Free vibrational analysis of variable thickness plate made of functionally graded porous materials using internal supports in contact with bounded fluid. (1st November 2022) - Farsani, Sajjad Riahi; Saadat, Zahra; Jafari-Talookolaei, Ramazan-Ali; Tikani, Reza; Ziaei-Rad, Saeed
Abstract: This paper investigates the free vibrations of functionally graded porous (FGP) plates with variable thickness and internal supports in contact with a fluid. The FGP plate is the vertical wall of a rigid tank containing fluid. Four different types of thickness changes are considered for the plate, and the modeling of the interaction between the fluid and considered plate is presented for the first time. In addition to having different boundary conditions, the plate with variable thickness has different internal supports, which is less considered in the literature. Three different porosity distributions and four types of variable thickness are considered. The displacement field is estimated using the first-order shear deformation theory (FSDT), and kinetic and strain energies are obtained according to that. The fluid is assumed to be incompressible, inviscid, and irrotational. Natural frequencies of the system are obtained by employing the Rayleigh-Ritz method. Additionally, the natural frequency results of the plate in contact with fluid, the FGP plate, the plate with variable thickness, and the plate with internal supports are separately compared with those reported in the literature. Ultimately, the impact of fluid's depth, porosity coefficient, taper ratio, and the location of internal supports on natural frequencies are studied. Highlights: Unidirectional linear, bidirectional linear, unidirectional parabolic, and bidirectional parabolic for variable thickness models. Three types of porosity distribution: uneven symmetrical, uneven asymmetric and evenly distributions. Arbitrary internal line supports restrain the variable thickness FGP plate. Rayleigh-Ritz method using two-variable orthogonal polynomials.