Shapeable objects may be of great importance to provide solutions for energy harvesting or to help to optimize technical processes. We propose the study of the dynamical behavior of a vanishing stiffness shell obtained by plastic deformations of a circular plate.
Preliminary experimental observations have already shown a rich nonlinear dynamics with many intriguing features. We plan both an experimental campaign and a theoretical model to demonstrate that the plate works virtually at zero stiffness, like in an ideal case, over a large span of the parameter space.
This is due to a parametric internal resonance between the Lagrangian parameter controlling the curvature and the angular coordinate controlling the curvature direction.
Whilst regular and chaotic motions are both possible, we study the parametric range in which the system dynamics is dominated by a constant-speed precession of the axis of maximal curvature. Interesting applications are envisaged in the field of energy harvesting.
To our knowledge the analysis of the dynamic behavior of structures with vanishing stiffness modes has never been studied in a satisfactory way.
From the technological point of view the properties which have been experimentally observed and, in particular, the constant-speed precession of the curvature axis described above are attractive properties for many Engineering applications.
Suffice to notice that these properties are very robust and are independent on the forcing amplitude for a wide range of values.
From the scientific point of view e are confident that the parametric instability leading to convey the system energy into the vanishing stiffness mode has never been described before at least in the context of structural analysis. As such it can be a basic mechanism for the transfer of energy in many other structural systems.