Kinematically triggered nonlinear vibrations of hencky-type pantographic sheets

Pantographic metamaterials are receiving increasing attention from the scientific community working in theoretical and numerical mechanics. Nevertheless, dynamic analysis of pantographic sheets in the large deformation regime is still a scarcely explored topic which deserves to be thoroughly investigated on its own. With the aim of contributing to filling this gap, we study kinematically triggered vibrations in pantographic sheets. More specifically, two tests are considered. At first, an initial nonzero velocity, i.e., an impulse, is applied to the pantographic sheet at a single fiber's end — such as in a dynamic pull test — which is left free to move afterwards. The second test addresses vibrations induced by a given accelerogram applied to a subset of nodes. In the spirit of Hencky's approach, the whole set of results is obtained by using a completely discrete mechanical model such that the fibers of the pantographic sheet are modeled as extensible Euler-Bernoulli beams, which are in turn discretized by means of rotational and extensional springs. The time integration scheme consists of a stepwise method based on the recently revisited scheme of Casciaro.