Wave propagation in pantographic 2D lattices with internal discontinuities

TL;DR

This paper investigates wave propagation in 2D pantographic lattices with internal discontinuities, highlighting the effects of boundary conditions and nonlinearities on wave transmission and potential applications in various engineering fields.

Contribution

It introduces a numerical analysis of wave dynamics in pantographic 2D structures, emphasizing the role of geometrical nonlinearities and boundary conditions in wave behavior.

Findings

Boundary conditions significantly affect wave transmission at discontinuities.

Large rotations can lead to nonlinear wave phenomena such as solitary waves.

Numerical simulations reveal complex wave interactions in pantographic lattices.

Abstract

In the present paper we consider a 2D pantographic structure composed by two orthogonal families of Euler beams. Pantographic rectangular 'long' waveguides are considered in which imposed boundary displacements can induce the onset of traveling (possibly non-linear) waves. We performed numerical simulations concerning a set of dynamically interesting cases. The system undergoes large rotations which may involve geometrical non-linearities, possibly opening the path to appealing phenomena such as propagation of solitary waves. Boundary conditions dramatically influence the transmission of the considered waves at discontinuity surfaces. The theoretical study of this kind of objects looks critical, as the concept of pantographic 2D sheets seems to have promising possible applications in a number of fields, e.g. acoustic filters, vascular prostheses and aeronautic/aerospace panels.