Dynamics of 1D nonlinear pantographic continua

Ivan Giorgio (1, 2) , Alessandro Della Corte (3, 1) , Francesco Dell 'Isola (1, 2)

1 M&MoCS - International Research Centre on Mathematics & Mechanics of Complex Systems
2 Department of Structural and Geotechnical Engineering
3 Department of Mechanical & Aerospace Engineering

In this paper a mechanical system consisting of a chain of masses connected by nonlinear springs and a pantographic microstructure is studied. A homogenized form of the energy is justified through a standard passage from finite differences involving the characteristic length to partial derivatives. The corresponding continuous motion equation, which is a nonlinear fourth-order PDE, is investigated. Traveling wave solutions are imposed and quasi-soliton solutions are found and numerically compared with the motion of the system resulting from a generic perturbation.

Domaines: Génie mécanique [physics.class-ph]

Ivan Giorgio, Alessandro Della Corte, Francesco Dell 'Isola. Dynamics of 1D nonlinear pantographic continua. 2016. ⟨hal-01400478⟩