Array of nanostrings electromagnetically interacting through repelling Lorentz forces

The collective stability behavior of a planar array of parallel nanostrings interacting through electromagnetic Lorentz forces is analyzed. The repelling coupling forces between the neighboring strings, organized in a snake-like arrangement and designed to deflect in a vertical, perpendicular to the array plane, direction, are generated solely by an electric current of alternating directions, which also results in the Joule heating of the strings. The analysis of the associated linearized eigenvalue problem provides the critical current corresponding to a push-out buckling with an intrinsic out-of-plane “zig-zag” mode. This bifurcation-type buckling is shown to precede the string loosening due to Joule heating, and to occur, in nano strings of realistic dimensions, at current density lower than the melting- or electromigration-related limits. The postbuckling behavior, governed by the inherent structural geometric and electromagnetic nonlinearities, is studied analytically and numerically. The results demonstrate the competing effects of the initial string tension and of the Joule heating on the array responses. In arrays constituting of finite numbers of strings, the critical buckling current is confined in a region bounded by the values obtained for the single string and infinite arrays.