Buckling Behavior of Nanobeams Placed in Electromagnetic Field Using Shifted Chebyshev Polynomials-Based...

Area of Science:

• Solid Mechanics
• Nanotechnology
• Electromagnetism

Background:

• Investigating the mechanical behavior of nanostructures is crucial for advanced material design.
• Nonlocal continuum mechanics theories are essential for capturing small-scale effects in nanobeams.
• Electromagnetic fields can significantly influence the stability of nanostructures.

Purpose of the Study:

• To determine the critical buckling load of Euler-Bernoulli nanobeams under electromagnetic fields.
• To apply Eringen's nonlocal theory to analyze nanobeam buckling.
• To explore the impact of boundary conditions and scaling parameters on buckling behavior.

Main Methods:

• Utilizing the Rayleigh-Ritz method with shifted Chebyshev polynomials for approximation.
• Employing Eringen's nonlocal elasticity theory.
• Deriving a closed-form solution for the Pined-Pined boundary condition using Navier's technique.

Main Results:

• Critical buckling loads were calculated for Pined-Pined, Clamped-Pined, Clamped-Clamped, and Clamped-Free boundary conditions.
• Numerical results for the Pined-Pined case were validated against the closed-form solution.
• The influence of various scaling parameters on the critical buckling load was investigated and presented.

Conclusions:

• The shifted Chebyshev polynomials provide an accurate and stable numerical method for nanobeam buckling analysis.
• The study presents novel results on the buckling behavior of nanobeams in electromagnetic fields.
• Buckling mode shapes were visualized, demonstrating the sensitivity of the critical buckling load to various parameters.