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.
Dynamics of 1D nonlinear pantographic continua / Giorgio, Ivan; DELLA CORTE, Alessandro; Dell'Isola, Francesco. - In: NONLINEAR DYNAMICS. - ISSN 0924-090X. - STAMPA. - 88:1(2017), pp. 21-31. [10.1007/s11071-016-3228-9]
Dynamics of 1D nonlinear pantographic continua
GIORGIO, IVAN
;DELLA CORTE, ALESSANDRO;DELL'ISOLA, Francesco
2017
Abstract
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.File | Dimensione | Formato | |
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