Direct observation of dynamic strain bifurcations and chaos in magnetostrictive amorphous ribbons

Abstract

A theory of bifurcations and chaos observed in an ion sheath

Dynamic characteristics of a subcritical bifurcation with inversion symmetry

“…This system has been used previously to observe various routes to chaos [19] as well as to verify experimentally certain universal models of nonlinear dynamics [20,21].…”

Dynamics of strain bifurcations in a magnetostrictive ribbon

“…In summary, we have developed a coupled oscillator model where the weak magnetic nonlinearity drives the highly nonlinear strain order parameter. The model explains several experimental results on the dynamics of the magnetostrictive ribbon such as (a) the period-doubling bifurcation as a function of h dc and keeping h ac fixed, (b) the quasiperiodic route to chaos as a function of h ac for a fixed dc field, and (c) induced and suppressed chaos under the influence of the resonant perturbing field h r [11][12][13][14][15]. However, the suppressed chaos seen here is for small δ while induced chaos is seen for large δ, which is the opposite of what has been reported.…”

“…Further, we work in one dimension and use dimensionless order parameters. We construct a minimal one-dimensional model with the strain order parameter ǫ and magnetic order parameter m. In our model the weak magnetic nonlinearity is taken to drive the highly nonlinear elastic degrees of freedom [11]. Then the total free energy has three contributions, namely, the strain free energy, magnetic free energy, and magneto-elastic free energy.…”

“…where the strain variable is ǫ = ∂u(y) ∂y , f local is the Landau free energy density, and the second term is the gradient free energy. Guided by the normal forms used [11][12][13][14][15], we use a sixth-order polynomial for the elastic free energy…”

A unified model for the dynamics of driven ribbon with strain and magnetic order parameters

“…Indeed rich dynamics has been realized in experiments on magnetostrictive metallic glass ribbon [22][23][24][25][26][27] , almost twenty years ago. In a series of papers, Vohra and his group reported a host of dynamical features in the study of strain bifurcations in magnetostrictive metallic glass ribbons subjected to the combined influence of sinusoidal (ac) and dc magnetic fields [22][23][24][25][26][27] .…”