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Fig. 6
Voltage (mv)
90
80
70
60
50
40
30
20
10
0
PZT
Subst
rate
Stress
Neutral axis
PZT
subst
rate
(a)
(b)
Neutral axis lies (a) within substrate (b) within PZT
0.5 1 1.5 2 2.5 3 3.5 4 4.5
thinkess ratio, substrate/PZT layers
Fig. 7 output voltage vs. thickness ratio when different Young’s module ratio
Table 2 best output, thickness ratio and bending stiffness in different substrate
Young’s modulus ratio 0.5 1.0 1.6 2.8
Best thickness ratio 3.61 2.11 1.40 0.98
Bending stiffness 0.063 0.026 0.017 0.012
Best Output (V) 0.071 0.078 0.084 0.090
V. Conclusion
Young's modulus ratio 2.8
Young's modulus ratio 1.6
Young's modulus ratio 1
In this paper, an analytical solution of a fixed-fixed beam
type piezoelectric transformer with Euler-Bernoulli beam
assumption is proposed. Mechanical response, voltage,
current, and power outputs of piezoelectrical transformers are
presented. The model is then used for parameter study. From
analytical model, output voltage depends on the lengthes of
two electrodes, the length of beam, and the Young’s modulus
ratio and thickness ratio between PZT layer and substrate.
The lengthes of input electrodes and output electrodes should
be 0.22L to achieve the largest output when the transformer
is excited at first resonance frequency. The output voltages
and the resonance frequnecies of transformers are
proportional and inversely proportional to the lengthes of
beams, respectively. The combination of Young’s modului
and thicknesses of PZT layer and substrate change the
position of netual axis and the bending stiffness of beam,
concurrently. However, output voltages of transfomers
depend not only on the postion of neutral axes but also on
bending stiffnesses.
11-13 May 2011, Aix-en-Provence, France
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