Buckling Analysis of Axially Functionally Graded Tapered Nano-Beams Resting on Elastic Foundation Based on Nonlocal Elasticity Theory

Abstract

The stability analysis of nonlocal axially functionally graded tapered beams has been investigated. Euler-Bernoulli beams at the micro-or nanoscale are modeled using Eringen's nonlocal elasticity theory. The governing equations are derived using the differential constitutive relations, and the Chebyshev collocation method is utilized to convert the differential equation of motion into a set of algebraic equations. Next, the boundary conditions are applied, and the resulting eigenvalue problem is solved to obtain the critical buckling loads. The effects of the Winkler modulus parameter, the shear modulus parameter, the breadth taper ratio, the height taper ratio, the nonlocal scale coefficient, and the boundary conditions on the critical buckling loads have been studied.

Electromagnetic instability analysis of functionally graded tapered nano-tweezers

“…Some investigators offered the variable geometry micro/nano-electromechanical systems (NEMS/MEMS) to attain the desired performances. As beams are the building block for many NEMS and MEMS, some researchers investigated the mechanical performances of micro and nano-scale tapered beam, including size-dependent free vibration [8], buckling [9][10][11], thermoelastic damping analysis [12], resonant frequency [13] and transverse vibration [14]. While most of the NEMS/MEMS studies are addressed uniform configurations, some of them examined the non-uniform NEMS/MEMS [15][16][17][18].…”