Analytical approach to investigation of free vibration of thin rectangular plate immersed in fluid, resting on Winkler and Pasternak foundations

Abstract

Dynamic behaviour of free vibration of rectangular plate is investigated. This study considered an analytical approach to investigation of free vibration of thin rectangular plate immersed in fluid, resting on Winkler and Pasternak foundations.The governing nonlinear partial differential equation is analyzed using two-dimensional differential transform method. The accuracy of the analytical solutions obtained is verified with existing results in literature and confirmed in excellent agreement. Thereafter, the analytical solutions are used for investigation of effect of elastic foundation, fluid and aspect ratio on vibrating plate.From the result, it is observed that, increase elastic foundation parameters increases natural frequency, increase aspect ratio increase natural frequency, influence of fluid decreases the natural frequency of the plate.Hopefully the present study will contribute to existing knowledge in field of vibration.

Keywords

• Free vibration
• natural frequency
• Winkler and Pasternak foundations
• virtual added mass
• two-dimensional differential transform method