A new class of rigorous solutions of the functional differential equation of motion for the mechanical impulses in the 1D nonhomogeneus granular chain A new rigorous solution of the functional differential equation for signal propagation through the vertical granular

Authors: Gerasymov O.I.

Year: 2011

Issue: 11

Pages: 198-202

Abstract

A new rigorous solution of the functional differential equation for signal propagation through the vertical granular chain with a nonlinear contacts has been found under the approximation of the weak nonlinearity in form of the Bessel function of first order. The linear combinations of the solutions we found in principle can satisfy an appropriate initial conditions. This new solution also is a significant supplement to the dispersive wave modes which has been discovered for such a system earlier and could be considered as an envelope function for them. The relevant experiments directed to the experimental studying of the discovered modes are under the current proceeding.

Tags: dynamic systems; energy/impulse transport; granular materials; Hertzian contact; nonlinear chain

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