An analytical method for vibration analysis of arbitrarily shaped non-homogeneous orthotropic plates of variable thickness resting on Winkler-Pasternak foundation

Song, Yuyu; Li, Qiuhong; Xue, Kaiping

doi:10.1016/j.compstruct.2022.115885

Cited by 10 publications

(1 citation statement)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Sofiyev et al [26] investigated the influences of two-parameter elastic foundations on the nonlinear free vibration of anisotropic shallow shell structures with variable parameters. Song et al [27] proposed an analytical method for linear vibration analysis of arbitrarily shaped non-homogeneous orthotropic plates of variable thickness resting on the Winkler-Pasternak foundation. Melaibari et al [28,29] examined the static response of 2D functionally graded porous plates resting on elastic foundations using midplane and neutral surfaces with movable constraints and differential quadrature method.…”

Section: Introductionmentioning

confidence: 99%

The Application of the Modified Lindstedt–Poincaré Method to Solve the Nonlinear Vibration Problem of Exponentially Graded Laminated Plates on Elastic Foundations

Avey,

Tornabene,

Aslanova

et al. 2024

Mathematics

View full text Add to dashboard Cite

The solution of the nonlinear (NL) vibration problem of the interaction of laminated plates made of exponentially graded orthotropic layers (EGOLs) with elastic foundations within the Kirchhoff–Love theory (KLT) is developed using the modified Lindstedt–Poincaré method for the first time. Young’s modulus and the material density of the orthotropic layers of laminated plates are assumed to vary exponentially in the direction of thickness, and Poisson’s ratio is assumed to be constant. The governing equations are derived as equations of motion and compatibility using the stress–strain relationship within the framework of KLT and von Karman-type nonlinear theory. NL partial differential equations are reduced to NL ordinary differential equations by the Galerkin method and solved by using the modified Lindstedt–Poincaré method to obtain unique amplitude-dependent expressions for the NL frequency. The proposed solution is validated by comparing the results for laminated plates consisting of exponentially graded orthotropic layers with the results for laminated homogeneous orthotropic plates. Finally, a series of examples are presented to illustrate numerical results on the nonlinear frequency of rectangular plates composed of homogeneous and exponentially graded layers. The effects of the exponential change in the material gradient in the layers, the arrangement and number of the layers, the elastic foundations, the plate aspect ratio and the nonlinearity of the frequency are investigated.

show abstract