Abstract
Bistable structures have seen significant attention in recent years for their potential uses in switching and energy harvesting. The behavior of these structures, however, is very sensitive to boundary conditions and initial geometry making their calibration for various applications a difficult task. Additionally, obtaining the force-deformation behavior of these highly (geometrically) nonlinear structures often requires computationally expensive continuation methods. This paper presents a very simple closed-form method which estimates several important characteristics of classical snap-through curves of transversely loaded beams. The estimation is based on a relationship between classic Euler buckling of beams under axial load and the snap-through of post-buckled and curved beams and arches under transverse loading that has recently been investigated by the authors.
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References
Harne, R.L., Wang, K.W.: A review of the recent research on vibration energy harvesting via bistable systems. Smart Mater. Struct. 22(2), 023001 (Online) (2013)
Plaut, R.H.: Buckling of shallow arches with supports that stiffen when compressed. J. Eng. Mech. 116(4), 973–976 (1990)
Stanciulescu, I., Mitchell, T., Chandra, Y., Eason, T.G., Spottswood, S.M.: A lower bound on snap-through instability of curved beams under thermomechanical loads. Int. J. Non Linear Mech. 47(5), 561–575 (2012)
Murphy, K.D., Virgin, L.N., Rizzi, S.A.: Experimental snap-through boundaries for acoustically excited, thermally buckled plates. Exp. Mech. 36(4), 312–317 (1996)
Nistor, M., Wiebe, R., Stanciulescu, I.: Relationship between Euler buckling and unstable equilibria of buckled beams. Int. J. Non Linear Mech. 95(1), 151–161 (2017)
Battini, J.M.: Co-rotational beam elements in instability problems. PhD Thesis, KTH Royal Institute of Technology, Stockholm (2002)
Wiebe, R.: Nonlinear dynamics of discrete and continuous mechanical systems with snap-through instabilities. PhD Thesis, Duke University, Durham NC (2012)
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© 2019 The Society for Experimental Mechanics, Inc.
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Wiebe, R., Nistor, M., Stanciulescu, I. (2019). On Euler Buckling and Snap-Through. In: Kerschen, G. (eds) Nonlinear Dynamics, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-74280-9_17
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DOI: https://doi.org/10.1007/978-3-319-74280-9_17
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