<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

Approximate Formulation of the Rigid Body Motions of an Elastic Rectangle Under Sliding Boundary Conditions

Acta Mechanica et Automatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Low-frequency analysis of in-plane motion of an elastic rectangle subject to end loadings together with sliding boundary conditions is considered. A...

Approximate Formulation of the Rigid Body Motions of an Elastic Rectangle Under Sliding Boundary Conditions

Data publikacji: 30 cze 2021

Zakres stron: 82 - 90

Otrzymano: 15 lut 2021

Przyjęty: 07 cze 2021

DOI: https://doi.org/10.2478/ama-2021-0012

Słowa kluczowe
elastic rectangle, low-frequency, rigid body motion, perturbation scheme, sliding boundary conditions

© 2020 Onur Şahin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Approximate Formulation of the Rigid Body Motions of an Elastic Rectangle Under Sliding Boundary Conditions

Data publikacji: 30 cze 2021

Zakres stron: 82 - 90

Otrzymano: 15 lut 2021

Przyjęty: 07 cze 2021

DOI: https://doi.org/10.2478/ama-2021-0012

Słowa kluczoweelastic rectangle, low-frequency, rigid body motion, perturbation scheme, sliding boundary conditions

© 2020 Onur Şahin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Słowa kluczowe
elastic rectangle, low-frequency, rigid body motion, perturbation scheme, sliding boundary conditions