RESEARCH PAPER
Approximate Formulation of the Rigid Body Motions of an Elastic Rectangle Under Sliding Boundary Conditions
1
Department of Mathematics, Giresun University, Gaziler, Prof. Ahmet Taner Kışlalı Cd., 28200 Giresun , Turkey
2
Department of Mathematics, Eskişehir Technical University, 2 Eylül Kampüsü, 26555 Eskişehir, Turkey
3
HUM Industrial Technology, INC, 911 Washington Ave, Suite 501 St. Louis, Missouri, USA
Submission date: 2021-02-15
Acceptance date: 2021-06-07
Online publication date: 2021-06-30
Publication date: 2021-06-01
Acta Mechanica et Automatica 2021;15(2):82-90
KEYWORDS
ABSTRACT
Low-frequency analysis of in-plane motion of an elastic rectangle subject to end loadings together with sliding boundary conditions is considered. A perturbation scheme is employed to analyze the dynamic response of the elastic rectangle revealing nonhomogeneous boundary-value problems for harmonic and biharmonic equations corresponding to leading and next order expansions, respectively. The solution of the biharmonic equation obtained by the separation of variables, a consequence of sliding boundary conditions, gives an asymptotic correction to the rigid body motion of the rectangle. The derived explicit approximate formulae are tested for different kinds of end loadings together with numerical examples demonstrating the comparison against the exact solutions.
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| eISSN: | 2300-5319 |
| ISSN: | 1898-4088 |
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