The Application Of Constrained Bifurcation Theory In Several Nonlinear Vibration Problems

Since the middle of last century, nonlinearity has been significant part in all kinds of research, nonlinearity dynamics accordingly become the mostly research aspect in dynamics and control subject. At the same time nonlinearity has been given more recognition in the engineering field. How to conduct designing with theory became a new research aspect. Constrained bifurcation singularity theory help to fully consider the effect of all constrains in many engineering conditions and get all the bifurcation models. So bifurcation theory will become an important method in engineering nonlinear vibration area in the future.In this paper, three parts included are as follow:Shape memory alloy (SMA) is one class of intelligent material system which has shown broad application area. A brief introduction of the main mechanical behavior of SMA including the shape memory effect and superelasticity was presented at first . Also maple software used to numerical compute transition sets and draw bifurcation diagrams. Finally, problems and results were discussed. Found that with the excitation force amplitude increase, when the hystersis loop is inspired ,the SMA woks effective.The problem of suppressing the vibrations of a nonlinear system with a cantilever beam of varying orientation subject to parametric and direct excitation was investigated. The method of multiple scales, was applied to get the average equation. Singularity analysis and numerical computation were used to analyze the solution. Transition sets and bifurcation diagrams were drew. Different parameter's influences on the distribution of transition sets was Discussed. Show that the system may cross different transition set under the different parameter.This paper analyze the data from the tests on nonlinear piecewise rigidity resonant screen with 32 m2 double mass. The key points of equipment were compared and analyzed. Emphasizes on movement condition at different working speeds of two screen boxes. Base on the analysis results to provides favorable guarantee and advantageous precondition for analyzing and improving this equipment.