Vibration of Initially Stressed Nonlocal Euler-Bernoulli Nano-Beams

Abstract

This paper is pertinent to the analytical solutions for vibration analysis of initially stressed Nonlocal Euler-Bernoulli nano-beams. In order to take into account of small length scale effect, this vibration problem formulation is depending upon both nonlocal Euler-Bernoulli and also Eringen’s nonlocal elasticity theory. The boundary conditions and governing equation are obtained by use of Hamiltonian’s principle. These equations are solved analytically with different initial stresses (both compressive and tensile) and boundary conditions. The effect of small length scale and the initial stress on the fundamental frequency are investigated. The solutions obtained are compared with the ones depending upon both classical Euler-Bernoulli and Timoshenko beam theory to comprehend the responses of nano-beams under the effect of initial stress and small scale in terms of frequencies for both theories. The results supply a better declaration for vibration analysis of nano-beams which are short and stubby with initial stress.