Steady state response of functionally graded nano-beams resting on viscous foundation to super-harmonic excitation

Abstract

This article attempts to investigate the effects of small scale parameter on steady state response of functionally graded nano-beams resting on a viscous foundation to super-harmonic excitation. A simple power-law distribution is used to model the variation of material property graded in the thickness direction. The dimensionless partial differential equation of motion is derived by using Euler-Bernoulli beam theory, von-Karman geometric nonlinearity and Eringen’s nonlocal elasticity theory. Using multiple scale method, one can find the governing equations of steady state response of functionally graded nano-beams excited by distributed harmonic force. The small scale parameter (e0a) is changed between 0 and 2 to investigate the effects of small scale on steady state response of excited functionally graded nano-beams due to lack of information. The study of the effects of small scale parameter on backbone curves shows that an increase in the small scale parameter often decreases the dimensionless peak response although the type of loading can change the relationship between small scale parameter and the dimensionless peak response.