The Effect of Modified Couple Stress Theory on Buckling and Vibration Analysis of Functionally Graded Double-Layer Boron Nitride Piezoelectric Plate Based on CPT

In this article, the effect of size-dependent on the buckling and vibration analysis of functionally graded (FG) double-layer boron nitride plate based on classical plate theory (CPT) under electro-thermo-mechanical loadings which is surrounded by elastic foundation is examined. This subject is developed using modified couple stress theory. Using Hamilton's principle, the governing equations of motion are obtained by applying a modified couple stress and von Karman nonlinear strain for piezoelectric material and Kirchhoff plate. These equations are coupled for the FG double-layer plate using Pasternak foundation and solved using Navier’s type solution. Then, the dimensionless natural frequencies and critical buckling load for simply supported boundary condition are obtained. Also, the effects of material length scale parameter, elastic foundation coefficients and power law index on the dimensionless natural frequency and critical buckling load are investigated. The results demonstrate that the dimensionless natural frequency of the piezoelectric plate increases steadily by growing the power law index. ‌‌Also, the effect of the power law index on the dimensionless critical buckling load of double layer boron nitride piezoelectric for higher dimensionless material length scale parameter is the most.