Effects of shear deformation and rotary inertia on the dynamics of anisotropic plates traversed by moving concentrated load
The effects of shear deformation and rotary inertia on the dynamics of anisotropic plates traversed by varying moving load resting on Vlasov foundation is investigated in this work. The problem is solved for concentrated loads with simply supported boundary conditions. An analytic solution based on...
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doaj-325a85fb6a164a15b8108bc5f2b2ea9f2020-11-25T02:23:40ZengPtolemy Scientific Research PressOpen Journal of Mathematical Sciences2616-49062523-02122019-10-013131032110.30538/oms2019.0074Effects of shear deformation and rotary inertia on the dynamics of anisotropic plates traversed by moving concentrated load10.30538/oms2019.00740 Yomi Monday Aiyesimi1Mohammed Jiya2Abdulhakeem Yusuf 3Gbolahan Bolarin4Department of Mathematics, Federal College of Education, Kontagora, Nigeria.Department of Mathematics, Federal University of Technology Minna, Nigeria.Department of Mathematics, University of Gambia, Sere Kunda, Gambia.Department of Mathematics, Federal University of Technology Minna, Nigeria.Department of Mathematics, Federal University of Technology Minna, Nigeria.The effects of shear deformation and rotary inertia on the dynamics of anisotropic plates traversed by varying moving load resting on Vlasov foundation is investigated in this work. The problem is solved for concentrated loads with simply supported boundary conditions. An analytic solution based on the Galerkin’s method is used to reduce the fourth order partial differential equation into a system of coupled fourth order differential equation and a modification of the Struble’s technique and Laplace transforms are used to solve the resulting fourth order differential equation. Results obtained indicate that shear deformation and rotary inertia have significant effect on the dynamics of the anisotropic plate on the Vlasov foundation. Solutions are obtained for both the moving force and the moving mass problems. From the graphical results obtained, the amplitude of vibrations of the plate under moving mass is greater than that of the moving force and increasing the value of rotary inertia \(R_{0}\) reduces the amplitude of vibration of the plate. increasing the mass ratio increases the amplitude of vibration of the plate.https://pisrt.org/psr-press/journals/oms-vol-3-2019/effects-of-shear-deformation-and-rotary-inertia-on-the-dynamics-of-anisotropic-plates-traversed-moving-concentrated-load/anisotropic plateshear deformationrotary inertiavlasov foundationmoving forcemoving mass. |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
10.30538/oms2019.0074 Yomi Monday Aiyesimi Mohammed Jiya Abdulhakeem Yusuf Gbolahan Bolarin |
spellingShingle |
10.30538/oms2019.0074 Yomi Monday Aiyesimi Mohammed Jiya Abdulhakeem Yusuf Gbolahan Bolarin Effects of shear deformation and rotary inertia on the dynamics of anisotropic plates traversed by moving concentrated load Open Journal of Mathematical Sciences anisotropic plate shear deformation rotary inertia vlasov foundation moving force moving mass. |
author_facet |
10.30538/oms2019.0074 Yomi Monday Aiyesimi Mohammed Jiya Abdulhakeem Yusuf Gbolahan Bolarin |
author_sort |
10.30538/oms2019.0074 |
title |
Effects of shear deformation and rotary inertia on the dynamics of anisotropic plates traversed by moving concentrated load |
title_short |
Effects of shear deformation and rotary inertia on the dynamics of anisotropic plates traversed by moving concentrated load |
title_full |
Effects of shear deformation and rotary inertia on the dynamics of anisotropic plates traversed by moving concentrated load |
title_fullStr |
Effects of shear deformation and rotary inertia on the dynamics of anisotropic plates traversed by moving concentrated load |
title_full_unstemmed |
Effects of shear deformation and rotary inertia on the dynamics of anisotropic plates traversed by moving concentrated load |
title_sort |
effects of shear deformation and rotary inertia on the dynamics of anisotropic plates traversed by moving concentrated load |
publisher |
Ptolemy Scientific Research Press |
series |
Open Journal of Mathematical Sciences |
issn |
2616-4906 2523-0212 |
publishDate |
2019-10-01 |
description |
The effects of shear deformation and rotary inertia on the dynamics of anisotropic plates traversed by varying moving load resting on Vlasov foundation is investigated in this work. The problem is solved for concentrated loads with simply supported boundary conditions. An analytic solution based on the Galerkin’s method is used to reduce the fourth order partial differential equation into a system of coupled fourth order differential equation and a modification of the Struble’s technique and Laplace transforms are used to solve the resulting fourth order differential equation. Results obtained indicate that shear deformation and rotary inertia have significant effect on the dynamics of the anisotropic plate on the Vlasov foundation. Solutions are obtained for both the moving force and the moving mass problems. From the graphical results obtained, the amplitude of vibrations of the plate under moving mass is greater than that of the moving force and increasing the value of rotary inertia \(R_{0}\) reduces the amplitude of vibration of the plate. increasing the mass ratio increases the amplitude of vibration of the plate. |
topic |
anisotropic plate shear deformation rotary inertia vlasov foundation moving force moving mass. |
url |
https://pisrt.org/psr-press/journals/oms-vol-3-2019/effects-of-shear-deformation-and-rotary-inertia-on-the-dynamics-of-anisotropic-plates-traversed-moving-concentrated-load/ |
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