Bending and free vibration of functionally graded piezoelectric beam based on modified strain gradient theory

A size-dependent functionally graded piezoelectric beam model is developed using a variational formulation. It is based on the modified strain gradient theory and Timoshenko beam theory. The material properties of functionally graded piezoelectric beam are assumed to vary through the thickness according to a power law. The new model contains three material length scale parameters and can capture the size effect, unlike the classical beam theory. To illustrate the new functionally graded piezoelectric beam model, the static bending and free vibration problems of a simply supported beam are numerical solved. These results may be useful in the analysis and design of smart structures constructed from piezoelectric materials.