A numerical investigation on impulse-induced nonlinear longitudinal waves in pantographic beams. (January 2022)

• Record Type: Journal Article
• Authors: Turco, Emilio; Barchiesi, Emilio; dell'Isola, Francesco
• Is Part Of: Mathematics and mechanics of solids. Volume 27:Number 1(2022)
• Page Start: 22
• Page End: 48
• Publication Date: 2022-01
• Subjects: Mechanical metamaterials -- discrete models -- nonlinear longitudinal waves -- stepwise analysis -- impulsive loads -- pantographic structures; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/10812865211010877
• Languages: English
• ISSNs: 1081-2865

Abstract

This contribution presents the results of a campaign of numerical simulations aimed at better understanding the propagation of longitudinal waves in pantographic beams within the large-deformation regime. Initially, we recall the key features of a Lagrangian discrete spring model, which was introduced in previous works and that was tested extensively as capable of accurately forecasting the mechanical response of structures based on the pantographic motif, both in statics and dynamics. Successively, a stepwise integration scheme used to solve equations of motions is briefly discussed. The key content of the present contribution concerns the thorough presentation of some selected numerical simulations, which focus in particular on the propagation of stretch profiles induced by impulsive loads. The study takes into account different tests, by varying the number of unit cells, i.e., the total length of the system, spring stiffnesses, the shape of the impulse, as well as its properties such as duration and peak amplitude, and boundary conditions. Some conjectures about the form of traveling waves are formulated, to be confirmed by both further numerical simulations and analytical investigations.