Static and dynamic bifurcations in magnetoelastic ribbons (abstract)

The ΔE effect in certain field annealed amorphous ribbon is now about 10, i.e., Young’s modulus E, can be reversibly changed by a factor of 9 with the application of a field of less than 1 Oe. We have reported the field‐induced buckling of a vertically oriented ribbon. The ribbon buckles under its own weight due to the reduction of E with field H. Critical buckling values of H were found to be in good agreement with the eigenvalues of the linearized version of the operator describing the process. Here we present: (a) holographic data where the gradient in the fringe spacing obtained from the hologram of the straight and buckled states is a measure of the curvature; and (b) a rigorous mathematical formalism for extracting from experiment the nonlinear constitutive relation between the curvature θ’(s) and the bending couple m(s) where s is the distance along the ribbon. This process must be carried out (with H as a parameter) from H=0, to values of H somewhat above the anisotropy field, to effect a complete...