Free vibration of nonlocal piezoelectric nanoplates under various boundary conditions

•The natural frequencies are quite sensitive to the mechanical loading and electric loading.•The natural frequency is not sensitive to the thermal loading.•The nonlocal parameter has distinguished effect on mode shapes for CCCC and CCSS nanoplates.

This paper investigates the thermo-electro-mechanical vibration of the rectangular piezoelectric nanoplate under various boundary conditions based on the nonlocal theory and the Mindlin plate theory. It is assumed that the piezoelectric nanoplate is subjected to a biaxial force, an external electric voltage and a uniform temperature rise. The Hamilton's principle is employed to derive the governing equations and boundary conditions, which are then discretized by using the differential quadrature (DQ) method to determine the natural frequencies and mode shapes. The detailed parametric study is conducted to examine the effect of the nonlocal parameter, thermo-electro-mechanical loadings, boundary conditions, aspect ratio and side-to-thickness ratio on the vibration behaviors.

Graphical abstractThe effect of nonlocal parameter μ   on the fundamental mode shape of the electric potential ϕ⁎ϕ⁎ of the CCCC piezoelectric nanoplate.Figure optionsDownload full-size imageDownload as PowerPoint slide