Vibration of a coupled fractional viscoelastic multi-nanobeam systems

Abstract

This paper shows the transverse vibration analysis of complex multiple coupled nanobeams system. Observed system is composed of an arbitrary number of aligned nanobeam structures embedded in viscoelastic medium where damping features of nanobeams and viscoelastic medium are represented by the fractional viscoelastic models while small-scale effects are considered using the Eringen’s nonlocal elasticity. In addition, non-homogeneities of the system such as different nanobeams cross-sections or density are observed within the paper. Governing equations are derived using using the d’Alembert’s principle, differential form of nonlocal stress relation and local stress-strain viscoelastic constitutive equation of fractional Kelvin-Voigt type. Semi-analyitical solutions for the transient response of simply supported nanobeams in the system are obtained using the separation of variables method, Laplace and Mellin-Fourier integral transforms, residue theory and modal expansion method. The problem of decoupling the governing equations of a non-homogenous system is solved by adopting the methodology from the literature. Several numerical examples are given to show the effects of different physical parameters on the transient response of such a system. Presented dynamic analysis and results could be used in future theoretical studies with additional physical effects included into the model. There is also a potential for use of this type of analysis in design procedures of modern nanodevices for calculation of their dynamic behavior that is much faster compared to atomistic based models.