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Wind and Structures Volume 28, Number 6, June 2019 , pages 347-354 DOI: https://doi.org/10.12989/was.2019.28.6.347 |
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Conformable solution of fractional vibration problem of plate subjected to in-plane loads |
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Odunayo O. Fadodun, Babafemi O. Malomo, Olawanle P. Layeni and Adegbola P. Akinola
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| Abstract | ||
| This study provides an approximate analytical solution to the fractional vibration problem of thin plate governing anomalous motion of plate subjected to in-plane loads. The method of variable separable is employed to transform the fractional partial differential equations under consideration into a fractional ordinary differential equation in temporal variable and a bi-harmonic plate equation in spatial variable. The technique of conformable fractional derivative is utilized to solve the resulting fractional differential equation and the approach of finite sine integral transform method is used to solve the accompanying bi-harmonic plate equation. The deflection field which measures the transverse displacement of the plate is expressed in terms of product of Bessel and trigonometric functions via the temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem of thin plate in literature. This work shows that conformable fractional derivative is an efficient mathematical tool for tracking analytical solution of fractional partial differential equation governing anomalous vibration of thin plates. | ||
| Key Words | ||
| conformable solution; fractional vibration; in-plane loads; thin plate | ||
| Address | ||
| Odunayo O. Fadodun, Olawanle P. Layeni and Adegbola P. Akinola: Department of Mathematics, Obafemi Awolowo University, Ile-Ife, 220005, Nigeria Babafemi O. Malomo: Department of Mechanical Engineering, Obafemi Awolowo University, 220005, Nigeria | ||