You have a PZT-5A square plate with 1 cm side and 0.1 cm thickness. Ifyou apply 1kV to the plate in the poling direction. Calculate the resultingstrains in the 1, 2, and 3 directions.[Useful data: PZT-5A is tetragonal with point group 4mm,= -119 PC/N, d33 = 268 pC/N, d₁5 = 335 pC/N)d31X₁X₂X3X4X5X6d₁1 d21 d31d₁2 d22 d32d13 d 23 d33d₁4 d24d15 d25 d35d16 d26 d36,d34E₁EEEE₂E3✓Class 4mm(:::::).

Answered: You have a PZT-5A square plate with 1…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

You have a PZT-5A square plate with 1 cm side and 0.1 cm thickness. If
you apply 1kV to the plate in the poling direction. Calculate the resulting
strains in the 1, 2, and 3 directions.
[Useful data: PZT-5A is tetragonal with point group 4mm,
= -119 PC/N, d33 = 268 pC/N, d₁5 = 335 pC/N)
d31
X₁
X₂
X3
X4
X5
X6
d₁1 d21 d31
d₁2 d22 d32
d13 d 23 d33
d₁4 d24
d15 d25 d35
d16 d26 d36,
d34
E₁
EEE
E₂
E3
✓Class 4mm
(:::::).

Expert Solution

Step 1: Solution:

To solve this problem, we need to calculate the resulting strains in the 1, 2, and 3 directions of a PZT-5A square plate with specific properties.

First, let's analyze the given data:

PZT-5A is tetragonal with a point group of 4mm.
The piezoelectric coefficient values are:
d₃₁ = -119 pC/N
d₃₃ = 268 pC/N
d₁₅ = 335 pC/N

Now, we are given the following equation relating the strains (x_1, x_2, x_3, x_4, x_5, x₆ ) to the applied electric field (E₁ , E₂ , E₃ ):

$open square brackets table row cell x subscript 1 end cell row cell x subscript 2 end cell row cell x subscript 3 end cell row cell x subscript 4 end cell row cell x subscript 5 end cell row cell x subscript 6 end cell end table close square brackets equals open square brackets table row cell d subscript 11 end cell cell d subscript 21 end cell cell d subscript 31 end cell row cell d subscript 12 end cell cell d subscript 22 end cell cell d subscript 32 end cell row cell d subscript 13 end cell cell d subscript 23 end cell cell d subscript 33 end cell row cell d subscript 14 end cell cell d subscript 24 end cell cell d subscript 34 end cell row cell d subscript 15 end cell cell d subscript 25 end cell cell d subscript 35 end cell row cell d subscript 16 end cell cell d subscript 26 end cell cell d subscript 36 end cell end table close square brackets open square brackets table row cell E subscript 1 end cell row cell E subscript 2 end cell row cell E subscript 3 end cell end table close square brackets$

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