Dynamic Analysis of Circular Plates in Contact with Fluid and Resting on Two-Parameter Foundations

Document Type : Original Article


1 Department of Mechanical Engineering, University of Lagos, Akoka, Nigeria

2 Department of Civil and Environmental Engineering, University of Lagos, Akoka, Nigeria


The dynamic behaviour of a circular plate in contact with fluid and resting on two-parameter elastic foundations is of interest in the field of geotechnics, structure, highway, railway, oil and gas and mechanical engineering. In this work, the dynamic behaviour of circular plate in contact with fluid and resting on Winkler and Pasternak foundations is investigated. The coupled differential equation of the system is analysed using differential transformation method. Good agreements are established when the results of the analytical solutions are compared to the results of the experimental investigation as reported in literature. The analytical solutions obtained are used to investigate the effects of elastic foundation parameters on natural frequency, combine foundation parameters on natural frequency, plate in contact with fluid and that of radial and circumferential stress on mode shapes. From the results, it is observed that, increases in elastic foundation parameter increases the natural frequency in all cases. Presence of fluid reduces the natural frequency of the plate. Also, it is established that mode shapes are not altered by the presence of fluid. However, mode shape displacement occurs due to presence of radial and circumferential stresses. Since the study provides a physical insight into the vibration mode of the structure, it is expected that the study will enhance better understanding on the dynamic behaviour of a circular plate in contact with fluid and resting on two-parameters elastic foundation.


1. Motaghian, S., Mofid, M. and Akin, J. E., “On the free vibration
response of rectangular plates, partially supported on elastic
foundation”, Applied Mathematical Modelling, Vol. 36, No. 9,
(2012), 4473–4482.  
2. Rezaiefar, A. and Galal, K., “Free vibration of thin rectangular
steel plates with geometrically-nonlinear load-displacement
behavior”, Thin-Walled Structures, Vol. 129, (2018), 381–390.  
3. Adibi, T., Adibi, O. and Razavi, S. E., “A Characteristic-based
Solution of Forced and Free Convection in Closed Domains with
Emphasis on Various Fluids”, International Journal of
Engineering-Transactions B: Applications, Vol. 32, No. 11,
(2019), 1689–1695.  4. Benferhat, R., Daouadji, T.H., Mansour, M.S. and Hadji, L.,
“Effect of porosity on the bending and free vibration response of
functionally graded plates resting on Winkler-Pasternak
foundations”, Earthquakes and Structures, Vol. 10, No. 6,
(2016), 1429–1449.  
5. Özdemir, Y. I., “Forced vibration analysis of Mindlin plates
resting on Winkler foundation”, Challenge Journal of Structural
Mechanics, Vol. 4, No. 1, (2018), 18–26.  
6. Mohd Umair, S., Gulhane, N.P., Al-Robaian, A.R.A. and Khan,
S. A., “On Numerical Investigation of Semi-empirical Relations
Representing Local Nusselt Number at Lower Nozzle-target
Spacing’s”, International Journal of Engineering - Transaction
A: Basics, Vol. 32, No. 1, (2019), 137–145.  
7. Nikbakht, R. and Behnamfar, F., “Response Spectra of Structures
under Subway Induced Vibrations”, International Journal of
Engineering - Transaction C: Aspects, Vol. 31, No. 12, (2018),
8. Bayat, M., Pakar, I. and Bayat, M., “Analytical study on the
vibration frequencies of tapered beams”, Latin American
Journal of Solids and Structures, Vol. 8, No. 2, (2011), 149–162.  
9. Werfalli, N.M. and Karoud, A. A., “Free vibration analysis of
rectangular plates using Galerkin-based finite element method”,
International Journal of Mechanical Engineering, Vol. 2, No.
4, (2012), 59–67.  
10. Younesian, D., Saadatnia, Z., Askiri, H. and Esmailzadeh, E.,
“Analytical solution for oscillation of rectangular plate on
nonlinear Winkler Pasternak foundation”, In Proceedings of the
ASME 2011, International Design Engineering Technical
Conferences & Computers and Information in Engineering
Conference, USA, (2011), 1–6.  
11. Lamb, H., “On the Vibrations of an Elastic Plate in Contact with
Water”, Proceedings of the Royal Society of London. Series A,
Containing Papers of a Mathematical and Physical Character,
Vol. 98, No. 690, (1920), 205–216.  
12. Gascón-Pérez, M. and García-Fogeda, P., “Induced damping on
vibrating circular plates submerged in still fluid”, International
Journal of Applied Mechanics, Vol. 7, No. 6, (2015), 1–18.  
13. Zhou, J.K., “Differential transformation and its applications for
electrical circuits”, Huazhong University Press, Wuhan, China,
14. Shariyat, M. and Alipour, M. M., “Differential transform
vibration and modal stress analyses of circular plates made of
two-directional functionally graded materials resting on elastic
foundations”, Archive of Applied Mechanics, Vol. 81, No. 9,
(2011), 1289–1306.  
15. Leissa, A.W., “Vibration of plates, Office of Technology
Utlilization National Aeronautics and Space Adminstration,
Scientific and Technical Information Division, Ohio, (1969).