Vibration insight of a nonlocal viscoelastic coupled multi-nanorod system

Longitudinal vibration of viscoelastic multi-nanorod system (VMNS) is studied. Based on the D' Alembert's principles, nonlocal and viscoelastic constitutive relations, the system of m partial differential equations are derived which described the motion of the presented nano-system. Clamped–Clamped and Clamped–Free boundary conditions and two different chain systems, namely “Clamped-Chain” and “Free-Chain” are illustrated. The method of separations of variables and trigonometric method are utilized for solutions. The analytical expressions for critical viscoelastic parameters and asymptotic frequencies are presented. The predicted results are validated with results obtained by direct numerical simulations and results from literature. The effects of nonlocal parameter, number of nanorods, viscoelastic material constant and parameter of viscoelastic layer on the complex eigenvalue are discussed in details.