Transducer shape optimization for instability control of smart piezolaminated columns

Figures & data

Figure 1. Front growth.

Table 1. Material properties

Property	Poly vinylidene fluoride (PVDF)	Aluminum
Young's modulus (GPa), E1, E2	2.0, 2.0	70.0
Poisson's ratio, ν12	0.30	0.25
Shear modulus (GPa), G12	0.775	28.00
Piezoelectric strain constant, C m^−2, e31 = e32	−0.046	–
Thickness (mm)	0.50	1.0
Number of layers	2 (at top and bottom)	1
Density (N s m^−4)	1800	2700

Figure 2. Actuator design history.

Figure 3. Error history (example 1).

Figure 4. Design history for mode 1 transducer (example 2).

Figure 5. Response of mode 1 transducer (example 2).

Figure 6. Design history mode 2 transducer (example 2).

Figure 7. Response of mode 2 transducer (example 2).

Table 2. Properties of Plastic and PVDF sheets

Properties	Plastic	PVDF
Elastic constant (GPa)	5.358	2.0
Poisson's ratio	0.3	0.29
Density (kg m^−3)	1100	1800
Piezoelectric constant		−23 × 10^−12
Dielectricity, ξ33 (10^−9 F m^−1)		0.1062
Maximum operating voltage (V µm^−1)		30

Figure 8. Experimental setup.

Figure 9. Flow diagram.

Table 3. Active damping coefficients

	Applied gain		Damping coefficient (% of critical damping)
Tip mass (gm)	Experiment	Theory	Structural	Augmented	Ratio
0.0	400	407	4.85	6.70	1.381
3.02	375	384	4.70	6.40	1.361
6.04	350	331	5.00	6.60	1.320
10.36	300	300	5.15	6.70	1.300

Figure 10. Theoretical and experimental responses with different tip masses.

Figure 11. Response with varying gains.

Table 4. Variation of active damping with gain

Applied gain (approximately)	Damping co-efficient (%)
0	5.00
075	5.35
150	5.70
225	6.00
350	6.60