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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 February 27, 2026
Strong nonreciprocity in a bistable pendulum with contactless coupling to a monostable pendulum
Abstract This article studies the nonreciprocity of a system that consists of a bistable element coupled to a monostable element through a contactless magnetic interaction. To illustrate the concept, the bistable element is physically realized using a pendulum that interacts with a stationary magnet and the monostable element is a classical pendulum. A numerical model is implemented to simulate the nonlinear dynamics of the system. Both simulations and experiments show that the system exhibits a strong amplitude-dependent nonreciprocity in response to initial excitations. At small input amplitudes, the system has an intrawell response with minimal transmission of energy whether the excitation is exerted on the side of the bistable pendulum or on the other side. However, at high input amplitude, a strong nonreciprocal behavior is observed: excitation of the bistable pendulum causes an interwell response which considerably reduces the distance between the two pendulums and allows energy to be efficiently transmitted through the contactless magnetic interaction; excitation of the monostable pendulum does not cause any interwell response and results in limited energy transmission. The combination of bistability and contactless nonlinear interactions allows the system to exhibit very strong amplitude-dependent nonreciprocity, which may be useful in a wide range of applications.
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- Award ID(s):
- 2423960
- PAR ID:
- 10579443
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Nonlinear Dynamics
- ISSN:
- 0924-090X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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