M.Sc Student | Buch Oran |
---|---|

Subject | Dynamic Buckling of Nano-Beams |

Department | Department of Aerospace Engineering |

Supervisor | Professor Haim Abramovich |

Full Thesis text |

Nano-beam is one of the
morphologies of a nanoscale structure. Its large dimension, the length, is in
the range of *10 ^{-9}[m]*

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 *(e*_{0}*a)*^{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 *(e*_{0}*a)* 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.