Vibration Sensitivity Analysis of Nano-mechanical Piezo-Laminated Beams with Consideration of Size Effects

The presented article investigates vibration sensitivity analysis of Nano-mechanical piezo-laminated beams with consideration of size effects. To do this, the vibration governing equation of the stepped Nano-mechanical piezo-laminated beam is firstly derived by implementation of the nonlocal elasticity theory. The nonlocal formulation is considered for both of the beam and the piezoelectric layer and the obtained equation is solved analytically. Moreover, there is a need to recognize the importance and relative effects of the beam parameters on the natural frequencies and resonant amplitudes of the nonlocal beam. Therefore, the Sobol sensitivity analysis is utilized to investigate the relative effects of geometrical and the nonlocal parameters on the natural frequencies and the resonant amplitude of the nanobeam. The obtained results show that the length and the thickness of the piezoelectric layer have prominent effects on the vibration characteristics of the beam. Moreover, it is indicated that nonlocal parameter effect on the resonant amplitudes is more than resonant frequency. Also, the effect of the nonlocal term is more important at higher modes of vibration. Therefore, the nonlocal size effects cannot be ignored in vibration analysis of the nanobeam especially at higher modes.