Mechatronics : dynamics of electromechanical and piezoelectric systems

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Title:

Personal Author:

Preumont, A.

Publication Information:

Dordrecht, The Netherland : Springer, 2006

ISBN:

9781402046957

Subject Term:

Mechatronics

Dynamics

Piezoelectricity

Electromechanical devices

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Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010103130	TJ163.12 P73 2006	Open Access Book	Book	Searching... Unknown
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This volume treats Lagrange equations for electromechanical systems, including piezoelectric transducers and selected applications. It is essentially an extension to piezoelectric systems of the work by Crandall et al.:"Dynamics of Mechanical and Electromechanical Systems", published in 1968. The first three chapters contain classical material based on this and other well known standard texts in the field. Some applications are new and include material not published in a monograph before.

Preface	p. xiii
1 Lagrangian dynamics of mechanical systems	p. 1
1.1 Introduction	p. 1
1.2 Kinetic state functions	p. 2
1.3 Generalized coordinates, kinematic constraints	p. 4
1.3.1 Virtual displacements	p. 7
1.4 The principle of virtual work	p. 8
1.5 D'Alembert's principle	p. 10
1.6 Hamilton's principle	p. 11
1.6.1 Lateral vibration of a beam	p. 14
1.7 Lagrange's equations	p. 17
1.7.1 Vibration of a linear, non-gyroscopic, discrete system	p. 19
1.7.2 Dissipation function	p. 19
1.7.3 Example 1: Pendulum with a sliding mass	p. 20
1.7.4 Example 2: Rotating pendulum	p. 22
1.7.5 Example 3: Rotating spring mass system	p. 23
1.7.6 Example 4: Gyroscopic effects	p. 24
1.8 Lagrange's equations with constraints	p. 27
1.9 Conservation laws	p. 29
1.9.1 Jacobi integral	p. 29
1.9.2 Ignorable coordinate	p. 30
1.9.3 Example: The spherical pendulum	p. 32
1.10 More on continuous systems	p. 32
1.10.1 Rayleigh-Ritz method	p. 32
1.10.2 General continuous system	p. 34
1.10.3 Green strain tensor	p. 34
1.10.4 Geometric strain energy due to prestress	p. 35
1.10.5 Lateral vibration of a beam with axial loads	p. 37
1.10.6 Example: Simply supported beam in compression	p. 38
1.11 References	p. 39
2 Dynamics of electrical networks	p. 41
2.1 Introduction	p. 41
2.2 Constitutive equations for circuit elements	p. 42
2.2.1 The Capacitor	p. 42
2.2.2 The Inductor	p. 43
2.2.3 Voltage and current sources	p. 45
2.3 Kirchhoff's laws	p. 46
2.4 Hamilton's principle for electrical networks	p. 47
2.4.1 Hamilton's principle, charge formulation	p. 48
2.4.2 Hamilton's principle, flux linkage formulation	p. 49
2.4.3 Discussion	p. 51
2.5 Lagrange's equations	p. 53
2.5.1 Lagrange's equations, charge formulation	p. 53
2.5.2 Lagrange's equations, flux linkage formulation	p. 54
2.5.3 Example 1	p. 54
2.5.4 Example 2	p. 57
2.6 References	p. 59
3 Electromechanical systems	p. 61
3.1 Introduction	p. 61
3.2 Constitutive relations for transducers	p. 61
3.2.1 Movable-plate capacitor	p. 62
3.2.2 Movable-core inductor	p. 65
3.2.3 Moving-coil transducer	p. 68
3.3 Hamilton's principle	p. 71
3.3.1 Displacement and charge formulation	p. 71
3.3.2 Displacement and flux linkage formulation	p. 72
3.4 Lagrange's equations	p. 73
3.4.1 Displacement and charge formulation	p. 73
3.4.2 Displacement and flux linkage formulation	p. 73
3.4.3 Dissipation function	p. 74
3.5 Examples	p. 76
3.5.1 Electromagnetic plunger	p. 76
3.5.2 Electromagnetic loudspeaker	p. 77
3.5.3 Capacitive microphone	p. 79
3.5.4 Proof-mass actuator	p. 82
3.5.5 Electrodynamic isolator	p. 84
3.5.6 The Sky-hook damper	p. 86
3.5.7 Geophone	p. 87
3.5.8 One-axis magnetic suspension	p. 89
3.6 General electromechanical transducer	p. 92
3.6.1 Constitutive equations	p. 92
3.6.2 Self-sensing	p. 93
3.7 References	p. 94
4 Piezoelectric systems	p. 95
4.1 Introduction	p. 95
4.2 Piezoelectric transducer	p. 96
4.3 Constitutive relations of a discrete transducer	p. 99
4.3.1 Interpretation of k[superscript 2]	p. 103
4.4 Structure with a discrete piezoelectric transducer	p. 105
4.4.1 Voltage source	p. 107
4.4.2 Current source	p. 107
4.4.3 Admittance of the piezoelectric transducer	p. 108
4.4.4 Prestressed transducer	p. 109
4.4.5 Active enhancement of the electromechanical coupling	p. 111
4.5 Multiple transducer systems	p. 113
4.6 General piezoelectric structure	p. 114
4.7 Piezoelectric material	p. 116
4.7.1 Constitutive relations	p. 116
4.7.2 Coenergy density function	p. 118
4.8 Hamilton's principle	p. 121
4.9 Rosen's piezoelectric transformer	p. 124
4.10 References	p. 130
5 Piezoelectric laminates	p. 131
5.1 Piezoelectric beam actuator	p. 131
5.1.1 Hamilton's principle	p. 131
5.1.2 Piezoelectric loads	p. 133
5.2 Laminar sensor	p. 136
5.2.1 Current and charge amplifiers	p. 136
5.2.2 Distributed sensor output	p. 136
5.2.3 Charge amplifier dynamics	p. 138
5.3 Spatial modal filters	p. 139
5.3.1 Modal actuator	p. 139
5.3.2 Modal sensor	p. 140
5.4 Active beam with collocated actuator-sensor	p. 141
5.4.1 Frequency response function	p. 142
5.4.2 Pole-zero pattern	p. 143
5.4.3 Modal truncation	p. 145
5.5 Piezoelectric laminate	p. 147
5.5.1 Two dimensional constitutive equations	p. 148
5.5.2 Kirchhoff theory	p. 148
5.5.3 Stiffness matrix of a multi-layer elastic laminate	p. 149
5.5.4 Multi-layer laminate with a piezoelectric layer	p. 151
5.5.5 Equivalent piezoelectric loads	p. 152
5.5.6 Sensor output	p. 153
5.5.7 Remarks	p. 154
5.6 References	p. 156
6 Active and passive damping with piezoelectric transducers	p. 159
6.1 Introduction	p. 159
6.2 Active strut, open-loop FRF	p. 161
6.3 Active damping via IFF	p. 165
6.3.1 Voltage control	p. 165
6.3.2 Modal coordinates	p. 167
6.3.3 Current control	p. 169
6.4 Admittance of the piezoelectric transducer	p. 170
6.5 Damping via resistive shunting	p. 172
6.5.1 Damping enhancement via negative capacitance shunting	p. 175
6.5.2 Generalized electromechanical coupling factor	p. 176
6.6 Inductive shunting	p. 176
6.6.1 Alternative formulation	p. 181
6.7 Decentralized control	p. 183
6.8 General piezoelectric structure	p. 184
6.9 Self-sensing	p. 185
6.9.1 Force sensing	p. 186
6.9.2 Displacement sensing	p. 187
6.9.3 Transfer function	p. 187
6.10 Other active damping strategies	p. 191
6.10.1 Lead control	p. 191
6.10.2 Positive Position Feedback (PPF)	p. 192
6.11 Remark	p. 195
6.12 References	p. 195
Bibliography	p. 199
Index	p. 205

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