Analytical solutions of nonlocal forced vibration of a functionally graded double-nanobeam system interconnected by a viscoelastic layer

Abstract

Abstract The double-nanobeam system has important applications in nano-optomechanical systems (NOMS), its dynamic analysis is of importance to the effective design of nanodevices. This paper aims to present analytical solutions of the forced vibration of a functionally graded double-nanobeam system (FGDNS) interconnected by a viscoelastic layer supported on an elastic foundation subjected to time-harmonic external forces. Employing the Hamilton’s principle, the governing differential equations of the FGDNS are derived in the context of the Euler–Bernoulli beam theory and Eringen’s nonlocal elasticity theory. Green’s functions method in conjunction with the superposition principle are adopted to obtain the explicit expressions of the steady-state responses of the FGNDS. A unified strategy applied to various boundary conditions is proposed to determine unknown constants involved in the Green’s functions. Meanwhile, the implicit equation calculating the natural frequency of the FGDNS is proposed. Numerical calculations are performed to check the validity of the present solutions and to discuss the influences of the small-scale parameter, material distribution parameter, and connecting layer parameters on dynamic behaviors of the FGNDS. Results show that the bond between the two nanobeams can be significantly reinforced by increasing the stiffness and damping coefficient of the connecting layer; the small-scale effect can soften or harden the system, depending upon the boundary conditions and the size of the frequency of external force.