Mechanical Design of Microresonators Modeling and Applications

by Lobontiu, Nicolae

• ISBN13: 9780071455381
• ISBN10: 0071455388
• Edition: 1st
• Format: Hardcover
• Copyright: 2005-10-19
• Publisher: McGraw-Hill Education

Summary

Resonators act as a frequency reference or to filter specific frequencies. Used in such products as cell phones or computers, resonators will allow the user to take advantage of high bandwidths to process and send greater amounts of data. When used in medical devises such as MRIs they can detect microorganisms and biological molecules. The dilemma that Researcher face when building these micro resonators is that the smaller a resonator gets the less reliable it becomes. Based on his research at Cornell University, the author employs current modeling and fabrication technologies to bring a solution to this seemingly insurmountable problem one step closer. Microresonators are fundamental components in a host of MEMS applications beginning with the auto sector (safety systems, stability and rollover, occupant detection, tire pressure monitoring, biometric sensors for comfort programs), to the telecommunication industry (especially the radio-frequency domain with implementations such as switches, tunable capacitors and mechanical filters implemented in wavelength division multiplexing. Different research and development groups in

Author Biography

Nicolae O. Lobontiu, Ph.D., Ithaca, NY, is currently a research associate and instructor at the Sibley School of Mechanical and Aerospace Engineering, Cornell University where his has been extensive work in the areas of MEMS, compliant mechanisms, walking robots, morphing aero-structures, nastic structures. His has written two books and published over 24 papers and given 28 presentations on the subject of Nano/MEMS technology

Table of Contents

Preface	xi
Design at Resonance of Mechanical Microsystems	1	(44)
Introduction	1	(2)
Single-Degree-of-Freedom Systems	3	(19)
Free Response	3	(2)
Forced Response---the Resonance	5	(5)
Loss Mechanisms in Mechanical Microresonators	10	(12)
Multiple-Degree-of-Freedom Systems	22	(11)
Approximate Methods for Resonant Frequencies Calculation	22	(4)
Eigenvalues, Eigenvectors, and Mode Shapes	26	(4)
Lagrange's Equations	30	(3)
Mechanical-Electrical Analogies for Microsystems	33	(3)
Laplace Transforms, Transfer Functions, and Complex Impedances	36	(9)
References	42	(3)
Basic Members: Lumped- and Distributed-Parameter Modeling and Design	45	(60)
Introduction	45	(2)
Lumped-Parameter Modeling and Design	47	(44)
Lumped-Parameter Stiffnesses and Compliances	47	(8)
Lumped-Parameter Inertia Properties	55	(3)
Constant-Cross-Section Members	58	(13)
Variable-Cross-Section Members	71	(20)
Distributed-Parameter Modeling and Design	91	(14)
Line Micromembers	91	(7)
Circular Rings	98	(3)
Thin Plates and Membranes	101	(3)
References	104	(1)
Microhinges and Microcantilevers: Lumped-Parameter Modeling and Design	105	(62)
Introduction	105	(2)
Compliance Transforms by Reference Frame Translation	107	(4)
Compliances in Opposite-End Reference Frames	108	(2)
Compliances in Arbitrarily Translated Reference Frames	110	(1)
Micromembers Formed of Two Compliant Segments	111	(34)
Paddle Microcantilevers	115	(11)
Filleted Microcantilevers	126	(8)
Filleted Microhinges	134	(8)
Circularly Notched Microcantilevers	142	(3)
Hollow Microcantilevers	145	(5)
Rectangular Microcantilevers	146	(2)
Trapezoid Microcantilevers	148	(2)
Sandwiched Microcantilevers (Multimorphs)	150	(12)
Microcantilevers of Equal-Length Layers	150	(7)
Microcantilevers of Dissimilar-Length Layers	157	(5)
Resonant Microcantilever Arrays	162	(5)
References	164	(3)
Microbridges: Lumped-Parameter Modeling and Design	167	(60)
Introduction	167	(2)
Microbridges of Constant Cross Section	169	(9)
Bending Resonant Frequency	169	(6)
Torsion Resonant Frequency	175	(3)
Sandwiched Microbridges (Multimorphs)	178	(7)
Multimorph Microbridges of Equal-Length Layers	178	(4)
Multimorph Microbridges of Dissimilar-Length Layers	182	(3)
Microbridges of Variable Cross Section	185	(37)
Compliance Transform	185	(1)
Generic Formulation for Single-Profile (Basic Shape) Microbridges	186	(5)
Serially Compounded Microbridges	191	(31)
Resonator Microbridge Arrays	222	(5)
References	225	(2)
Resonant Micromechanical Systems	227	(66)
Introduction	227	(1)
Beam-Type Microresonators	227	(31)
Resonant Frequency Models for Microcantilevers	228	(9)
Resonant Frequency Models for Microbridges	237	(8)
Other Examples of Beam-Type Microresonators	245	(13)
Spring-Type Microresonators	258	(3)
Transduction in Microresonators	261	(10)
Electrostatic Transduction	262	(4)
Electromagnetic Transduction	266	(3)
Piezoelectric and Piezomagnetic Transduction	269	(2)
Resonant Microgyroscopes	271	(8)
Tuning Forks	279	(5)
Resonant Accelerometers	284	(9)
References	289	(4)
Microcantilever and Microbridge Systems for Mass Detection	293	(44)
Introduction	293	(6)
General Model of Point-Mass Addition Detection by Means of the Resonance Shift Method	299	(4)
Mass Detection by Means of Microcantilevers	303	(16)
Constant-Cross-Section Microcantilevers	304	(11)
Variable-Cross-Section Microcantilevers	315	(4)
Mass Detection by Means of Microbridges	319	(8)
Constant-Cross-Section Microbridges	320	(5)
Variable-Cross-Section Microbridges	325	(2)
Mass Detection by Means of Partially Compliant, Partial-Inertia Microdevices	327	(10)
Paddle Microcantilevers	328	(3)
Paddle Microbridges	331	(4)
References	335	(2)
Index	337