Nonlinear free vibration analyses of size-dependent functionally graded annular microplates possessing variable length scale parameter

Date

2023-3-31

Author

MIZRAK, SİNEM

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

213
views

321
downloads

Cite This

In this thesis study, the nonlinear dynamic behavior of functionally graded (FG) annular microplate is examined. The mechanical properties (i.e., modulus of elasticity, Poisson’s ratio, shear modulus of elasticity, density) of FG plates change continuously and smoothly in the thickness direction. The nonlinearity is caused by von Karman’s large deformation assumption. The boundary conditions are assumed as simply supported and the governing partial differential equations for nonlinear free vibration of a FG annular microplate are presented. The size dependency is taken account by using the Modified Couple Stress Theory (MCST) in the derivation of equations. Hamilton’s principle is utilized to obtain the partial differential equations of motion and boundary conditions. The associated equations are discretized by using Differential Quadrature Method (DQM) and solved by utilizing two different methods, which are strain energy equivalence method and Harmonic Balance Method (HBM). In addition, Rayleigh-Ritz (RR) Method is also utilized to obtain eigenvalue equation instead of DQM. The numerical results for dimensionless natural frequencies are represented. The influence of the length scale effect on numerical results is also investigated.

Subject Keywords

Nonlinear Free Vibration, Modified Couple Stress Theory, Functionally Graded Annular Microplate, Variable Length Scale Parameter, Harmonic Balance Method, Rayleigh-Ritz Method

URI

https://hdl.handle.net/11511/103065

Collections

Graduate School of Natural and Applied Sciences, Thesis