Modified size-dependent theory for investigation of dynamic stability and critical voltage of piezoelectric curved system

Abstract

Nowadays, using piezoelectric materials for electrical purposes has attracted much attention among researchers. So, in the current report, dynamic stability and critical voltage analysis of an nanoplate resting on an elastic foundation. The current nanostructure has been made of piezoelectric material. Modified couple stress theory (MCST) and Nonlocal theory (NT) are mixed (modified nonlocal couple stress theory) with one nonlocal and one length scale parameter for modeling the current nanostructure has been presented. Higher-order shear deformation plate theory (HSDPT), and Hamilton’s principle have been used for obtaining the boundary and governing equations of the piezoelectric nanoplate. A two-dimensional generalized differential quadrature element method (2D-GDQEM) has been presented for solving the displacement domains of the current nanostructure. By comparing the outputs of the current report and those of published articles, there is good agreement between the results. Finally, the results show that elastic foundation coefficients (Winkler and Pasternak type), boundary conditions, applied voltage, size-dependent parameters (length scale and nonlocal ones), and geometry properties have important role in the critical voltage and dynamic stability performance of the piezoelectric nanostructure. The outputs of the current report can be used for future researchers of NEMS by incorporating modified nonlocal couple stress theory (MNCST).