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.
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