Nonlocal elasticity based vibration of initially pre-stressed coupled nanobeam systems

Vibration analyses of coupled nanobeam system under initial compressive pre-stressed condition are presented. An elastically connected double-nanobeam-system is considered. Expressions for bending-vibration of pre-stressed double-nanobeam-system are formulated using Eringenʹs nonlocal elasticity model. An analytical method is proposed to obtain natural frequencies of the nonlocal double-nanobeam-system (NDNBS). Nano-scale effects and coupling spring effects in (i) in-phase type, (ii) out-of-phase type vibration; and (ii) vibration with one nanobeam fixed are examined. Scale effects in higher natural frequencies of NDNBS are also highlighted in this manuscript. Results reveal the difference (quantitatively) by which the pre-load affects the nonlocal frequency in the in-phase type and out-of-phase type vibrations mode of NDNBS.