Microstructure-dependent piezoelectric beam based on modified strain gradient theory

A microstructure-dependent piezoelectric beam model was developed using a variational formulation, which is based on the modified strain gradient theory and the Timoshenko beam theory. The new model contains three material length scale parameters and can capture the size effect, unlike the classical beam theory. To illustrate the new piezoelectric beam model, the static bending and the free vibration problems of a simply supported beam are numerically solved. These results may be useful in the analysis and design of smart structures that are constructed from piezoelectric materials.