M.Sc Thesis

M.Sc StudentBuch Oran
SubjectDynamic Buckling of Nano-Beams
DepartmentDepartment of Aerospace Engineering
Supervisor ASSOCIATE PROF. Haim Abramovich
Full Thesis textFull thesis text - English Version


Nano-beam is one of the morphologies of a nanoscale structure. Its large dimension, the length, is in the range of 10-9[m] Due to exceptionally good physical, mechanical, and electrical properties nano-sized structures have attracted much investment to develop innovatory applications in a wide range of disciplines.

In the present work, a generalized non-local beam theory, based on the Eringen’s equations of were included in the Timoshenko type beam equations of motion, to study the buckling and free vibrations of Nano-beams. The two coupled equilibrium equations were decoupled yielding two independent equations. A computer code was written using  MATLAB to calculate  the eigenvalues, in the form of buckling loads and natural frequencies and their associated mode shapes. Then the influence of the axial compression load on the natural frequencies of Nano-beams was also investigated yielding an interaction curve between frequency squared and the compressive load. A parametric investigation was performed for the various variables of the problem, like boundary conditions, length and slenderness of the Nano-beam, and the influence of the non-local parameter (e0a)2 on the buckling loads, natural frequencies and load-frequency relation.

Based on the results of the first part,  the second part presents the investigation of the dynamic buckling of Nano-beams. The concept “dynamic buckling” describes the stability behavior of a beam under a pulse type load. It was shown in the literature that in case the time period of the applied load is in the vicinity of the natural frequency of the beam, the “dynamic” buckling load might be lower than the static load. The goal of the investigation was to see the influence of the non-local parameter (e0a) on the stability of Nano-beams.

The Nano-beam model includes the effects of Timoshenko (local), surface elasticity and Eringen (small scale effect, non-local). An axial time depended load was applied on the beam. The time dependence had the form of a half sine, while the period time was varied from static-like values to dynamic-like values. The nonlinear behavior of the Nano-beam was investigated as function of the time dependent axial load.

The combined equations of motion of the beam were solved by a MATLAB computer program for a simply supported beam.

Within the scope of this work, the presently known knowledge on Nano-beam buckling was expanded to the dynamic realm. Understanding the behavior of Nano-beams in the dynamic region will enable a practical use of Nano-beams under time depended loads.