Nonlinear vibration analysis of fractional viscoelastic nanobeam

Abstract Considering the size-dependent influence ignored by classical continuum mechanics, a new non-classical Euler-Bernoulli beam model is proposed in this paper. The new fractional viscoelastic nanobeam model is set up by using the fractional viscoelastic Kelvin-Voigt model and Hamilton's principle. And the new model studies the total effects of nonlocal elasticity, modified couple stress, and surface energy. The model represented the fractional integral-partial differential governing equation is solved by Galerkin's and predictor-corrector method. Firstly, the effects of nonlocal elasticity, modified couple stress, surface energy, and their coupling impact on the nonlinear time response of free vibration of fractional viscoelastic nanobeam are analyzed. Secondly, the nonlinear time response of free and forced vibration of fractional viscoelastic nanobeam are studied in the context of the nonlocal couple-stress elasticity and the surface energy theory. Finally, the effects of initial displacement, fractional order, viscoelasticity coefficient, damping coefficient, length-to-thickness ratio, force amplitude, and excitation frequency on the nonlinear vibration time response of the fractional viscoelastic nanobeam are analyzed.