Chaotic response of a harmonically excited mass on an isolator with non-linear stiffness and damping characteristics

Chaotic oscillations of a harmonically excited mass on a non-linear isolator are investigated. The magnitude of the strictly dissipative damping force on the mass, provided by the isolator, is assumed to be proportional to thepth power of velocity. Both symmetric and asymmetric non-linear restoring forces are considered. Two typical routes to chaos, namely through period-doubling and intermittency, reported already in the literature for linear viscous damping (i.e.,p= 1), are seen to be present with the damping exponentp= 2 andp= 3. Thus the bifurcation structure seems to be unaffected by the damping exponentp.Of course, the values of the damping coefficient (constant of proportionality) needed for complete elimination of the subharmonic and chaotic responses depend on the value of p.A parametric study is presented to indicate the role of the damping exponent, damping coefficient and asymmetry on the onset of chaos. It has been shown that non-linear damping can be used as a passive mechanism to suppress chaos