Abstract
The theory and data visualization of flexible closed cylindrical nanoshells nonlinear dynamics under the strip loads action are constructed. The theory is based on hypotheses: Kirchhoff-Love, modified couple stress theory, geometric non-linearity adopted in the T. von Karman form. To obtain the de-sired differential equations, the Hamilton-Ostrogradsky principle was used, which makes it possible to obtain the desired differential equations in mixed form describing nano effects. For reduction to the Cauchy problem in spatial coordinates, the Bubnov-Galerkin method in higher approximations is ap-plied. Further, the Cauchy problem is solved by methods such as Runge-Kutta and Newmark. The convergence of the Bubnov-Galerkin method is studied depending on the number of terms in the original functions expansion in spatial coordinates. The oscillations transition scenario from harmonic to chaotic depending on the number of series members in the Bubnov-Garekin method, as well as depending on the type of load, geometric and size-dependent parameters, is investigated. The numerical experiment results were visualized by nonlinear dynamics methods and using wavelet analysis. It was revealed that the oscillations type substantially depends on these parameters; two types of chaos are observed: chaos and hyperchaos. This was revealed according to the chaos criterion given by Gulik, and the Lyapunov exponents study by the methods of Rosenstein, Kantz, and Wolf. A chaos type analysis was carried out based on the signs of Lyapunov exponents spectrum calculated by the Sano-Sawada method.
Highlights
The nonlinear dynamics problems visualization allows a qualitative assessment of the complex mechanical structures behavior at a new level
An analysis of the nanoshell chaotic oscillations type is carried out according to the chaos criterion given by Gulik [11], as well as on the basis of the Lyapunov exponents spectrum signs calculating by the Sano-Sawada method [12].To confirm the reliability of the results obtained, the senior Lyapunov indices are calculated by several methods: Wolf [13], Kantz [14], Rosenstein [15] and Sano-Sawada
In the Bubnov-Galerkin method, the series members number was taken equal to N = 5, 7, 9, 11, 13, 15 for each of the size-dependent coefficient values = 0,0.1,0.3,0.5, 0.7
Summary
The nonlinear dynamics problems visualization allows a qualitative assessment of the complex mechanical structures behavior at a new level. The modern technology constituent elements are subject to external dynamic action of a forceful nature. Krysko necessitates a comprehensive study of the structures behavior [1,2,3], determining their limiting states and identifying the type of chaotic oscillations. The type of chaotic state was studied using classical systems as an example [5,6]. This article is aimed at constructing a theory and data visualization for the chaotic oscillations analysis of flexible closed cylindrical nanoshells under the strip loads action
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
