Nonlocal longitudinal vibration of viscoelastic coupled double-nanorod systems

• Nonlocal damped axial vibration of nanorods coupled by viscoelastic medium is considered.
• Closed-form exact expressions are derived for the natural frequencies and damping factors.
• Clamped–Clamped and Clamped–Free boundary conditions are considered.
• The increase of nonlocal parameter reduces the influence of nanorod's damping coefficient in the imaginary part of the eigenvalues.

A theoretical study of the free longitudinal vibration of a nonlocal viscoelastic double-nanorod system (VDNRS) is presented in this paper. It is assumed that a light viscoelastic layer continuously couples two parallel nonlocal viscoelastic nanorods. The model is aimed at representing dynamic interactions in nanocomposite materials. The exact solution for the longitudinal vibration of a double-nanorod system is determined for two types of boundary conditions, Clamped–Clamped (C–C) and Clamped–Free (C–F). D'Alembert's principle is applied to derive the governing equations of motion in terms of the generalized displacements for a nonlocal viscoelastic constitutive equation. The solutions of a set of two homogeneous partial differential equations are obtained by using the classical Bernoulli–Fourier method. Numerical results are presented to show the effect of material length scale parameter, damping from viscoelastic constitutive equations, damping of light viscoelastic layer and boundary conditions for the free longitudinal vibration of a viscoelastic double-nanorod system.

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