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May 12, 2026Mathematics and Mechanics of Complex Systems3 citationsOpen Access

Elastic rarefaction solitary waves in monolayered pantographic waveguides with nearly inextensible links verified by discrete micromodeling

Key Points

The aim is to investigate the propagation of rarefaction solitary waves in monolayered pantographic waveguides with nearly inextensible links.
Utilized a homogenized continuum model to understand wave propagation.
Conducted time-dependent simulations at a discrete scale.
Examined influences of total number of cells, displacement rate, and extensional stiffness on wave behavior.
For an odd number of cells, solitary waves remain largely unaltered post-collision.
An even number of cells causes extreme compression between crests, leading to complete cell closure.
Two propagating tails form as a result of wave interaction in specific configurations.

Abstract

This study demonstrates, via a homogenized continuum model, that monolayered pantographic waveguides with nearly inextensible flexural elements support the propagation of rarefaction solitary waves, whose crests correspond to complete cell closure.To validate the continuum approach and explore key parametric effects, time-dependent simulations are conducted at a discrete scale examining the influence of the total number of cells, the applied displacement rate, and the extensional stiffness of the flexural elements on solitary wave propagation.The interaction of solitary waves is also investigated.Results reveal that, for an odd number of cells, the solitary waves emerge from the collision relatively unaltered, whereas for an even number of cells, the region between the two crests experiences extreme compression, culminating in complete cell closure and the formation of two propagating tails.

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