PSI - Issue 5

Baris Arslan et al. / Procedia Structural Integrity 5 (2017) 171–178 Baris Arslan et al. / Structural Integrity Procedia 00 (2017) 000 – 000

174

4

In this study, the square PZT patch has a dimension of 10×10×0.5 mm and modelled using C3D8E element, which has an 8-node linear brick. The electrical potentials of the top and the bottom surfaces of the PZT patches are coupled to the electrical potentials of the master nodes assigned to each surface using linear constraint equations[31]. The electrical potentials and the reaction charges can be applied to and monitored on these master nodes. During the analysis, 0.5V of electrical potential is applied using the boundary condition on both master nodes.

In Abaqus [31], the piezoelectric behaviour is described by equations:

1

( e E D E D d E          

)

2

Q e D E     

Where;  is the stress vector (GPa) , q is the electrical displacement vector

2 (C/m ) ,  is the strain vector, E is the φ D is the electric permittivity matrix (F/m) and φ e 2 (C/m ) and strain (m/V) . The material matrices are

E D is the elasticity matrix (GPa) ,

electrical field vector (V/m) ,

, φ d are the piezoelectric matrices respectively defined in stress

determined as following by using piezoelectric material properties for PZT-5H [24]; Stiffness matrix;

      

      

127.20 80.21 84.67 0 0 0 80.21 127.20 84.67 0 0 0 84.67 84.67 117.43 0 0 0 0 0 0 22.98 0 0 0 0 0 0 22.98 0 0 0 0 0 0 23.4 7

  E D

G

Pa





Piezoelectric coupling matrix (Strain);

Permittivity matrix;

  

  

  

  

0 0 0 0 741 0 0 0 0 741 0 0 274 274 593 0 0 0  

31.3 0 0 0 31.3 0 0 0 3

  d 

  D 

9



9 10 mm/V 

10 F/mm



 



 

4

3. Analyses and Results

3.1. Electromechanical Impedance

The method for EMIS computation is based on the direct solution steady-state dynamic analysis, which is used to calculate the steady-state dynamic linearized response of a system to harmonic excitation. In a direct-solution steady state analysis, the steady-state harmonic response is calculated directly in terms of the physical DOF of the model using the mass, damping, and stiffness matrices of the system [31]. Direct harmonic analyses are run within the frequency range between 0-20 kHz with no material damping. Due to the fact that all forms of damping are ignored, the real-only system matrix is factored. The type of frequency spacing is selected as linear and the specified frequency range is divided by 1000 points. Indeed, the direct solution is able to bias the excitation frequencies toward the approximate values that generate a response peak by employing the bias parameter. The bias parameter can be used to provide closer spacing of the results points, either toward the middle or toward the ends of each frequency interval. The bias parameter is selected as 1.0 for a range frequency interval [31]. Nodal electric charges, k Q , are obtained at the end of each analysis, afterwards, are derived by time in order to obtain electrical current intensity, k I , in Matlab. Finally, EMIS results are obtained from the Eq. 4 [12].