FREE VIBRATION ANALYSIS OF FUNCTIONALLY GRADED NANOBEAMS USING DOUBLET MECHANICS THEORY

Abstract

Free vibration analysis of functionally graded (FG) nanobeams is examined using doublet mechanics theory. The material properties of FG nanobeams change with the thickness coordinate. Most of the size dependent continuum models (nonlocal stress gradient, strain gradient and couple stress theories) predict only softening or hardening material behaviour. Except of these size dependent theories doublet mechanics predicts both softening and hardening responses of the material like experiments in micro/nano-structures. A periodic nanostructure model is considered in FG nanobeams which has a simple crystal square lattice type. Softening or hardening material behaviour has been observed by changing chiral angle of the considered FG periodic nanobeams in the present doublet mechanics theory. Mechanical material responses are directly affected by the atomic structure of the considered material in the doublet mechanics theory. After developing the mathematical formulations of FG periodic nanobeams, Ritz method is applied to obtain the vibration solution for different boundary conditions.

Cite as:

 Ramya Rashmi Rout, Rati Ranjan Dash, & Mamata Kumari Padhy. (2022). Free Vibration Analysis Of Functionally Graded Nanobeams Using Doublet Mechanics Theory. Research and Development in Machine Design, 5(2), 1–15. https://doi.org/10.5281/zenodo.6956869