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Bistable shallow arches are ubiquitous in many engineering systems ranging from compliant mechanisms and biomedical stents to energy harvesters and passive fluidic controllers. In all these scenarios, the bistable states of the arch and the sudden transitions between them via snap-through instability are harnessed. However, bistable arches have been traditionally studied and characterized by triggering snap-through instability using quasi-static forces. Here, we analytically examine the effect of oscillatory loads on bistable arches and investigate the dynamic behaviors ranging from intrawell motion to periodic and chaotic interwell motion. The linear and nonlinear dynamic responses of both elastically and plastically deformed shallow arches are presented. Introducing an energy potential criterion, we classify the structure’s behavior within the parameter space. This energy-based approach allows us to explore the parameter space for high-dimensional models of the arch by varying the force amplitude and excitation frequency. Bifurcation diagrams, Lyapunov exponents, and maximum critical energy plots are presented to characterize the dynamic response of the system. Our results reveal that unstable solutions admitted through higher modes govern the critical energy required for interwell motion. This study investigates the rich nonlinear dynamic behavior of the arch element and it introduces an energy potential criterion that can scale easily to classify motion of arrays of bistable arches for future developments of multistable mechanical metamaterials.
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This content will become publicly available on October 1, 2026
Flow-Induced Snap Through of Bistable Arches With Generalized Boundary Conditions
Fluid–structure interactions (FSIs) can be successfully leveraged to develop passive fluid control systems and active structures that respond to targeted flow conditions. When bistable structures interact with flowing fluids, interesting dynamics, such as large reconfigurations due to snap-through instability, can arise. Here, we demonstrate how to control the flowrate of a viscous fluid in a channel by tuning the boundary conditions of a bistable arch (i.e., postbuckled beam) incorporated along the channel sidewall. We introduce a torsionally supported postbuckled beam immersed in fluid flow to investigate flow–deformation relationships, surface pressure distributions, and critical flowrates. Varying torsional spring stiffness allows to span from clamped-clamped to hinged-hinged, and all intermediate stiffness rotational boundary conditions. We develop an analytical model and numerical continuation methods to determine the critical flowrate required to snap the bistable arch and the effects of the support’s torsional stiffness. Thanks to this approach, we demonstrate a wide range of attainable critical flowrates that can be tuned by varying the boundary conditions of the bistable arch.
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- Award ID(s):
- 2239841
- PAR ID:
- 10610542
- Publisher / Repository:
- The American Society of Mechanical Engineers (ASME)
- Date Published:
- Journal Name:
- Journal of Applied Mechanics
- Volume:
- 92
- Issue:
- 10
- ISSN:
- 0021-8936
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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