Analytical Solution and Parametric Study of Free Transverse Vibration of Nano Scale Beam

Abstract

In this project free vibration of the nano scale beam based on the non-local continuum models has been studied. Corresponding equation of motion is of fourth order ordinary differential equation. The boundary conditions have been taken as simply supported boundary. Frequency parameters of the said problem have been obtained by solving the fourth order differential equation. Various parametric studies are done and corresponding Tables and Plots are incorporated to understand the nanotechnology aspects related to non-local and local nano beams. The results in terms of parametric investigations obtained may give an idea about design of nano beams.