Transient amplification of broken symmetry in elastic snap-through
A snap-through bifurcation occurs when a bistable structure loses one of its stable states and moves rapidly to the remaining state. For example, a buckled arch with symmetrically clamped ends can snap between an inverted and a natural state as the ends are released. A standard linear stability anal...
| Main Authors: | , , , , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/181369 |
| _version_ | 1824455985043865600 |
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| author | Wang, Qiong Giudici, Andrea Huang, Weicheng Wang, Yuzhe Liu, Mingchao Tawfick, Sameh Vella, Dominic |
| author2 | School of Mechanical and Aerospace Engineering |
| author_facet | School of Mechanical and Aerospace Engineering Wang, Qiong Giudici, Andrea Huang, Weicheng Wang, Yuzhe Liu, Mingchao Tawfick, Sameh Vella, Dominic |
| author_sort | Wang, Qiong |
| collection | NTU |
| description | A snap-through bifurcation occurs when a bistable structure loses one of its stable states and moves rapidly to the remaining state. For example, a buckled arch with symmetrically clamped ends can snap between an inverted and a natural state as the ends are released. A standard linear stability analysis suggests that the arch becomes unstable to asymmetric perturbations. Surprisingly, our experiments show that this is not always the case: symmetric transitions are also observed. Using experiments, numerics, and a toy model, we show that the symmetry of the transition depends on the rate at which the ends are released, with sufficiently fast loading leading to symmetric snap-through. Our toy model reveals that this behavior is caused by a region of the system's state space in which any initial asymmetry is amplified. The system may not enter this region when loaded fast (hence remaining symmetric), but will traverse it for some interval of time when loaded slowly, causing a transient amplification of asymmetry. Our toy model suggests that this behavior is not unique to snapping arches, but rather can be observed in dynamical systems where both a saddle-node and a pitchfork bifurcation occur in close proximity. |
| first_indexed | 2025-02-19T03:46:54Z |
| format | Journal Article |
| id | ntu-10356/181369 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:46:54Z |
| publishDate | 2024 |
| record_format | dspace |
| spelling | ntu-10356/1813692024-11-30T16:48:40Z Transient amplification of broken symmetry in elastic snap-through Wang, Qiong Giudici, Andrea Huang, Weicheng Wang, Yuzhe Liu, Mingchao Tawfick, Sameh Vella, Dominic School of Mechanical and Aerospace Engineering Engineering Asymmetric perturbations Bistable structures A snap-through bifurcation occurs when a bistable structure loses one of its stable states and moves rapidly to the remaining state. For example, a buckled arch with symmetrically clamped ends can snap between an inverted and a natural state as the ends are released. A standard linear stability analysis suggests that the arch becomes unstable to asymmetric perturbations. Surprisingly, our experiments show that this is not always the case: symmetric transitions are also observed. Using experiments, numerics, and a toy model, we show that the symmetry of the transition depends on the rate at which the ends are released, with sufficiently fast loading leading to symmetric snap-through. Our toy model reveals that this behavior is caused by a region of the system's state space in which any initial asymmetry is amplified. The system may not enter this region when loaded fast (hence remaining symmetric), but will traverse it for some interval of time when loaded slowly, causing a transient amplification of asymmetry. Our toy model suggests that this behavior is not unique to snapping arches, but rather can be observed in dynamical systems where both a saddle-node and a pitchfork bifurcation occur in close proximity. Published version This work was partially supported by the UK Engineering and Physical Sciences Research Council via Grant No. EP/ W016249/1 (D. V.). Q. W., Y. W., and S. T. acknowledge support from the Defense Advanced Research Projects Agency DARPA SHRIMP HR001119C0042. W. H. acknowledges the start-up funding from Newcastle University, UK. M. L. acknowledges support via start-up funding from the University of Birmingham. 2024-11-27T01:57:16Z 2024-11-27T01:57:16Z 2024 Journal Article Wang, Q., Giudici, A., Huang, W., Wang, Y., Liu, M., Tawfick, S. & Vella, D. (2024). Transient amplification of broken symmetry in elastic snap-through. Physical Review Letters, 132(26), 267201-. https://dx.doi.org/10.1103/PhysRevLett.132.267201 0031-9007 https://hdl.handle.net/10356/181369 10.1103/PhysRevLett.132.267201 38996296 2-s2.0-85197898092 26 132 267201 en Physical Review Letters © The Authors. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. application/pdf |
| spellingShingle | Engineering Asymmetric perturbations Bistable structures Wang, Qiong Giudici, Andrea Huang, Weicheng Wang, Yuzhe Liu, Mingchao Tawfick, Sameh Vella, Dominic Transient amplification of broken symmetry in elastic snap-through |
| title | Transient amplification of broken symmetry in elastic snap-through |
| title_full | Transient amplification of broken symmetry in elastic snap-through |
| title_fullStr | Transient amplification of broken symmetry in elastic snap-through |
| title_full_unstemmed | Transient amplification of broken symmetry in elastic snap-through |
| title_short | Transient amplification of broken symmetry in elastic snap-through |
| title_sort | transient amplification of broken symmetry in elastic snap through |
| topic | Engineering Asymmetric perturbations Bistable structures |
| url | https://hdl.handle.net/10356/181369 |
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