Turbulent phenomena in flexible plates and shells

Abstract

The aim of this chapter is to present a study of periodic and chaotic dynamics of plates and shells and weak turbulent behavior exhibited by these solid structural members modeled as 2D infinite objects. Besides the new results obtained with respect to the transition from a regular to weak turbulent and weak hyper turbulent behavior, we also present novel methods and approaches to get reliable and validated results of numerical analysis of nonlinear partial differential equations. In particular, besides the standard numerical techniques for chaos monitoring, new effective approaches are presented and applied including the wavelet-based analysis, charts of vibration regimes, computation of the spectra of Lyapunov exponents via generalization of the classical Benettin’s approach, and application of the neural network technique. This common strategy aimed at numerical computations through various types of robust discretization allowed us to obtain novel scenarios of transition from regular/laminar (periodic, quasiperiodic) to spatiotemporal chaotic (weak turbulent) dynamics of flexible shells either parametrically excited (Sect. 2) or through the periodic shear load action in the shell volume unit (Sect. 3), flexible multilayer rectangular (Sect. 4) and cylindrical shells with gaps (Sect. 5), as well as a flexible plate of infinite length (Sect. 6).