Analytical Modeling on Vibration Analysis of Cracked Functionally Graded Plate Submerged in Fluid

Abstract

Background: It is established that the vibration response of submerged structures is quite different than that calculated in vacuum. Therefore, the study of vibration characteristics of submerged plate structures is important for safety and its designing purpose. Objective: To investigate the fundamental frequency of partially cracked Functionally Graded (FG) submerged plate based on analytical approach. Methods: The governing differential equation of the cracked-submerged plate is derived based on Kirchhoff’s thin classical plate theory in conjunction with the potential flow theory. The line spring model is used to incorporate the effect of crack in the form of additional bending whereas the effect of fluid medium is incorporated in form fluids forces associated with inertial effects of its surrounding fluids. The Bernoulli’s equation and velocity potential function are used to define the fluid forces acting on plate surface. Results: An approximate solution for governing equation of coupled fluid-plate system is obtained by using the Galerkin’s method. For validation of the present results, they are compared with the existing results of the previous published work, which are in good agreements. New results for natural frequencies as affected by gradient index, crack length, level of submergence and immersed depth of plate are presented for Simply Supported (SSSS) boundary condition. Conclusion: It has been concluded that the presence of crack and fluidic medium significantly affect the natural frequencies of the plate. It is observed that the increase in the length of crack and level of submergence decreases the fundamental frequency. In this paper, few patents have been discussed.