An Investigation of Vibrations of Linearly Growing Discrete Chain of Atoms in Nano-structures

摘要

The vibration of linearly growing atoms in a nanostructure are investigated by formulating the respective system of equations using the Euler-Lagrange equation with Rayleigh's modification. This process models a vibrating atom attached to a stationary wall, the second atom attached to the first atom and vibrating with the same position coordinates as the first, the same applies for the third, fourth, fifth, sixth up to the tenth vibrating atom. The resulting system are systems second order ordinary differential equations which are transformed to first order ordinary differential equations and their respective column vector forms are formulated. Simulation of the systems of first order ordinary differential equations would be carried out using the computer algebra system Mathematica for the regular and random case. From the simulations, it was observed that the amplitudes of vibration increased for the discrete attachment of atoms and the frequency of vibration decreased. The simulation results obtained in the regular case compares satisfactorily with existing results in the literature.