Extension and flapwise bending vibration analysis of a rotating piezolaminated composite Timoshenko beam

In this study, extension and flapwise bending vibration analysis of a rotating piezolaminated composite Timoshenko beam is performed both analytically and via finite element method. In the analytical part, energy expressions are derived by including the parameters for the hub radius, rotational speed, rotary inertia, shear deformation, slenderness ratio and ply orientation. The Differential Transform Method is used to transform the differential equations of motion and the boundary conditions into simple analytical expressions. In the finite element part, derived energy expressions are used to obtain the element stiffness and mass matrices. In order to model the piezoelectric effect correctly, some preliminary steps are performed and not only loads but also structural properties of the piezoelectric layers are added to the beam model. Numerical examples are solved to validate the correctness and accuracy of the built models.