Asymptotic model of long-wave vibrations of an ultrathin strip-beam taking into account surface effects
DOI:
https://doi.org/10.21638/spbu01.2024.312Abstract
The paper is concerned with the derivation of asymptotically consistent equations governing long-wave vibrations of an ultrathin elastic strip-beam taking into account surface effects within the framework of the Gurtin-Murdoch theory of the surface elasticity. Two dimensional equations of motion of an elastic isotropic medium are used as the initial ones. In the general case, the strip-beam is under the action of variable unsteady surface forces. The presence of residual shear stresses is assumed on the face surfaces. The ratio of the strip thickness to the characteristic length of bending deformation is considered as a small parameter. Within the framework of the Gurtin-Murdoch theory, two cases are considered, providing for the presence of large a) residual stresses on the faces, b) effects of surface inertia. Using the method of asymptotic integration over the transverse direction, relations for displacements and stresses in an ultra-thin strip-beam are obtained, and equivalent one dimensional the Timoshenko type equations taking into account surface effects are derived. As an example, free vibrations of a simply supported beam accounting for the surface effects are considered.Keywords:
ultrathin strip-beam, surface elasticity, residual stresses, long-wave vibrations, asymptotic, equivalent 1D models
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Published
2024-10-15
How to Cite
Mikhasev, G. I., & Le, N. D. (2024). Asymptotic model of long-wave vibrations of an ultrathin strip-beam taking into account surface effects. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 11(3), 557–569. https://doi.org/10.21638/spbu01.2024.312
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Section
Mechanics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.