A Comparison between finite element and separation of variables method in investigating frequency behavior of Bimorph piezoelectric beam

in recent years, Variety of analytical methods have been used to calculate the output piezoelectric energy, but it is new something the use of finite element method and compared using analysis software with numerical methods. And also check the types of circuit connection of piezoelectric layers So in this article particular form of numerical analysis method is called separation of variables method compared with the finite element method, To take advantage of these methods is to be determined. The model is a Bimorph beam with two piezoelectric layers and a central elastic layer. This Bimorph beam starts vibrating at various frequencies as a result of base excitation. First, frequency behavior of the Bimorph beam is simulated using the separation of variables method. In this method, the equations of motion in parallel and series connection of piezoelectric layers are obtained as separate parameters. The coupled mechanical and electrical equations are derived using the solution of equations obtained from the separation of variables method. Finally, the output voltage, current and power are obtained in terms of frequency.
Then, the Bimorph beam is modeled based on finite element method using ABAQUS software. after the illustrating Output voltage, current and power diagrams is illustrated for a certain range of frequencies and the results of the finite element method and the steady state method are compared to validate the model.