An undulatory structure and methods for the fabrication and use thereof. The undulatory structure includes a buckled sheet and one or more work input elements for deforming the buckled sheet in an undulating manner wherein each point in a series of points on a sinuously-shaped profile of the buckled sheet travels at least partially along a figure eight-shaped path. The undulatory structure can be adapted for use as a solid-state transducer wherein the buckled sheet provides mechanical advantage without appreciable opposition from elastic restoring forces, thereby achieving improved force, displacement and efficiency characteristics.