Nonlinear Dynamical Stability Analysis of the Circular Three-Dimensional Frame

The three dimensional frame is simplified into flat plate by the method of quasi-plate. The nonlinear relationships between the surface strain and the ntidst plane displacement are established According to the thin plate nonlinex dynantical theory,the nonlinear dynantical equations of threedimensional frame in the orthogonal coordinates system are obtained Then the equatiorn are translated into the axial symmetry nonlinear dynamical equations in the polar coordinates system. Some dimensionless quantities different from the plate of uniform thickness are introduced under the boundxy conditions of fixed edges,then these fundamental equations are simplified with these dimensionless quantities. A cubic nonlinear vibration equation is obtained with the method of Galerkin. The stability and bifurcation of the circular three-dimernional frame are steadied under the condition of without outer motivation. The contingent chaotic vibration of the three-dimensional frame is studied with the method of Melnikov. Some phase figures of contingent chaotic vibration are plotted with digital artifivial method.