On the mechanical behavior of slender, slightly curved, compressed microbridges

We consider a clamped–clamped, slender beam–column that is slightly curved in its unloaded static equilibrium state. Perhaps the best practical example of this type of structure is a microbeam used in sensing and actuating devices. If the clamped ends are forced toward each other, or if stiff supports inhibit axial expansion that is fostered by fabrication processes and/or operational heating, then the column bends beyond its initial curvature. If the axial force approaches the buckling load, then the static flexural deflection can be relatively large, greater than the column's depth. We show that the dependence of moderately large static deflection upon compressive force is mathematically linear, and that nonlinearity arises only in the relationship of column shortening to transverse deflection. This leads to a linear finite-element method for static structural analysis of non-uniform columns, with which we simulate the behavior of a 62.5 µm long microbridge of 0.5 µm thin-film gold. This microbridge was observed experimentally to bend 4–5 µm under compression. We also examine previous studies of bending vibration about moderately large static deflection. Calculations and experimental measurements of the dependence of the fundamental natural frequency on axial compression and initial curvature indicate practical significance relative to design of microbridge resonators