Nonlinear vibration of piezoelectric nanoplates using nonlocal Mindlin plate theory

ABSTRACT

This article investigates the nonlinear vibration of piezoelectric nanoplate with combined thermo-electric loads under various boundary conditions. The piezoelectric nanoplate model is developed by using the Mindlin plate theory and nonlocal theory. The von Karman type nonlinearity and nonlocal constitutive relationships are employed to derive governing equations through Hamilton's principle. The differential quadrature method is used to discretize the governing equations, which are then solved through a direct iterative method. A detailed parametric study is conducted to examine the effects of the nonlocal parameter, external electric voltage, and temperature rise on the nonlinear vibration characteristics of piezoelectric nanoplates.

KEYWORDS:

• Mindlin plate theory
• nonlinear vibration
• nonlocal theory
• piezoelectric materials
• size effect

Additional information

Funding

The authors gratefully acknowledge the support provided by the National Natural Science Foundation of China under Grant numbers 11272040 and 11322218. Prof. J. Yang and Prof. S. Kitipornchai are also grateful for the two research grants from the Australian Research Council under the Discovery Project scheme (DP130104358, DP140102132).