Vibration Analysis of Functionally Graded Piezoelectric Actuators (eBook)

Dr. Pankaj Sharma received his bachelor's in Mechanical Engineering from the College of Technology & Engineering Udaipur (formerly C.T.A.E. Udaipur) in 2000. He completed his master's (Machine Design) from Indian Institute of Technology Varanasi (formerly IT-BHU) in 2002, and his PhD from Rajasthan Technical University (RTU) Kota in 2017. He has been engaged in teaching for over thirteen years, and has also published several articles in peer-reviewed journals and conference proceedings. Since 2013, he has been working as Assistant Professor at the Department of Mechanical Engineering, RTU Kota. His research mainly focuses on design, vibration, and functionally graded piezoelectric actuators. 

Preface 6
Acknowledgements 8
Contents 9
About the Author 11
1 An Overview 12
1.1 Introduction 12
1.2 Scope of the Book 13
2 Fundamentals of Piezoceramics 14
2.1 Introduction to Piezoelectric Materials and Piezoceramics 14
2.2 Conventional Axis Nomenclature for Piezoceramics 16
2.3 Constitutive Equations 17
2.3.1 Stress–Strain Relation 17
2.3.2 Strain–Displacement Relation 19
2.3.3 Maxwell Equation 19
2.3.4 Equations of Equilibrium 20
References 20
3 Basics of FGM and FGPM 21
3.1 Introduction of FGM 21
3.2 Material Gradient of FGM 22
3.2.1 Power Law Function (P-FGM) 22
3.2.2 Exponential Law Function (E-FGM) 23
3.2.3 Sigmoid Law Function (S-FGM) 23
3.3 Introduction of FGPM/Need of FGPM 25
3.4 Applications of FGPMs 26
3.4.1 Bimorph Actuator 26
3.4.2 Ultrasonic Transducer 26
References 26
4 Fundamentals of DQ Method 28
4.1 Introduction 28
4.2 Types of Differential Quadrature (DQ) Methods 29
4.2.1 Polynomial Differential Quadrature (PDQ) Method 29
4.2.2 Fourier Differential Quadrature (FDQ) Method 30
4.2.3 Generalized Differential Quadrature (GDQ) Method 31
4.3 Implementation of Boundary Conditions 32
4.3.1 100-Technique 33
4.3.2 Modified Weighting Coefficient Matrix Approach (MWCM) 33
4.3.3 Direct Substitution of the Boundary Conditions into Governing Equations (SBCGE) 33
4.3.4 General Approach 34
4.4 Summary 34
References 34
5 Vibration Analysis of FGPM Beam 36
5.1 Introduction 38
5.2 Governing Equations 38
5.3 Solution Methodology 41
5.3.1 Approximate Solution: GDQ Method 41
5.3.2 Exact Solution 44
5.4 Discussions 46
5.5 Summary 52
References 52
6 Vibration Analysis of FGPM Annular Plate 54
6.1 Introduction 54
6.2 Governing Equations 55
6.3 Solution Methodology 60
6.4 Discussions 64
6.4.1 Convergence Study 64
6.4.2 Validation Study 65
6.4.3 Parametric Study 66
6.5 Summary 73
References 79
7 Summary and Conclusions 80
7.1 For FGPM Beam 80
7.2 For FGPM Annular Plate 81
Reference 81