Bending and free vibration of functionally graded piezoelectric microbeams based on the modified couple stress theory

A size-dependent model for bending and free vibration of functionally graded piezoelectric (FGP) microbeam is developed by using modified couple stress theory and a unified higher order beam theory. This model can be specialized to various beam models, such as Euler–Bernoulli, Timoshenko as well as Reddy beam ones and vice versa. The governing equations of motion and associated boundary conditions are derived from Hamilton’s principle. Only one material length scale parameter is introduced to capture the size effect. The analytical solutions of simply supported FGP microbeam are presented by using Navier approach to bring out the effect of the material length scale parameter on the bending and free vibration of microbeam. Numerical simulations are presented to account for the effect of various parameters, such as material length scale parameters, volume fraction indexes, and slenderness ratios on the responses of static bending and free vibration of FGP microbeam.