Exact analytical solution for a pie-shaped wedge thick plate under oscillating load

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 solu...

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Bibliographic Details
Published in:Acta mechanica 2017-12, Vol.228 (12), p.4435-4450
Main Authors: Menshykov, O., Menshykova, M., Vaysfeld, N.
Format: Article
Language:English
Subjects:
Boundary value problems
Classical and Continuum Physics
Contact stresses
Control
Dynamical Systems
Engineering
Engineering Thermodynamics
Finite element analysis
Heat and Mass Transfer
Integral transforms
Linear transformations
Load
Original Paper
Oscillators
Sliding
Sliding contact
Solid Mechanics
Theoretical and Applied Mechanics
Thickness measurement
Tribology
Vibration
Wedges
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Summary: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 Lamé’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.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-017-1938-9