Vibration Analysis Of Piezoelectric Smart Beams By Using FEM And Impedance Method

Piezoelectric materials have been applied in all kinds of engineering field as actuatorsand sensors, because they can effectively achieve transformation between mechanicalenergy and electrical energy. In structural applications, bonded or embedded piezoelectricmaterials are used to provide vibration signals in order to achieve vibration control andhealth monitoring. Therefore, it has important scientific significance and practical value toanalyse the dynamic characteristics of piezoelectric smart structures. Based onelectromechanical coupling characteristics between piezoelectric materials and hoststructure, harmonic vibration of piezoelectric smart beams is studied by using impedancemethod combined with FEM in this paper.At first, the equivalent impedance matrixes of elastic beam element and bimorphbeam element can be gained form Timoshenko beam theory. Smart beams which thenumber and location of piezoelectric patches are unknown can be regarded as acombination of finite elastic beam elements and bimorph beam elements. And dynamicresponse of the system will be analysed with impedance equations presented in this paper.Research shows that the proposed method results are more agreed with FEM results thanthe results obtained from Bernonlli-Euler beam theory when study objects are deep beamsin high frequency range.Secondly, independent piezoelectric patch is equivalent to a stretch mass-damping-spring(M-C-K) system according to the equivalent relationship between electricalimpedance and mechanical impedance. Bending FE model is regarded as two M-C-Ksystems bonded on the top and the bottom of the beam respectively. Dynamic responses ofthe smart beams with different supporting conditions are calculated by using the proposedFE model in this paper. And the results compare with the traditional FE model results shows that the proposed method can effectively analyze the dynamic characteristics ofelastic beams driving by bending actuators in all kinds of boundary conditions. Theproposed method has distinct advantages in calculation cost and analysis efficiencycomparing with the early FE model, and it establishes the foundation of further analysis oflarge and complex structures.Finally, external circuit electrical parameters will be brought in FE model based onthe equivalent circuit model. Initial application of the proposed FE model is introduced inaspect of sensoring and actuation of smart structures. It shows that external impedance hasobvious impact on the amplitude but less impact on the response frequency no matterpiezoelectric stack is a actuator or sensor.