Micromechanical Structure With Stable Linear Positive And Negative Stiffness

Document Type




Publication Date




Source Publication

MEMS and Nanotechnology

Source ISSN



We introduce a novel micromechanical structure that exhibits two regions of stable linear positive and negative stiffness. Springs, cantilevers, beams and any other geometry that display an increasing return force that is proportional to the displacement can be considered to have a “Hookean” positive spring constant, or stiffness. Less well known is the opposite characteristic of a reducing return force for a given deflection, or negative stiffness. Unfortunately many simple negative stiffness structures demonstrate either unstable buckling which can require extraneous moving constraints during deflection, so as not to deform out of useful shape, or are highly nonlinear such as the disk cone spring. In MEMS, buckling caused by stress at the interface of silicon and thermally grown SiO2 causes tensile and compressive forces that will warp structures if the silicon layer is thin enough. The structure presented here utilizes this effect but overcomes its limitations and empirically demonstrates linearity in both regions. The structure is manufactured using only common micromachining techniques and can be made in situ with other devices.


MEMS and Nanotechnology, Conference Proceedings of the Society for Experimental Mechanics Series, Vol. 4 (2011): 137-143. DOI.

Ronald A. Coutu was affiliated with the Air Force Institute of Technology at the time of publication.