Nonlinear Forced Axisymmetric Vibrations Of Thin Circular Plate And Shallow Spherical Shell

The nonlinear forced axisymmetric vibration of a thin isotropic circular plate subjected harmonic excitation loading is examined in details. The nonlinear axisymmetric stability and the nonlinear forced axisymmetric vibration of an isotropic shallow spherical shell subjected uniform and harmonic excitation loadings are investigated in details, respectively. Main contents of this thesis are as the follows:1. Based on von Karman plate theory and Hamilton's principle, nonlinear governing equations of axisymmetric forced vibration of a thin isotropic circular plate are derived. The time variable is eliminated by using Kantorovich time average proceeding on a public period of the free vibration and the forced vibration. Partial differential equations of the problem are converted into a set of differential equations with the space variable. Considering the interaction between static deformation and dynamic response, the numerical solutions are obtained under clamped and simply supported boundary conditions by using a shooting method, respectively. The effects of loading parameters on the dynamic response under two boundary conditions are investigated through lots of charts. The dynamic response of the plate and jumping phenomenon in the principal resonance zone are discussed in details.2. Based on shallow shell theory, displacement-type axisymmetric nonlinear basic equations of an isotropic shallow spherical shell under uniform external pressure are derived. The numerical results of a peripheral clamped and simply supported boundary conditions are obtained by employing a shooting method. Some characteristic curves of load versus deflection of the shell for different arch high are given. Some typical configuration curves are given under two different boundary conditions, In addition, stiffness and stability of the shallow spherical shell are also discussed.3. Based on shallow shell theory, the displacement-type nonlinear governingequations of forced vibration of an isotropic shallow spherical shell are derived under considering transverse inertia and ignoring in-plane inertia and rotational inertia conditions. The time variable is eliminated by using Kantorovich time average proceeding on a public period of the free vibration and the forced vibration. Partial differential equations of the problem are converted into a set of differential equations on the space variable. Considering the interaction between static deformation and dynamic response, the numerical solutions are obtained under clamped and simply supported boundary conditions by employing a shooting method, respectively. The effects of loading parameters on the dynamic response under two boundary conditions are investigated through lots of charts. The dynamic response of the shell and jumping phenomenon in the principal resonance zone are discussed in details.