Document Type
Article
Publication Date
10-3-2006
Publication Title
New Journal of Physics
Department
Department of Physics and Astronomy
Abstract
We describe a sequence of Euler buckling instabilities associated with the transverse modes of a mesoscopic beam subjected to compressional strain. As the strain is increased, successively higher normal mode frequencies are driven to zero; each zero signals an instability in the corresponding normal mode that can be realized if all lower instabilities are suppressed by constraints. When expressed in terms of the critical buckling modes, the potential energy functional takes the form of a multimode Ginzburg–Landau system that describes static equilibria in the presence of symmetry breaking forces. This model is used to analyse the complex equilibrium shapes that have been observed experimentally in strained mesoscopic beams. Theoretically predicted critical strain values agree with the appearances of higher order mode structures as the length-to-width aspect ratio increases. The theory also predicts upper bounds on the individual mode amplitudes that are consistent with the data. Based on insights from the theory, we suggest possible origins of the buckling patterns.
DOI
10.1088/1367-2630/8/10/223
Original Citation
W E Lawrence et al 2006 New J. Phys. 8 223
Dartmouth Digital Commons Citation
Lawrence, W. E.; Wybourne, M. N.; and Carr, S. M., "Compressional Mode Softening and Euler Buckling Patterns in Mesoscopic Beams" (2006). Dartmouth Scholarship. 1902.
https://digitalcommons.dartmouth.edu/facoa/1902