donnell-Kármán theory of thin shell and von-Kármán theory of thin plate ) and Kelvin-Voigt constitutive relation.Their chaotic behavior are investigated by using Galerkin method, Melnikov function, the bifurcation diagrams, the time-history curve, phase portrait and Poincarémap.