Volume 13, Issue 4
An Analytical Solution for Nonlinear Vibration Analysis of Functionally Graded Rectangular Plate in Contact with Fluid

Soheil Hashemi & Ali Asghar Jafari

Adv. Appl. Math. Mech., 13 (2021), pp. 914-941.

Published online: 2021-04

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  • Abstract

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.

  • Keywords

Nonlinear vibration, functionally graded materials, fluid pressure, first order shear deformation theory, modified Lindstedt-Poincare method.

  • AMS Subject Headings

74B99, 74E30, 74F10, 74G10, 74H45

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-13-914, author = {Soheil Hashemi , and Ali Asghar Jafari , }, title = {An Analytical Solution for Nonlinear Vibration Analysis of Functionally Graded Rectangular Plate in Contact with Fluid}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {13}, number = {4}, pages = {914--941}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0333}, url = {http://global-sci.org/intro/article_detail/aamm/18757.html} }
TY - JOUR T1 - An Analytical Solution for Nonlinear Vibration Analysis of Functionally Graded Rectangular Plate in Contact with Fluid AU - Soheil Hashemi , AU - Ali Asghar Jafari , 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 -

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.

Soheil Hashemi & Ali Asghar Jafari. (1970). An Analytical Solution for Nonlinear Vibration Analysis of Functionally Graded Rectangular Plate in Contact with Fluid. Advances in Applied Mathematics and Mechanics. 13 (4). 914-941. doi:10.4208/aamm.OA-2019-0333
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