Vol. 9, No. 3, 2021

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Kinematically triggered nonlinear vibrations of Hencky-type pantographic sheets

Emilio Turco and Emilio Barchiesi

Vol. 9 (2021), No. 3, 311–335
Abstract

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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Keywords
mechanical metamaterials, discrete models, nonlinear dynamical analysis, stepwise analyses
Mathematical Subject Classification
Primary: 74H45
Supplementary material

Figure 5 video clip

Milestones
Received: 22 March 2021
Revised: 7 May 2021
Accepted: 10 June 2021
Published: 8 February 2022

Communicated by Anil Misra
Authors
Emilio Turco
Department of Architecture, Design and Urban Planning
University of Sassari
Alghero
Italy
International Research Center for Mathematics & Mechanics of Complex Systems
Università dell’Aquila
L’Aquila
Italy
Emilio Barchiesi
Dipartimento di Ingegneria Strutturale e Geotecnica
Università di Roma “La Sapienza”
Rome
Italy
École Nationale d’Ingénieurs de Brests
UMR CNRS 6027 (IRDL)
Brest
France
Instituto de Investigación Científica
Universidad de Lima
Santiago de Surco
Peru
Department of Architecture, Design and Urban Planning
University of Sassari
Alghero
Italy
International Research Center for Mathematics & Mechanics of Complex Systems
Università dell’Aquila
L’Aquila
Italy