forced vibration of piezoelectric nanowires based on nonlocal elasticity theory

in this paper, a numerical solution procedure is presented for the forced vibration of a piezoelectric nanowire under thermo-electro-mechanical loads based on the nonlocal elasticity theory within the framework of timoshenko beam theory. using hamilton’s principle, the nonlocal governing differential equations are derived. the governing equations and the related boundary conditions are discretized by using the differential quadrature method (dqm). the numerical results are obtained for both free and forced vibration of piezoelectric nanowires. the effects of the nonlocal parameter together with the other parameters such as temperature change, length and external electric voltage on the size-dependent forced vibration of the piezoelectric nanowires are studied. it is shown that the nonlocal effect (small scale effect) plays a prominent role in the forced vibration of piezoelectric nanowires and this effect cannot be neglected for small external characteristic lengths. as the nonlocal parameter increases, the distribution of electric potential becomes more non-uniform across the thickness of the nanowire. furthermore, it is observed that the amplitude of piezoelectric nanowires increases with increasing nonlocal parameter. this means that the stiffness of piezoelectric nanowires reduces with increasing the effect of small scale.