Mechanical design of microresonators : modeling and applications / Nicolae Lobontiu.

Format:

Book

Author/Creator:

Lobontiu, Nicolae.

Series:

McGraw-Hill nanoscience and technology series

Language:

English

Subjects (All):

Microelectromechanical systems--Design and construction.

Microelectromechanical systems.

Electric resonators--Design and construction.

Electric resonators.

Vibrators--Design and construction.

Vibrators.

Detectors--Design and construction.

Detectors.

Physical Description:

xiii, 342 pages : illustrations ; 24 cm.

Place of Publication:

New York : McGraw-Hill, [2006]

Summary:

EFFECTIVE SOLVE RELIABILITY PROBLEMS IN MICRORESONATORS

This informative text utilizes very efficient modeling and design methods combined with examples to shed light on the complex problem of reliability enhancement in microresonators.

The highly specialized data needed to put maximum reliability into minimum size: Algorithms enabling the modeling, analysis, synthesis, and optimized design of nano/micro resonators Basic mechanical principles of resonant sensors and vibratory gyroscopes Design and operation of various types of resonant mechanical microtransducers Microresonant mass detection

CONTENT THAT REFLECTS STATE-OF-THE-ART RESEARCH Design of Microresonators * Lumped-Parameter Design * Distributed-Parameter Design * Transduction Design * Single- and Multiple-Component Microresonators * Mass Detection by Microresonators

Contents:

Chapter 1 Design at Resonance of Mechanical Microsystems 1

1.2 Single-Degree-of-Freedom Systems 3

1.2.1 Free Response 3

1.2.2 Forced Response-the Resonance 5

1.2.3 Loss Mechanisms in Mechanical Microresonators 10

1.3 Multiple-Degree-of-Freedom Systems 22

1.3.1 Approximate Methods for Resonant Frequencies Calculation 22

1.3.2 Eigenvalues, Eigenvectors, and Mode Shapes 26

1.3.3 Lagrange's Equations 30

1.4 Mechanical-Electrical Analogies for Microsystems 33

1.5 Laplace Transforms, Transfer Functions, and Complex Impedances 36

Chapter 2 Basic Members: Lumped- and Distributed-Parameter Modeling and Design 45

2.2 Lumped-Parameter Modeling and Design 47

2.2.1 Lumped-Parameter Stiffnesses and Compliances 47

2.2.2 Lumped-Parameter Inertia Properties 55

2.2.3 Constant-Cross-Section Members 58

2.2.4 Variable-Cross-Section Members 71

2.3 Distributed-Parameter Modeling and Design 91

2.3.1 Line Micromembers 91

2.3.2 Circular Rings 98

2.3.3 Thin Plates and Membranes 101

Chapter 3 Microhinges and Microcantilevers: Lumped-Parameter Modeling and Design 105

3.2 Compliance Transforms by Reference Frame Translation 107

3.2.1 Compliances in Opposite-End Reference Frames 108

3.2.2 Compliances in Arbitrarily Translated Reference Frames 110

3.3 Micromembers Formed of Two Compliant Segments 111

3.3.1 Paddle Microcantilevers 115

3.3.2 Filleted Microcantilevers 126

3.3.3 Filleted Microhinges 134

3.3.4 Circularly Notched Microcantilevers 142

3.4 Hollow Microcantilevers 145

3.4.1 Rectangular Microcantilevers 146

3.4.2 Trapezoid Microcantilevers 148

3.5 Sandwiched Microcantilevers (Multimorphs) 150

3.5.1 Microcantilevers of Equal-Length Layers 150

3.5.2 Microcantilevers of Dissimilar-Length Layers 157

3.6 Resonant Microcantilever Arrays 162

Chapter 4 Microbridges: Lumped-Parameter Modeling and Design 167

4.2 Microbridges of Constant Cross Section 169

4.2.1 Bending Resonant Frequency 169

4.2.2 Torsion Resonant Frequency 175

4.3 Sandwiched Microbridges (Multimorphs) 178

4.3.1 Multimorph Microbridges of Equal-Length Layers 178

4.3.2 Multimorph Microbridges of Dissimilar-Length Layers 182

4.4 Microbridges of Variable Cross Section 185

4.4.1 Compliance Transform 185

4.4.2 Generic Formulation for Single-Profile (Basic Shape) Microbridges 186

4.4.3 Serially Compounded Microbridges 191

4.5 Resonator Microbridge Arrays 222

Chapter 5 Resonant Micromechanical Systems 227

5.2 Beam-Type Microresonators 227

5.2.1 Resonant Frequency Models for Microcantilevers 228

5.2.2 Resonant Frequency Models for Microbridges 237

5.2.3 Other Examples of Beam-Type Microresonators 245

5.3 Spring-Type Microresonators 258

5.4 Transduction in Microresonators 261

5.4.1 Electrostatic Transduction 262

5.4.2 Electromagnetic Transduction 266

5.4.3 Piezoelectric and Piezomagnetic Transduction 269

5.5 Resonant Microgyroscopes 271

5.6 Tuning Forks 279

5.7 Resonant Accelerometers 284

Chapter 6 Microcantilever and Microbridge Systems for Mass Detection 293

6.2 General Model of Point-Mass Addition Detection by Means of the Resonance Shift Method 299

6.3 Mass Detection by Means of Microcantilevers 303

6.3.1 Constant-Cross-Section Microcantilevers 304

6.3.2 Variable-Cross-Section Microcantilevers 315

6.4 Mass Detection by Means of Microbridges 319

6.4.1 Constant-Cross-Section Microbridges 320

6.4.2 Variable-Cross-Section Microbridges 325

6.5 Mass Detection by Means of Partially Compliant, Partial-Inertia Microdevices 327

6.5.1 Paddle Microcantilevers 328

6.5.2 Paddle Microbridges 331.

Notes:

Includes bibliographical references and index.

ISBN:

0071455388

OCLC:

60882019