1. Smart Materials in System Sensing and Control Dr. M. Sunar Mechanical Engineering Department King Fahd University of Petroleum & Minerals

2. INTRODUCTION SMART MATERIALS Definition Media where different fields interact in a distributed fashion These fields could be mechanical, thermal electrical, magnetic and/or optical

3. Example Phenomena Piezoelectricity: Mechanical and Electrical Fields Magnetostriction: Mechanical and Magnetic Fields Thermopiezoelectricity: Mechanical, Thermal and Electrical Fields

4. Smart Sensors Piezo Ceramic/Piezo Film (PZT, PVDF): Input is mechanical strain, output is electrical charge. Pyro Ceramic (PZT): Input is temperature gradient, output is electrical charge. Fiber Optic Strain Gauge: Input is mechanical strain, output is optical.

5. Smart Actuators Piezo Ceramic/Piezo Film (PZT, PVDF): Input is electrical signal, output is mechanical strain. Magnetostrictive (Terfenol): Input is magnetic field, output is mechanical force/moment. Shape Memory (Nitinol): Input is electrical heating, output is mechanical strain.

6. MATHEMATICAL FORMULATION Linear Theory of Thermo-Piezoelectro-Magnetism (Mechanical, Thermal, Electrical and Magnetic Fields) Define a thermodynamic potential G as G = G (S, E, B,  ) = 1/2(S T cS  E T  E + B T   1 B   2 )  S T eE  E T P   S T  S T  B  B T r   B T bE

7. where S: vector of strain E: vector of electrical field B: vector of magnetic flux density  : small temperature change c, , , , P, , e, r, b: constitutive coefficients

8. Constitutive Equations of Thermo-Piezoelectro-Magnetism T = cS  eE   B  D = e T S +  E  b T B  P  H =  T  S  bE    1 B  r   = T S + P T E  r T B   where

9. Differential Equations of Thermo-Piezoelectro-Magnetism Define two energy functionals  and 

10. where  : entropy density  : absolute temperature u: vector of mechanical displacement P b, P s : vectors of body and surface forces  : electrical potential  v : volume charge density  : surface charge W: heat source density

11. A: vector of magnetic potential J: vector of volume current density h: vector of external heat flux A: vector normal to the surface H E ` : matrix of external magnetic field intensity K: matrix of heat conduction coefficients

12. Define Hamilton’s Principle as where Ki = Kinetic Energy =

13. Note the variation  G =  S T T   E T D +  B T H    and the relations

14. We obtain the following fundamental equations:

15. FINITE ELEMENT METHOD Note the following FE approximations u e = N u u i  e = N   i A e = N A A i  e = N   i where N: shape function matrix

16. Note that S e = L u u e = [L u N u ] u i = B u u i B e = L A A e = [L A N A ] A i = B A A i

17. Finite Element Equations

18. PIEZOELECTRICITY Linear Equations of Piezoelectricity (Mechanical and Electrical Fields) T = cS  eE D = e T S +  E Finite Element Equations of Piezoelectricity

19. Piezoelectric Bimorph Finger Poling Direction Piezoelectric Layer +V -V Finite Element Mesh

20. Analytical Result w(x) = 1.5 e 31 V/Y (x/h) 2 where e 31 : piezoelectric constant Y: Young’s modulus h: thickness of piezoelectric layer

21. Tip Deflection (w) vs Horizontal Distance (x)

22. Thermopiezoelectricity Linear Equations of ThermoPiezoelectricity (Mechanical, Thermal and Electrical Fields) T = cS  eE  D = e T S +  E  P   = T S + P T E  

23. Finite Element Equations for Thermopiezoelectricity

24. MAGNETOSTRICTION Linear Equations of Magnetostriction (Mechanical and Magnetic Fields) T = cS   B H =  T  S    1 B Finite Element Equations of Magnetostriction

25. Piezoelectro-Magnetic Composite Beam Poling Direction Magnetostrictive Layer Piezoelectric Layer -V h Finite Element Mesh

26. Analytical Result u 3 (x) = e 31 Vb (y n -h/4) / (2Y m I) x 2 where b: depth of system y n : distance of neutral axis from system’s bottom surface Y m : Young’s modulus of elasticity for magnetoceramic I: area moment of inertia of system about its neutral axis

27. Tip Deflection (u3) vs Horizontal Distance (x)

28. Magnetic Field H 3 in A/m for Magnetostrictive Layer Analytical FEM Top Surface 11.44 11.42 Bottom Surface -21.99-21.88

29. APPLICATIONS Tactile/acceleration sensing and trajectory tracking of robotic manipulators Blade vibration measurement and control in turbo-machinery Noise control in acoustical systems Damage detection in composites

30. Sensors and actuators have load carrying capabilities. Controller smart material

31. Smart Structures Highly Integrated Sensors and Actuators Composites, Electronics & Functions

32. Instability Control

33. Rotorcraft System

34. SENSING OF BLADE VIBRATIONS Objectives To investigate validity of using piezoelectric layers To investigate method of sandwiching piezoelectric layers at the connection between blade and disk To select appropriate methods for transmitting measured signals

35. Current Status Measurement and control of blades are essential in turbo-machinery Current methods: laser doppler, strain gages and casing accelerometers Laser doppler: need of many sensors, sensitivity and limitations with regard to rotations Strain gages: not resistant to high temperature and location Casing accelerometer: modes of vibration not identified

36. Piezoceramic Materials Resistant to high temperature Ability of high strains Precision High bandwidth

37. Method Stationary Cantilever Beam Blade Piezoceramic

38. Figure 5.13 Experimental instrumentation schematic Experimental Schematic

39. Figure 5.7 : Beam-PZT material Frame experiment Experimental Setup

40. Figure 5.6 : BM500 piezoelectric material BM500 Piezoelectric Material

41. Transient Response to a Step Input

42. Steady-State Response to a Sinusoidal Input

43. Future Work Sensing and Control of Blade Vibrations using Piezoelectric and Magnetostrictive Materials Modeling of Nonlinearities in Thermo- Piezoelectricity and Magnetostriction (dependence of material constants on temperature, hysteresis, etc.)

44. CONCLUSION Research in smart materials will continue to grow in different directions. Development of smart sensors which are very sensitive to the mechanical states of host structures, and that of smart actuators which have high strain capacities, resistant to environmental effects and cost-effective are essential. Efficient power, signal processing and conditioning units for smart sensors and actuators are needed.