Nonlocal viscoelasticity based vibration of double viscoelastic piezoelectric nanobeam systems

The present work deals with the analysis of free and forced vibrations of double viscoelastic piezoelectric nanobeam systems (DVPNBSs) incorporating nonlocal viscoelasticity theory and Euler–Bernoulli beam model. The two viscoelastic piezoelectric nanobeams (VPNBs) are coupled by visco-Pasternak medium. Viscoelastic property of VPNBs is simulated by Kelvin–Voigt and Maxwell models. In order to obtain the natural frequency and frequency response of the coupled system under the harmonic excitation, an exact solution is presented. The free and forced vibrations of DVPNBS are considered in three cases namely out-of-phase vibration, in-phase vibration and vibration with one VPNB fixed. A detailed parametric study is carried out to demonstrate the influence of nonlocal parameter, visco-Pasternak constants, voltage, Kelvin–Voigt and Maxwell coefficients on the vibration characteristic of DVPNBS. Results indicate that the natural frequencies of DVPNBS are significantly influenced by nonlocal effects. In addition, effects of damping coefficient of the viscoelastic medium and internal damping of the material on the frequency of the coupled system are vice versa. Furthermore, the imposed external voltage is an effective controlling parameter for vibration of the coupled system.