NDLI: Nonlinear dynamical stability analysis of the circular three-dimensional frame

Content Provider	Springer Nature Link
Author	Xin zhi, Wang Gang, Wang Yan ying, Zhao Kai yuan, Yeh
Copyright Year	2004
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.
Starting Page	367
Ending Page	372
Page Count	6
File Format	PDF
ISSN	02534827
Journal	Applied Mathematics and Mechanics
Volume Number	25
Issue Number	4
e-ISSN	15732754
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2004-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	three-dimensional frame quasi-plate method bifurcation chaos Applications of Mathematics Mathematical Modeling and Industrial Mathematics Mechanics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Mechanics of Materials Mechanical Engineering

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