1 ME 556 Smart Materials and Structures

ME 556
Smart Materials and Structures
Homework #1
Due:
1.
Monday 23.03.2015, 4 PM
(2 pts) [From textbook, p. 4.14] A piezoelectric stack with a short-circuit stiffness of 5 N/μm is driving a load
with a mass of 500 grams and a stiffness of 3.5 N/μm. The free displacement of the stack at 100 V is 40 μm.
Plot and label the frequency response of the stack displacement per unit voltage over the frequency range 1 to
10,000 Hz.
2. (2.5 pts) [From textbook, p. 4.17] A piezoelectric extender
operating in the 13 mode has the cross-sectional geometry
shown in figure below.
a) Compute the strain in the 1 direction for an applied field of
0.75 MV/m. Assume that brass has a modulus of 117 GPa and that the piezoelectric material is APC 856.
b) Also calculate the tip displacement of the right end, if the bimorph is fixed from the left end and 200 V is
applied to each piezoelectric layer.
3.
(2.5 pts)
a)
Starting with the constitutive relationships for a piezoelectric material in matrix form, derive the following
transducer relationships for a piezoelectric material operated in 13 mode:
b) Using this equation, express f and v in terms of u1 and q
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