Bifurcation of Rupture Path-Linear and Nonlinear Damping

Abstract

Bifurcation of rupture path is studied for the effect of linear and nonlinear cubic damping. Momentum equation with Rayleigh factor was transformed into ordinary differential form. Bernoulli differential equation was obtained and solved by the method separation of variables. Analytical solutions yield the bifurcation of linear and nonlinear cubic damping was visible at imaginary part when the wave was non dispersive. For the dispersive wave, bifurcation of rupture path was invisible due to lower cubic damping. Amplitude attenuated during the seismic moment. Imaginary parts of the solutions illustrate the intersection or collision of soliton, for which, the bifurcation of rupture path is initiated. Intersection is not visible if the energy is well dispersed. Wave profile illustrates the existing of linear exciting and nonlinear damping effect during seismic moment.