Modeling of torsion actuation of beams using inclined piezoelectric actuators

The present work is preliminary studies on the development of finite element model for static analysis of advanced beam structure subjected to axial, transverse, and torsion loads in addition to the torsion actuation due to the piezoelectric actuators. These types of smart structures can be used as element of mechanical system, helicopter rotor blade, and/or blades for turbomachinery. The equation of motion of the structure system is derived using the energy variation approach. The model assumes that the structure behaves as a Bernoulli–Euler beam in bending and extension, while torsion is introduced by utilizing a cross-sectional warping function, which dependent upon the cross- section geometry of the structure. A linear and hermit cubic shape functions are used to model the axial and transverse deformations, while quadratic interpolation shape function is introduced to model the torsion deformation. The bending, torsion, and axial coupling are introduced in the stiffness and mass matrices. The electric potential is considered as function of the thickness and the length of the beam element. A MATLAB interactive code is developed to validate the model. The obtained results are compared to the available analytical and finite element results and found reasonable.