Energy derivation and extension-flapwise bending vibration analysis of a rotating piezolaminated composite timoshenko beam

In this study, extension and flapwise bending vibrations of a rotating piezolaminated composite Timoshenko beam are analyzed. Energy expressions are derived using several explanatory tables and figures. Parameters for the hub radius, rotational speed, rotary inertia, shear deformation, slenderness ratio, and ply orientation are incorporated into the equations of motion. The differential transform method is used to transform the differential equations of motion and the boundary conditions into simple analytical expressions. Numerical results are obtained to investigate the effects of the applied voltage, ply orientation, rotational speed, and hub radius on the natural frequencies and tip deflection.