Exact analytical solution for a pie-shaped wedge thick plate under oscillating load
| Autor: | Marina Menshykova, Nataly Vaysfeld, Oleksandr Menshykov |
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| Rok vydání: | 2017 |
| Předmět: |
Mechanical Engineering
Mathematical analysis Computational Mechanics Base (geometry) Geometry 02 engineering and technology Bending of plates Edge (geometry) 01 natural sciences Wedge (geometry) Stress (mechanics) 020303 mechanical engineering & transports Exact solutions in general relativity 0203 mechanical engineering 0103 physical sciences Solid mechanics Boundary value problem 010301 acoustics Mathematics |
| Zdroj: | Acta Mechanica. 228:4435-4450 |
| ISSN: | 1619-6937 0001-5970 |
| DOI: | 10.1007/s00707-017-1938-9 |
| Popis: | A finite elastic wedge-shaped thick plate is considered. One of the faces is based on a rigid base, and the other is exposed to a dynamic oscillating load through an absolutely rigid overlay. On the side faces, conditions of sliding contact are fulfilled; at its end, the stresses are given. The solution is based on a special linear transformation of Lame’s equations and application of the vector integral transformations method. The proposed approach leads to a one-dimensional vector boundary value problem for which an exact solution is constructed. The analysis of the eigenfrequency value distribution and an estimation of the edge resonance frequency are done. An analogous problem is solved for the case when at the lower wedge plate’s face the sliding conditions are given. In order to establish the possibility of separation of the lower base, a comparison of the obtained values of the stress on the bottom plate with the stresses arising in the analogous formulation of the static problem for wedge plate considering its own weight is worked out. |
| Databáze: | OpenAIRE |
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