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In this paper, a nonlocal continuum plate model is developed for the transverse vibration of double-piezoelectric-nanoplate systems (DPNPSs) with initial stress under an external electric voltage. The Pasternak foundation model is employed to take into account the effect of shearing between the two piezoelectric nanoplates in combination with normal behavior of coupling elastic medium. Size effects are taken into consideration using nonlocal continuum mechanics. Hamilton?s principle is used to derive the differential equations of motion. The governing equations are solved for various boundary conditions by using the differential quadrature method (DQM). In addition, exact solutions are presented for the natural frequencies and critical electric voltages of DPNPS under biaxial prestressed conditions in in-phase and out-of-phase vibrational modes. It is shown that the natural frequencies of the DPNPS are quite sensitive to both nonlocal parameter and initial stress. The effects of in-plane preload and small scale are very important in the resonance mode of smart nanostructures using piezoelectric nanoplates. [ABSTRACT FROM AUTHOR]

Abstract: In this article, a single nonlocal beam model is developed and applied to investigate the flapwise bending–vibration characteristics of a rotating nanocantilever. A rotating nanocantilever is found as blades of a nanoturbine. Employing Eringen’s nonlocal elasticity theory, the governing differential equations for the abovementioned problem are derived. Differential quadrature method (DQM) is being utilized and nondimensional nonlocal frequencies are obtained. The effects of the small-scale, angular velocity and hub radius are examined and discussed. It is shown that small-scale effects play a significant role in the vibration response of a rotating nanocantilever. Further as rotational angular velocity increases, the small-scale effect on the frequency response is increased for first modes of vibration while it is decreased for higher modes of vibration. [Copyright &y& Elsevier]