Snap-through of arches and buckled beams under unilateral displacement control

Abstract

Arches and beams buckled upward are analyzed. The structure is pushed downward from above at a specific location along the span until snap-through occurs and the structure jumps to an inverted equilibrium shape. Each beam or arch is modeled as an inextensible elastica. Critical displacements are computed for buckled beams with both ends pinned, both ends clamped, or one end clamped and the other end pinned. Circular arches with pinned ends are also investigated. The ends are immovable. The critical displacement is obtained directly from a theoretical equilibrium shape of the initial unloaded structure. Numerical results are presented for four height-to-span ratios of the initial structure, showing the critical displacement for any application point along the span. At the onset of snap-through, the imposed displacement is at or below the horizontal chord connecting the ends.

Theoretical and Experimental Investigation of the Nonlinear Behavior of an Electrostatically Actuated In-Plane MEMS Arch

“…We assume an initial guess for the initial rise b o , and hence w o , and also iterate on the nondimensional axial force N, then solve the eigen value problem of equation (18) to match the ratio of the nondimensional frequencies ω 3 /ω 1 with the ratio of the experimentally measured resonance frequencies f 3 / f 1 . It is worth mentioning that the measured resonance frequencies are corrected to account for the measured damping ratios of each mode.…”

“…Sari and Pakdemirli [17] studied slightly curved resonant microbeam having non-ideal boundary conditions resting on elastic foundation. Plaut [18] studied the snap-through instability of arches and buckled beams and computed the critical bucking displacements for different beams under different boundary conditions. Hu et al [19] investigated exploiting the buckling phenomenon in arches and buckled beams in smart systems.…”

Analytical modeling for rapid design of bistable buckled beams

“…Still, off-center actuation possesses unique behavioral properties that make it suitable for many applications. For example, compared with center actuation, off-center actuation usually requires a smaller actuating force but a longer actuating stroke [23,24].…”

“…These critical behavioral values are determined by design parameters, i.e. the geometry (including the length, width and thickness of the slender beam), precompression [18], actuation position [22,26], and boundary conditions [23]. Due to the complex coupling between snap-through characteristics and design parameters, it is often challenging to design a bistable structure efficiently.…”

Snap-buckling in asymmetrically constrained elastic strips

“…The bending direction can, however, be reversed by indenting the cylindrical section; the reversal occurs as another elastic instability, called snap-through buckling (or snap buckling). Although snap buckling has a long history of both study and industrial applications, for example, in keyboards and switching devices [36][37][38][39][40][41][42], it is currently receiving increasing attention [43][44][45] in various scientific fields, for example, in studies of mechanical metamaterials [46][47][48][49], small robots [50], or nastic motions in plants [51][52][53][54][55]. To highlight the impact of asymmetric boundary constraints on the mechanics of an elastic geometric structure, here we investigate boundary-driven snap-through buckling of an intrinsically flat elastic strip.…”