Tunable bistability of a clamped elastic beam

Abstract

Bistable structures featuring two stable shapes are commonplace in natural and engineered systems. They can quickly snap from one stable state to the other in response to certain external stimuli, and so have found a range of applications in microswitches, actuators, energy harvesters, and mechanical metamaterials. Buckled beams represent a sub-class of bistable structures extensively studied, yet the relation between relevant boundary conditions and their bifurcation behaviors remains incompletely understood. Here we examine the bifurcation behavior of a buckled, elastic beam with both ends clamped in the absence of any external body force. Through a systematic investigation combining experiments, theory, and computational analysis, we identify that the beam can go through saddle–node bifurcation or pitchfork bifurcation (subcritical or supercritical) under asymmetric or symmetric boundary conditions, respectively. We construct the stability diagram in terms of the independent control parameters that can provide a precise prediction of the critical point upon bifurcation. Our results can not only provide powerful guidance on the design of fast switches, mechanical metamaterials, energy harvesters, or micro-electro-mechanical systems (MEMS) that exploit the bistability of elastic beams with clamped ends, but also have implications on a variety of biophysical phenomena and biomimetic structures.