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3.6  Example 2: Dynamic response of a piezoelectric disk

In this next example, we consider a piezoelectric disk of thickness=2mm and radius=8mm which has electrodes on the top and bottom surfaces. The material used is PIC181 from PI Ceramics. The mesh and corresponding electrodes are generated with the following script and represented in Figure 3.7. (d_piezo('TutoDiskImpedance-s1') )

% See full example as Matlab code in d_piezo('ScriptTutoDiskImpedance')
t_avc('Definestyles');

%% Step 1 Build and represent mesh and electrodes
model=d_piezo('MeshPIC181disk th=2e-3 r=8e-3 ner=10 nez=4 nrev=16');
feplot(model); cf=fecom; cf.mdl.name='PIC 181 piezo disk mesh'; iimouse('resetview')
t_avc('setstyle',cf)

% Visualize electrodes
fecom('curtabCase',{'Top Actuator';'Bottom Actuator'}) % 
fecom(';showline;proviewon;triax') % 
cf.mdl.name='PIC 181 piezo disk electrodes'
t_avc('setstyle',cf)

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Figure 3.7: Piezo electric disk made of bulk PIC181 material (radius=8mm, thickness=2mm): mesh(left) and electrodes(right)

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We compute the dynamic response of the disk subjected to an imposed voltage on the top electrode (the bottom electrode is grounded in the model), the frequency range is from 20 to 200 kHz. We represent the voltage distribution on the disk, as well as the electric field at 20 kHz in Figure 3.8. (d_piezo('TutoDiskImpedance-s2') )

%% Step 2 : Define range of frequencies and compute dynamic response
frq=linspace(20e3,200e3,256);
def=fe_simul('dfrf',stack_set(model,'info','Freq',frq)); 


% visualize potential
feplot(model,def); cf=fecom; 
fecom(';showpatch;colordata21;'); cf.mdl.name='PIC 181 piezo disk voltage'
t_avc('setstyle',cf) ; 
cf.osd_('cbtr{string,Voltage(V)}')
fecom('colorscaleone') %To have the correct scale

% View electric field
fecom(';showline;scd 1e-4')
p_piezo('viewElec EltSel "matid1" DefLen 1e-4',cf); 
cf.mdl.name='PIC 181 piezo disk E-field'
% To have a single color change clim (must be done with axProp to bypass normal)
st=cf.ua.axProp; st(3:4)={'@axes',{'clim',[480 510]}};cf.ua.axProp=st;
t_avc('setstyle',cf)
cf.osd_('cbtr{string,E(V/m)}')

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Figure 3.8: Response of a piezoelectric disk made of bulk PIC181 material (radius=8mm, thickness=2mm) at 20kHz, voltage distribution(left) and electric field (right)

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A charge sensor is defined on the piezoelectric disk, allowing to compute the charge accumulated at each frequency for an accumulated input voltage. It is represented in Figure 3.9(left). (d_piezo('TutoDiskImpedance-s3') )

%% Step 3: Compute q/V as a function of the frequency
sens=fe_case(model,'sens');
C1=fe_case('SensObserve âˆ'DimPos 2 3 1',sens,def);
C1=sdsetprop(C1,'PlotInfo','sub','magpha','scale','xlin;ylog');
ci=iiplot; 
iicom(ci,'curveInit',C1.name,C1); iicom('submagpha');
t_avc('setstyle',ci);

The electric impedance is defined as Z=V/I = 1/(j ω)   V/Q and represented in Figure 3.9(right). The anti-resonance in the impedance curve around 140kHz corresponds to the short-circuited radial resonance frequency of the disk, while the resonance around 160kHz corresponds to the open-circuit resonance frequency of the disk. The spacing between these two frequencies can be used to compute the electromechanical coefficient of the disk for the first radial resonance. (d_piezo('TutoDiskImpedance-s4') )

%% Step 4: Compute and plot electric impedance
% extract impedance
C2=C1; C2.Y=1./(2*pi*1i*C2.X{1}.*C2.Y); C2.X{2}={'Imp(Ohm)'};
iicom(ci,'curveInit',C2.name,C2); iicom('submagpha');
t_avc('setstyle',ci);

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Figure 3.9: Response of a piezoelectric disk made of bulk PIC181 material (radius=8mm, thickness=2mm) from 20kHz to 200kHz, Q/V(left) and electric impedance (Ohm) (right)

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