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Surface layer and nonlocal parameter effects on the in-phase and out-of-phase natural frequencies of a double-layer piezoelectric nanoplate under thermo-electro-mechanical loadings

M. Karimi, A. Reza Shahidi and S. Ziaei-Rad 

Microsystem Technologies, Volume 23, Issue 10, April 2017, Pages 4903–4915



The in-phase and out-of-phase natural frequencies of double-layer piezoelectric nanoplates (DPNP) are studied under thermo-electro-mechanical loadings using the surface layer and nonlocal elasticity theories. For this purpose, two nanoplates are coupled via an elastic medium that induces van der Waals forces while the DPNP is surrounded by the Winkler and shear moduli of elastic foundations. Both in-phase and out-of-phase fundamental frequencies are investigated and compared under different boundary conditions. The Hamilton’s principle is employed to derive the governing equations and the finite difference method is subsequently used to solve them. The finite difference solution thus obtained is validated against the results obtained from the Navier’s method. A different aspect of the study involves the investigation of the effects of nonlocal parameters, thermo-electro-mechanical forces, various boundary conditions, and elastic foundations on the surface layer vibration of a DPNP. It is observed that the effects of surface energy layers on the in-phase and out-of-phase vibrations increase with increasing values of the nonlocal parameter and external electric voltage but that they reduce with rising mechanical and thermal loadings, elastic foundation, and stiffness for the boundary conditions defined. The results of the present work are expected to be used in designing NEMS/MEMS components using smart composite nanostructures.



A. Frequency Ratio; B. Elastic Foundation; C. Shear Modulo; D. Nonlocal Parameter; E. Residual Surface Stress


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