TY - JOUR
T1 - An Analytical Solution for Nonlinear Vibration Analysis of Functionally Graded Rectangular Plate in Contact with Fluid
AU - Hashemi , Soheil
AU - Jafari , Ali Asghar
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 914
EP - 941
PY - 2021
DA - 2021/04
SN - 13
DO - http://doi.org/10.4208/aamm.OA-2019-0333
UR - https://global-sci.org/intro/article_detail/aamm/18757.html
KW - Nonlinear vibration, functionally graded materials, fluid pressure, first order shear deformation theory, modified Lindstedt-Poincare method.
AB - <p style="text-align: justify;">In this paper, the nonlinear vibrations analysis of functionally graded (FG) rectangular plate in contact with fluid are investigated analytically using first order shear deformation theory (FSDT) for the first time. The pressure exerted on the free surface of the plate by the fluid is calculated using the velocity potential function and the Bernoulli equation. With the aid of von Karman nonlinearity strain-displacement relations and Galerkin procedure the partial differential equations of motion are developed. The nonlinear equation of motion is then solved by modified Lindstedt-Poincare method (MLPM). The effects of some system parameters such as vibration amplitude, fluid density, fluid depth ratio, volume fraction index and aspect ratio on the nonlinear natural frequency of the plate are discussed in detail.</p>