Abstract
The three-dimensional frame is simplified into flat plate by the method of quasiplate. The nonlinear relationships between the surface strain and the midst plane displacement are established. According to the thin plate nonlinear dynamical theory, the nonlinear dynamical equations of three-dimensional frame in the orthogonal coordinates system are obtained. Then the equations 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 boundary 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-dimensional frame are studied 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 artificial method.
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Contributed by Yeh Kai-yuan
Foundation item: the National Natural Science Foundation of Gansu Province (ZS021-A25-007-Z)
Biography: Wang Xin-zhi (1940∼), Professor
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Xin-zhi, W., Gang, W., Yan-ying, Z. et al. Nonlinear dynamical stability analysis of the circular three-dimensional frame. Appl Math Mech 25, 367–372 (2004). https://doi.org/10.1007/BF02437519
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DOI: https://doi.org/10.1007/BF02437519