CHAPTER 4 DESIGN AND ANALYSIS OF CANTILEVER BEAM ELECTROSTATIC ACTUATORS
|
|
- Marshall Black
- 5 years ago
- Views:
Transcription
1 61 CHAPTER 4 DESIGN AND ANALYSIS OF CANTILEVER BEAM ELECTROSTATIC ACTUATORS 4.1 INTRODUCTION The analysis of cantilever beams of small dimensions taking into the effect of fringing fields is studied and the parameters are estimated. Extracting the mechanical properties of MEMS devices has always been a challenge in terms of test time and test cost due to difficulties associated with accurate characterization of thin films. A technique for diagnosing the mechanical parameters of a cantilever-beam accelerometer using purely electrical test stimulus was given by Vishwanath Natarajan et al (2006). Governing equations of an electrostatically actuated clamped clamped and a cantilever narrow microbeam; and an expression for the distributed electrostatic force that simulates well the fringing field effects was derived by Romesh C. Batra (2006). The dependence of the critical tilting angle and pullin voltage on the sizes of structure was investigated by Jian-Gang Guo (2004). Patrick B. Chu et al (2005) showed that, in the ANSYS modeling design, short spring elements have insignificant contribution to the torsional resonant frequency but have more effect on the higher modes. A method to overcome pull-in effect of electrostatic actuators was developed for an electrostatic micromirror. The method was applied to both parallel- plate and torsional actuators and performance was studied by Jinghong Chen et al (2005).
2 62 Nitin Agarwal et al (2009) reported the variations in various design parameters such as material properties, geometrical features, and/or operating conditions on the performance of electrostatic MEMS devices. For rapid computational prototyping of such devices, it is required to accurately model the interaction of various physical fields such as mechanical and electrical. Typical MEMS structures consist of arrays of thin beams with cross sections in the order of microns ( m) and lengths in the order of ten to hundreds of microns. Sometimes, MEMS structural elements are plates. An example is a small rectangular silicon plate with sides in the order of mm and thickness of the order of microns that deforms when subjected to electric fields. Owing to its small size, significant forces and/or deformations can be obtained with the application of low voltages (Arik 2005). Computational analysis of deformation of MEMS parallel plate actuators due to electrostatic stresses has also been the main objective. MEMS cantilevers are the major components for micro sensors and actuators. Deformable structures are frequently encountered in MEMS. Micro Structures undergo deformations because of electrostatic forces caused by applied potentials. The cantilever beam is shown in Figure 4.1 is fixed in the x-y plane at z = 0. The beam in Figure 4.1 is fixed in the x-y plane at z = 0 and z = l. the beam is subjected to a uniform force (F) that is caused by acceleration. The beams have length (l), width (w), and height (h). The force on the beam is determined by F = ma (4.1) where m is the mass of the beam and a is the acceleration.
3 63 x y Figure 4.1 Structure of Cantilever beam with Dimensions Figure 4.2 shows the initial and deformed configuration of the parallel plate actuator. The upper plate is fixed at the left end and free at the other end. The lower plate is fixed and hence cannot deform. The upper plate is held at a voltage V with respect to the fixed plate. Positive charges are induced on the upper plate and negative charges on the fixed plate. This results in an attractive force between the two plates. Hence the upper plate bends downwards due to electrostatic stresses. V Figure 4.2 Schematic of deformed Cantilever beam As seen in Figure. 4.2, when a voltage is applied, static charges are induced on the surfaces of the plates. Since the upper plate is held at a positive voltage, the charges induced on the upper plate will be positive so as to keep the voltage at any point on the upper plate equal to applied voltage V (conductor surface is an equipotential surface).the fixed plate is held at zero potential. Now, the positive charges on the upper plate will result in positive potentials at the surface of the fixed plate. Hence, negative charges will be
4 64 induced on the surface of the fixed plate so as to nullify the positive potentials due to positive charges on the upper plate and maintain any point on the fixed plate at zero potential. On the whole, the effect of applying an external voltage to the system is to induce positive charges on the upper plate and negative charges on the fixed plate. The distribution of these charges depends on applied voltage and geometry of the system. The geometry of the system is the dimensions of the plate, distance between plates etc., and deflection of the upper plate from current position to a new position. The opposite polarity charges on the plates gives rise to attractive forces between the plates. The lower plane being fixed cannot deform. The upper plate is fixed at left end and free at the other end. It deflects according to mechanical properties of the material used for plates. 4.2 ELECTROSTATIC ANALYSIS When the upper plate deflects the geometry of the plate changes and the charge distribution changes consequently. Thus, the forces also change and therefore the plate cannot remain at the current (deflected) position. The new force will have a corresponding deflection relative to initial configuration and the plate will make a transition to this position. This position is not stable as well. For the same reasons as before the plate again deflects to a new position and this process continues and can have two possible end states. 1. The successive changes in deflection become smaller and smaller and further deflection become negligible. This state as is referred to as equilibrium position. 2. The deflection becomes large enough so that the upper plate touches the fixed plate. This state is referred as pull-in.
5 65 The pull-in voltages for cantilever beam is given by V pi Ew d 4 l o 3 (4.2) 4.3 NATURAL FREQUENCY ANALYSIS If the MEMS variable capacitor operating frequency is the same as the mechanical resonance frequency, then the variable capacitor is capable of introducing unwanted distortion at that frequency. The first mechanical resonance frequency of a cantilever beam for bending oscillations is given in Equation (4.3). An increase in elastic modulus or the moment of inertia will tend to increase the mechanical resonance frequency. Increasing the beam width or the beam height will increase the moment of inertia. Increasing the beam mass or length will decrease the frequency. f R E I 4 l (4.3) In the above equations µ is the mass per unit length of the beam. For typical MEMS variable capacitor designs, the mechanical resonant frequencies are normally at khz range. Since the operating frequencies are at least times the mechanical bandwidth, these devices are unlikely to produce a significant amount of harmonic content. As the voltage is increased, the force increase, which decreases the air gap, further increases the force. In the case of the cantilever beam, Figure 4.1, the force causes a maximum deflection at the tip of the cantilever. For the cantilever beam of Figure 4.1 the maximum deflection is
6 66 y max Fl 8El 3 (4.4) where E is the effective modulus. This deflection occurs at Z l. For narrow beams w 5h Young s modulus. For wide beams 2 the plate modulus E 1 v, the effective modulus E is equal to w 5h, where v is Poisson s ratio., the effective modulus becomes 4.4 RESULTS AND DISCUSSION Finite Element Analysis with ROM has been completed successfully to understand the physical nature of the micro cantilever beam. Since most of the MEMS devices do not have the same characteristics as they were designed and predicted and always needed a trail and error method using simulations with the support of software tools to get the actual characteristics. Microbeams of different lengths, widths and height are simulated thoroughly to understand the change in the characteristics of the beams as with device geometry. The simulated output is shown in Figure 4.3. Figure 4.3 Simulated Output of cantilever beam
7 67 As described in the previous chapters, the goal of the reduced-order modeling is to generate a fast and accurate description of the coupled-physics systems to characterize their static or dynamic responses. Reduced Order Modeling (ROM) substantially reduces time since the dynamic behavior of most structures can be accurately represented by a few eigen modes. With advantages of reduced order modeling microcantilevers beams are simulated using ANSYS finite element software. First the capacitance between the beams is extracted and results for maximum deflection and pull-in voltages are obtained through non linear modal analysis. The results obtained for the capacitance with the dimension of beam length of 80 m, width of 15 m, height of 4 m is shown in the Figure 4.4. Then maximum deflection for a load step increase in the voltage and the pull-in voltages are also calculated. A detailed comparison is made for different dimensions of length and width of the beams. Since only simulations help the designers to predict accurately the characteristics of the beams parameters of the beam. The comparisons for pull-in voltage for various widths of the beams are shown in the Figure 4.5. Figure 4.4 Ansys output of cantilever beam for capacitance
8 68 pull in voltages in volts Length in m 15 m width of Beam 10 m width of Beam 5 m width of Beam 2 m width of Beam 1 m width of Beam Figure 4.5 Variation of pull-in voltage in cantilever beam for different beam widths It is seen form the Figure 4.5, there is no drastic deviation in the pull-in voltages for the width b=15,10,5 m of the micro beams. But the pull-in voltage drastically increases for b=2 m and b=1 m. A non linear modal analysis that is used to determine the vibration characteristics, such as natural frequencies and mode shapes of the cantilever beams. It was also a starting point for the harmonic analyses. The natural frequencies and mode shapes are important parameters in the design of a structure for dynamic loading conditions (Arik et al 2005). The best way of determining the vibrational extracting modes is determining the specified frequency at which the devices will display range amplitudes of vibration. A solution method for efficiently solving coupled-field problems involving flexible structures is ROM. This ROM method is based on a modal representation of the structural response. The deformed structural domain is described by a factored sum of the mode shapes (eigenvectors). The resulting ROM is essentially an analytical expression for the response of a system to
9 69 any arbitrary excitation. This methodology has been implemented for coupled electrostatic-structural analysis and is applicable to micro-electromechanical systems (MEMS). The solver tool enables essential speed up for two reasons: A few eigen modes accurately represents the dynamic behavior of most structures. This is particularly true for MEMS. Modal representations of electrostatic-structural domains are very efficient because just one equation per mode and one equation per conductor are necessary to describe the coupled domain system entirely. This modal method can be applied to nonlinear systems. Geometrical nonlinearities, such as stress stiffening, can be taken into account if the modal stiffness is computed from the second derivatives of the strain energy with respect to modal coordinates. Capacitance stroke functions provide nonlinear coupling between Eigen modes and the electrical quantities if stroke is understood to be modal amplitude. The process involves the following distinct steps and is shown as a flow chart Figure 4.6. The model preparation step creates the necessary finite element model for the generation pass. The generation pass executes a modal analysis of the structure. It also executes an optional static analysis to determine the deformation state of the structure under operating conditions. Using this information, the generation pass then selects the modes and performs computations to create a reduced order model. The use pass uses the reduced order model in an analysis. The reduced order model is stored in a ROM database and a polynomial coefficients file, and utilized by a ROM element.
10 70 The expansion pass extracts the full DOF set solution and computes stresses on the original structure created in the model preparation phase. A VHDL-AMS mathematical model of the ROM structure may be exported for use in electrical design automation (EDA) system simulators. The ROM method is applicable to 2-D and 3-D models. The generation pass requires multiple finite element solutions of the structural and electrostatic domains, where the structure is displaced over its operating range. Model Preparation Generation pass ROM Use pass Include to system environment Expansion pass Use pass Figure 4.6 Flowchart of Reduced Order Modeling scheme To support both morphing and remesh operations for the multiple finite element solutions, PLANE121, SOLID122, or SOLID123 elements must model the electrostatic domain. INFIN110 or INFIN111 elements can model the open boundary of electrostatic fields. 2-D or 3-D structural or shell elements can model the structural domain. Care was taken while preparing the model of the electrostatic domain to ensure that morphing or remeshing will succeed over the deflection range of the structure. The ROM characterization requires that the device operate primarily in one dominant direction (X, Y, or
11 71 Z in the global Cartesian system). This includes not only the transversal shift of most rigid bodies (inertial sensors), but also cantilever and plate bending (RF filters, pressure gauges, ultrasonic transducers) and swivel motions (micromirrors). Material properties must be elastic and temperature independent. Stress stiffening and prestress effects are available. First two modes are extracted, Figures 4.7 to 4.9 show typical results of the analysis for the first and second modes for different dimensions. Eigen values Figure 4.7 Variation of the first two modes of cantilever beam with beam length 100 m The modal outputs for the first two modes are shown in the Figure 4.7. It is observed from the Figure 4.7, a large variation is observed for the second mode and almost the same output is maintained for first mode even for variation in the width of the beams.
12 E E-06 Eigen values m o des 2.00E E E-06 MODE 1 MODE E E width of the beams( m) Figure 4.8 Variation of the first two modes of cantilever beam with beam length 80 m From the Figure 4.8, curves are similar to l =100 m. So we can say that there is no change in the mode shape for change in the length of the beams. 3.50E-06 Eigen values m odes 3.00E E E E E-06 MODE 1 MODE E E Length of the beams( m) Figure 4.9 Variation of the first two modes of cantilever beam with beam width 15 m
13 73 It was found that for breadth of 15 m, 10 m and 5 m there is no change in the mode shape. A change was observed for breadth of 2 m. This shape change may be due to small dimension and need to be analysed. 3.00E E-15 EIGEN m VALUES odes 2.00E E E E-16 MODE 1 MODE E Length of the beams( m) Figure 4.10 Variation of the first two modes of cantilever beam with beam width 1 m When compared with fixed beams, cantilever beam s first mode changes are not prominent as shown in the Figure 4.9.but for mode 2; it is similar to that of clamped beam. It is found that both the modes of peaks at l = 95 µm, b = 15 µm and h = 2 µm. It was also observed that for mode 2, the changes at the maximum value are prominent. 2.00E E+07 natural frequencies in MHz 1.60E E E E E E E E E length in micrometers w idth 15 mm m w idth 10 mm m w idth 55mm m w idth 22mm m w idth 11mm m Figure 4.11 Variation of natural frequencies with the length and width of the cantilever beam
14 74 The variation in the natural frequency obtained is given in the Figure It is seen from the Figure 4.11 a large variation is seen for width of beams 2 m and 1 m. Table 4.1 Effect on Natural frequencies and Eigen values in cantilever beam for beam height 2 µm Beam Width ( m) Beam Length m) Natural Frequencies (MHz) Eigen values Mode 1 Mode E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-06
15 75 The results show that the fundamental frequency increases with decreasing beam length. It is worth noting that the fundamental frequency increases dramatically below the 100 m beam length mark. As a result, careful design is needed for small structures of small length and comparison of various parameters of cantilever beam is shown in Table 4.2. Table 4.2 Comparison of various parameters in cantilever beam for Length m) beam height 2 µm Breadth m) Lower and upper bound displacement for 1 and 2 Modes ( m) Pull-in Voltage (V) Mode 1 Mode 2 Minimum Maximum ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
16 76 Table 4.2 (Continued) Length m) Breadth m) Lower and upper bound displacement for 1 and 2 Modes ( m) Pull-in Voltage (V) Mode 1 Mode 2 Minimum Maximum ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± CONCLUSION The performance of cantilever beam was estimated for various dimensions of the beams. The effect of fringing field was taken in to account and analysis has been carried out using reduced order modeling. It was found that pull-in voltage is reduced compared to clamped beams. The mode shapes were also obtained to analyze and estimate the performance of the beams. The maximum deflection for the cantilever beam structure has been determined as m.
CHAPTER 5 FIXED GUIDED BEAM ANALYSIS
77 CHAPTER 5 FIXED GUIDED BEAM ANALYSIS 5.1 INTRODUCTION Fixed guided clamped and cantilever beams have been designed and analyzed using ANSYS and their performance were calculated. Maximum deflection
More informationFinite Element Analysis of Piezoelectric Cantilever
Finite Element Analysis of Piezoelectric Cantilever Nitin N More Department of Mechanical Engineering K.L.E S College of Engineering and Technology, Belgaum, Karnataka, India. Abstract- Energy (or power)
More informationJOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 13, NO. 5, OCTOBER Sudipto K. De and N. R. Aluru, Member, IEEE, Associate Member, ASME
JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 13, NO. 5, OCTOBER 2004 737 Full-Lagrangian Schemes for Dynamic Analysis of Electrostatic MEMS Sudipto K. De N. R. Aluru, Member, IEEE, Associate Member,
More informationMicrostructure cantilever beam for current measurement
264 South African Journal of Science 105 July/August 2009 Research Articles Microstructure cantilever beam for current measurement HAB Mustafa and MTE Khan* Most microelectromechanical systems (MEMS) sensors
More informationAn Accurate Model for Pull-in Voltage of Circular Diaphragm Capacitive Micromachined Ultrasonic Transducers (CMUT)
An Accurate Model for Pull-in Voltage of Circular Diaphragm Capacitive Micromachined Ultrasonic Transducers (CMUT) Mosaddequr Rahman, Sazzadur Chowdhury Department of Electrical and Computer Engineering
More informationStructural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian
Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian ahmadian@iust.ac.ir Dynamic Response of MDOF Systems: Mode-Superposition Method Mode-Superposition Method:
More informationSensors & Transducers 2016 by IFSA Publishing, S. L.
Sensors & Transducers, Vol. 96, Issue, January 206, pp. 52-56 Sensors & Transducers 206 by IFSA Publishing, S. L. http://www.sensorsportal.com Collapse Mode Characteristics of Parallel Plate Ultrasonic
More informationNatural vibration frequency of classic MEMS structures
Natural vibration frequency of classic MEMS structures Zacarias E. Fabrim PGCIMAT, UFRGS, Porto Alegre, RS, Brazil Wang Chong, Manoel Martín Pérez Reimbold DeTec, UNIJUI, Ijuí, RS, Brazil Abstract This
More informationDesign and Analysis of Various Microcantilever Shapes for MEMS Based Sensing
ScieTech 014 Journal of Physics: Conference Series 495 (014) 01045 doi:10.1088/174-6596/495/1/01045 Design and Analysis of Various Microcantilever Shapes for MEMS Based Sensing H. F. Hawari, Y. Wahab,
More informationOutline. 4 Mechanical Sensors Introduction General Mechanical properties Piezoresistivity Piezoresistive Sensors Capacitive sensors Applications
Sensor devices Outline 4 Mechanical Sensors Introduction General Mechanical properties Piezoresistivity Piezoresistive Sensors Capacitive sensors Applications Introduction Two Major classes of mechanical
More informationEE C245 ME C218 Introduction to MEMS Design Fall 2007
EE C245 ME C218 Introduction to MEMS Design Fall 2007 Prof. Clark T.-C. Nguyen Dept. of Electrical Engineering & Computer Sciences University of California at Berkeley Berkeley, CA 94720 Lecture 17: Energy
More informationLecture 20. Measuring Pressure and Temperature (Chapter 9) Measuring Pressure Measuring Temperature MECH 373. Instrumentation and Measurements
MECH 373 Instrumentation and Measurements Lecture 20 Measuring Pressure and Temperature (Chapter 9) Measuring Pressure Measuring Temperature 1 Measuring Acceleration and Vibration Accelerometers using
More informationExperimental Modal Analysis of a Flat Plate Subjected To Vibration
American Journal of Engineering Research (AJER) 2016 American Journal of Engineering Research (AJER) e-issn: 2320-0847 p-issn : 2320-0936 Volume-5, Issue-6, pp-30-37 www.ajer.org Research Paper Open Access
More informationActive elastomer components based on dielectric elastomers
Gummi Fasern Kunststoffe, 68, No. 6, 2015, pp. 412 415 Active elastomer components based on dielectric elastomers W. Kaal and S. Herold Fraunhofer Institute for Structural Durability and System Reliability
More informationLecture 19. Measurement of Solid-Mechanical Quantities (Chapter 8) Measuring Strain Measuring Displacement Measuring Linear Velocity
MECH 373 Instrumentation and Measurements Lecture 19 Measurement of Solid-Mechanical Quantities (Chapter 8) Measuring Strain Measuring Displacement Measuring Linear Velocity Measuring Accepleration and
More informationANALYSIS AND NUMERICAL MODELLING OF CERAMIC PIEZOELECTRIC BEAM BEHAVIOR UNDER THE EFFECT OF EXTERNAL SOLICITATIONS
Third International Conference on Energy, Materials, Applied Energetics and Pollution. ICEMAEP016, October 30-31, 016, Constantine,Algeria. ANALYSIS AND NUMERICAL MODELLING OF CERAMIC PIEZOELECTRIC BEAM
More informationDesign and Analysis of dual Axis MEMS Capacitive Accelerometer
International Journal of Electronics Engineering Research. ISSN 0975-6450 Volume 9, Number 5 (2017) pp. 779-790 Research India Publications http://www.ripublication.com Design and Analysis of dual Axis
More informationDesign And Analysis of Microcantilevers With Various Shapes Using COMSOL Multiphysics Software
Design And Analysis of Microcantilevers With Various Shapes Using COMSOL Multiphysics Software V. Mounika Reddy 1, G.V.Sunil Kumar 2 1,2 Department of Electronics and Instrumentation Engineering, Sree
More informationIntroduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams.
Outline of Continuous Systems. Introduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams. Vibrations of Flexible Strings. Torsional Vibration of Rods. Bernoulli-Euler Beams.
More informationMEMS PARALLEL PLATE ACTUATORS: PULL-IN, PULL-OUT AND OTHER TRANSITIONS
MEMS PARALLEL PLATE ACTUATORS: PULL-IN, PULL-OUT AND OTHER TRANSITIONS Subrahmanyam Gorthi, Atanu Mohanty and Anindya Chatterjee* Supercomputer Education and Research Centre, Indian Institute of Science,
More informationThickness Optimization of a Piezoelectric Converter for Energy Harvesting
Excerpt from the Proceedings of the COMSOL Conference 29 Milan Thickness Optimization of a Piezoelectric Converter for Energy Harvesting M. Guizzetti* 1, V. Ferrari 1, D. Marioli 1 and T. Zawada 2 1 Dept.
More informationChapter 5. Vibration Analysis. Workbench - Mechanical Introduction ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved.
Workbench - Mechanical Introduction 12.0 Chapter 5 Vibration Analysis 5-1 Chapter Overview In this chapter, performing free vibration analyses in Simulation will be covered. In Simulation, performing a
More information10 Measurement of Acceleration, Vibration and Shock Transducers
Chapter 10: Acceleration, Vibration and Shock Measurement Dr. Lufti Al-Sharif (Revision 1.0, 25/5/2008) 1. Introduction This chapter examines the measurement of acceleration, vibration and shock. It starts
More informationExample 37 - Analytical Beam
Example 37 - Analytical Beam Summary This example deals with the use of RADIOSS linear and nonlinear solvers. A beam submitted to a concentrated load on one extremity and fixed on the other hand is studied.
More informationTable of Contents. Preface... 13
Table of Contents Preface... 13 Chapter 1. Vibrations of Continuous Elastic Solid Media... 17 1.1. Objective of the chapter... 17 1.2. Equations of motion and boundary conditions of continuous media...
More informationThe New Boundary Condition Effect on The Free Vibration Analysis of Micro-beams Based on The Modified Couple Stress Theory
International Research Journal of Applied and Basic Sciences 2015 Available online at www.irjabs.com ISSN 2251-838X / Vol, 9 (3): 274-279 Science Explorer Publications The New Boundary Condition Effect
More informationAnalytical Design of Micro Electro Mechanical Systems (MEMS) based Piezoelectric Accelerometer for high g acceleration
Analytical Design of Micro Electro Mechanical Systems (MEMS) based Piezoelectric Accelerometer for high g acceleration Arti Arora 1, Himanshu Monga 2, Anil Arora 3 Baddi University of Emerging Science
More informationKurukshetra University INDIA
American International Journal of Research in Science, Technology, Engineering & Mathematics Available online at http://www.iasir.net ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629
More informationPresented By: EAS 6939 Aerospace Structural Composites
A Beam Theory for Laminated Composites and Application to Torsion Problems Dr. BhavaniV. Sankar Presented By: Sameer Luthra EAS 6939 Aerospace Structural Composites 1 Introduction Composite beams have
More informationHow Does a Microcantilever Work?
How Does a Cantilever Work? Participant Guide Description and Estimated Time to Complete The microcantilever is a widely used component in microsystems devices or microelectromechanical systems (MEMS).
More informationIntroduction to Microeletromechanical Systems (MEMS) Lecture 9 Topics. MEMS Overview
Introduction to Microeletromechanical Systems (MEMS) Lecture 9 Topics MicroOptoElectroMechanical Systems (MOEMS) Grating Light Valves Corner Cube Reflector (CCR) MEMS Light Modulator Optical Switch Micromirrors
More informationGENERAL CONTACT AND HYSTERESIS ANALYSIS OF MULTI-DIELECTRIC MEMS DEVICES UNDER THERMAL AND ELECTROSTATIC ACTUATION
GENERAL CONTACT AND HYSTERESIS ANALYSIS OF MULTI-DIELECTRIC MEMS DEVICES UNDER THERMAL AND ELECTROSTATIC ACTUATION Yie He, James Marchetti, Carlos Gallegos IntelliSense Corporation 36 Jonspin Road Wilmington,
More informationDynamic Capacitance Extraction of A Triaxial Capacitive Accelerometer
Dynamic Capacitance Extraction of A Triaxial Capacitive Accelerometer Zhenchuan Yang, Gang LI, Yilong Hao, Guoying Wu Institute of Microelectronics, Peking University, Beijing, 100871 China Abstract Capacitive
More informationEE C245 ME C218 Introduction to MEMS Design
EE C245 ME C218 Introduction to MEMS Design Fall 2007 Prof. Clark T.-C. Nguyen Dept. of Electrical Engineering & Computer Sciences University of California at Berkeley Berkeley, CA 94720 Lecture 16: Energy
More informationNonlinear Dynamic Analysis of Cracked Micro-Beams Below and at the Onset of Dynamic Pull-In Instability
Journal of Solid Mechanics Vol., No. (8) pp. -3 Nonlinear Dynamic Analysis of Cracked Micro-Beams Below and at the Onset of Dynamic Pull-In Instability R. Hassannejad *, Sh. Amiri Jahed Department of Mechanical
More informationA Comparison of Pull-in Voltage Calculation Methods for MEMS-Based Electrostatic Actuator Design
A Comparison of Pull-in Voltage Calculation Methods for MEMS-Based Electrostatic Actuator Design Abstract Sazzadur Chowdhury, M. Ahmadi, W. C. Miller Department of Electrical and Computer Engineering University
More informationModeling and simulation of multiport RF switch
Journal of Physics: Conference Series Modeling and simulation of multiport RF switch To cite this article: J Vijay et al 006 J. Phys.: Conf. Ser. 4 715 View the article online for updates and enhancements.
More informationDesign and Simulation of Micro-cantilever
Design and Simulation of Micro-cantilever Suresh Rijal 1, C.K.Thadani 2, C.K.Kurve 3,Shrikant Chamlate 4 1 Electronics Engg.Dept.,KITS,Ramtek, 2 Electronics and Comn.Engg.Dept.,KITS,Ramtek, 3 Electronics
More informationFoundations of MEMS. Chang Liu. McCormick School of Engineering and Applied Science Northwestern University. International Edition Contributions by
Foundations of MEMS Second Edition Chang Liu McCormick School of Engineering and Applied Science Northwestern University International Edition Contributions by Vaishali B. Mungurwadi B. V. Bhoomaraddi
More informationMidterm 2 PROBLEM POINTS MAX
Midterm 2 PROBLEM POINTS MAX 1 30 2 24 3 15 4 45 5 36 1 Personally, I liked the University; they gave us money and facilities, we didn't have to produce anything. You've never been out of college. You
More informationDesign of a MEMS Capacitive Comb-drive Accelerometer
Design of a MEMS Capacitive Comb-drive Accelerometer Tolga Kaya* 1, Behrouz Shiari 2, Kevin Petsch 1 and David Yates 2 1 Central Michigan University, 2 University of Michigan * kaya2t@cmich.edu Abstract:
More informationSENSORS and TRANSDUCERS
SENSORS and TRANSDUCERS Tadeusz Stepinski, Signaler och system The Mechanical Energy Domain Physics Surface acoustic waves Silicon microresonators Variable resistance sensors Piezoelectric sensors Capacitive
More information874. The squeeze film effect on micro-electromechanical resonators
874. The squeeze film effect on micro-electromechanical resonators Shih-Chieh Sun 1, Chi-Wei Chung, Chao-Ming Hsu 3, Jao-Hwa Kuang 4 1,, 4 Department of Mechanical and Electromechanical Engineering National
More information1 Force Sensing. Lecture Notes. 1.1 Load Cell. 1.2 Stress and Strain
Lecture Notes 1 Force Sensing 1.1 Load Cell A Load Cell is a structure which supports the load and deflects a known amount in response to applied forces and torques. The deflections are measured to characterize
More informationSTRAIN GAUGES YEDITEPE UNIVERSITY DEPARTMENT OF MECHANICAL ENGINEERING
STRAIN GAUGES YEDITEPE UNIVERSITY DEPARTMENT OF MECHANICAL ENGINEERING 1 YEDITEPE UNIVERSITY ENGINEERING FACULTY MECHANICAL ENGINEERING LABORATORY 1. Objective: Strain Gauges Know how the change in resistance
More information202 Index. failure, 26 field equation, 122 force, 1
Index acceleration, 12, 161 admissible function, 155 admissible stress, 32 Airy's stress function, 122, 124 d'alembert's principle, 165, 167, 177 amplitude, 171 analogy, 76 anisotropic material, 20 aperiodic
More informationFinite Element Analysis Lecture 1. Dr./ Ahmed Nagib
Finite Element Analysis Lecture 1 Dr./ Ahmed Nagib April 30, 2016 Research and Development Mathematical Model Mathematical Model Mathematical Model Finite Element Analysis The linear equation of motion
More informationFinite Element Static, Vibration and Impact-Contact Analysis of Micromechanical Systems
Finite Element Static, Vibration and Impact-Contact Analysis of Micromechanical Systems Alexey I. Borovkov Eugeny V. Pereyaslavets Igor A. Artamonov Computational Mechanics Laboratory, St.Petersburg State
More informationMagneto-Mechanical Modeling and Simulation of MEMS Sensors Based on Electroactive Polymers
Magneto-Mechanical Modeling and Simulation of MEMS Sensors Based on Electroactive Polymers F.J.O. RODRIGUES, L.M. GONÇALVES, J.H. CORREIA, P.M. MENDES University of Minho, Dept. Industrial Electronics,
More informationElectric Potential Energy Chapter 16
Electric Potential Energy Chapter 16 Electric Energy and Capacitance Sections: 1, 2, 4, 6, 7, 8, 9 The electrostatic force is a conservative force It is possible to define an electrical potential energy
More informationIntroduction to structural dynamics
Introduction to structural dynamics p n m n u n p n-1 p 3... m n-1 m 3... u n-1 u 3 k 1 c 1 u 1 u 2 k 2 m p 1 1 c 2 m2 p 2 k n c n m n u n p n m 2 p 2 u 2 m 1 p 1 u 1 Static vs dynamic analysis Static
More informationb. The displacement of the mass due to a constant acceleration a is x=
EE147/247A Final, Fall 2013 Page 1 /35 2 /55 NO CALCULATORS, CELL PHONES, or other electronics allowed. Show your work, and put final answers in the boxes provided. Use proper units in all answers. 1.
More informationCOPYRIGHTED MATERIAL. Index
Index A Admissible function, 163 Amplification factor, 36 Amplitude, 1, 22 Amplitude-modulated carrier, 630 Amplitude ratio, 36 Antinodes, 612 Approximate analytical methods, 647 Assumed modes method,
More informationINF5490 RF MEMS. LN03: Modeling, design and analysis. Spring 2008, Oddvar Søråsen Department of Informatics, UoO
INF5490 RF MEMS LN03: Modeling, design and analysis Spring 2008, Oddvar Søråsen Department of Informatics, UoO 1 Today s lecture MEMS functional operation Transducer principles Sensor principles Methods
More informationCharacterization of MEMS Devices
MEMS: Characterization Characterization of MEMS Devices Prasanna S. Gandhi Assistant Professor, Department of Mechanical Engineering, Indian Institute of Technology, Bombay, Recap Characterization of MEMS
More informationEE C245 ME C218 Introduction to MEMS Design
EE C245 ME C218 Introduction to MEMS Design Fall 2007 Prof. Clark T.-C. Nguyen Dept. of Electrical Engineering & Computer Sciences University of California at Berkeley Berkeley, CA 94720 Lecture 22: Capacitive
More informationExample 3.7 Consider the undeformed configuration of a solid as shown in Figure 3.60.
162 3. The linear 3-D elasticity mathematical model The 3-D elasticity model is of great importance, since it is our highest order hierarchical model assuming linear elastic behavior. Therefore, it provides
More informationEFFECT OF TAPER AND TWISTED BLADE IN STEAM TURBINES
EFFECT OF TAPER AND TWISTED BLADE IN STEAM TURBINES Tulsidas.D 1, M.Shantharaja 2 1 Department of Mechanical Engineering, Acharya Institute of Technology, Bangalore-560107, (India) 2 Department of Mechanical
More informationThe Influence of Couple Stress Components and Electrostatic Actuation on Free Vibration Characteristics of Thin Micro-Plates
MATEC Web of Conferences 5, 0008 (06) DOI: 0.05/ matecconf/0650008 MIMT 06 The Influence of Couple Stress Components and Electrostatic Actuation on Free Vibration Characteristics of Thin Micro-Plates Amir
More informationDr.Vinod Hosur, Professor, Civil Engg.Dept., Gogte Institute of Technology, Belgaum
STRUCTURAL DYNAMICS Dr.Vinod Hosur, Professor, Civil Engg.Dept., Gogte Institute of Technology, Belgaum Overview of Structural Dynamics Structure Members, joints, strength, stiffness, ductility Structure
More informationInternational Journal of Scientific & Engineering Research, Volume 5, Issue 7, July-2014 ISSN
ISSN 2229-5518 692 In literature, finite element formulation uses beam element or plate element for structural modelling which has a limitation on transverse displacement. Atkinson and Manrique [1] studied
More information7.Piezoelectric, Accelerometer and Laser Sensors
7.Piezoelectric, Accelerometer and Laser Sensors 7.1 Piezoelectric sensors: (Silva p.253) Piezoelectric materials such as lead-zirconate-titanate (PZT) can generate electrical charge and potential difference
More informationD && 9.0 DYNAMIC ANALYSIS
9.0 DYNAMIC ANALYSIS Introduction When a structure has a loading which varies with time, it is reasonable to assume its response will also vary with time. In such cases, a dynamic analysis may have to
More informationMeasurement Techniques for Engineers. Motion and Vibration Measurement
Measurement Techniques for Engineers Motion and Vibration Measurement Introduction Quantities that may need to be measured are velocity, acceleration and vibration amplitude Quantities useful in predicting
More informationEE 5344 Introduction to MEMS CHAPTER 6 Mechanical Sensors. 1. Position Displacement x, θ 2. Velocity, speed Kinematic
I. Mechanical Measurands: 1. Classification of main types: EE 5344 Introduction MEMS CHAPTER 6 Mechanical Sensors 1. Position Displacement x, θ. Velocity, speed Kinematic dx dθ v =, = ω 3. Acceleration
More informationDynamics of structures
Dynamics of structures 2.Vibrations: single degree of freedom system Arnaud Deraemaeker (aderaema@ulb.ac.be) 1 Outline of the chapter *One degree of freedom systems in real life Hypothesis Examples *Response
More informationA New Design and Optimization of Capacitive MEMS Accelerometer
A New Design and Optimization of Capacitive MEMS Accelerometer M. Sarvghad Moghadam a,*, H. Arefi b, Kh. Mafinezhad a,c a Sadjad institute of higher education, Emamat Avenue, Mashhad 9188148848, Iran b
More informationA new cantilever beam-rigid-body MEMS gyroscope: mathematical model and linear dynamics
Proceedings of the International Conference on Mechanical Engineering and Mechatronics Toronto, Ontario, Canada, August 8-10 2013 Paper No. XXX (The number assigned by the OpenConf System) A new cantilever
More informationSENSOR DEVICES MECHANICAL SENSORS
SENSOR DEVICES MECHANICAL SENSORS OUTLINE 4 Mechanical Sensors Introduction General mechanical properties Piezoresistivity Piezoresistive sensors Capacitive sensors Applications INTRODUCTION MECHANICAL
More informationEE C247B / ME C218 INTRODUCTION TO MEMS DESIGN SPRING 2014 C. Nguyen PROBLEM SET #4
Issued: Wednesday, Mar. 5, 2014 PROBLEM SET #4 Due (at 9 a.m.): Tuesday Mar. 18, 2014, in the EE C247B HW box near 125 Cory. 1. Suppose you would like to fabricate the suspended cross beam structure below
More informationModal Analysis: What it is and is not Gerrit Visser
Modal Analysis: What it is and is not Gerrit Visser What is a Modal Analysis? What answers do we get out of it? How is it useful? What does it not tell us? In this article, we ll discuss where a modal
More informationINTRODUCTION TO PIEZO TRANSDUCERS
PIEZO SYSTEMS, INC. 65 Tower Office Park Woburn, MA 01801 USA Tel: 781 933 4850 Fax: 781 933 4743 email: sales@piezo.com Find Search for a product or category HOME PRODUCTS CUSTOM OEM CATALOG TECHNICAL
More informationAdvanced Vibrations. Distributed-Parameter Systems: Exact Solutions (Lecture 10) By: H. Ahmadian
Advanced Vibrations Distributed-Parameter Systems: Exact Solutions (Lecture 10) By: H. Ahmadian ahmadian@iust.ac.ir Distributed-Parameter Systems: Exact Solutions Relation between Discrete and Distributed
More informationDept. of Electrical & Computer Engineering, Dept. of Mechanical Engineering University of Bridgeport, Bridgeport, CT /08/2015
Design and Analysis of Three DOF Piezoelectric Vibration Energy Harvester Ravi Teja Purra Reddy, Xingguo Xiong, Junling Hu Dept. of Electrical & Computer Engineering, Dept. of Mechanical Engineering University
More informationProgram System for Machine Dynamics. Abstract. Version 5.0 November 2017
Program System for Machine Dynamics Abstract Version 5.0 November 2017 Ingenieur-Büro Klement Lerchenweg 2 D 65428 Rüsselsheim Phone +49/6142/55951 hd.klement@t-online.de What is MADYN? The program system
More informationThe Analysis of Aluminium Cantilever Beam with Piezoelectric Material by changing Position of piezo patch over Length of Beam
The Analysis of Aluminium Cantilever Beam with Piezoelectric Material by changing Position of piezo patch over Length of Beam Mr. Lalit R. Shendre 1, Prof. Bhamare V.G. 2 1PG Student, Department of Mechanical
More informationPhysical Modeling and Simulation Rev. 2
11. Coupled Fields Analysis 11.1. Introduction In the previous chapters we have separately analysed the electromagnetic, thermal and mechanical fields. We have discussed their sources, associated material
More informationDesign and Simulation of Comb Drive Capacitive Accelerometer by Using MEMS Intellisuite Design Tool
Design and Simulation of Comb Drive Capacitive Accelerometer by Using MEMS Intellisuite Design Tool Gireesh K C 1, Harisha M 2, Karthick Raj M 3, Karthikkumar M 4, Thenmoli M 5 UG Students, Department
More informationTransducers. Today: Electrostatic Capacitive. EEL5225: Principles of MEMS Transducers (Fall 2003) Instructor: Dr. Hui-Kai Xie
EEL55: Principles of MEMS Transducers (Fall 3) Instructor: Dr. Hui-Kai Xie Last lecture Piezoresistive Pressure sensor Transducers Today: Electrostatic Capacitive Reading: Senturia, Chapter 6, pp. 15-138
More informationINSTRUMENTATION ECE Fourth Semester. Presented By:- Sumit Grover Lect., Deptt. of ECE
INSTRUMENTATION ECE Fourth Semester Presented By:- Sumit Grover Lect., Deptt. of ECE Detailed Contents Objectives Sensors and transducer Classification of transducers Temperature transducers Resistance
More informationChapter 4 Analysis of a cantilever
Chapter 4 Analysis of a cantilever Before a complex structure is studied performing a seismic analysis, the behaviour of simpler ones should be fully understood. To achieve this knowledge we will start
More informationQuintic beam closed form matrices (revised 2/21, 2/23/12) General elastic beam with an elastic foundation
General elastic beam with an elastic foundation Figure 1 shows a beam-column on an elastic foundation. The beam is connected to a continuous series of foundation springs. The other end of the foundation
More informationPiezoelectric Multilayer Beam Bending Actuators
R.G. Bailas Piezoelectric Multilayer Beam Bending Actuators Static and Dynamic Behavior and Aspects of Sensor Integration With 143 Figures and 17 Tables Sprin ger List of Symbols XV Part I Focus of the
More informationA Vertical Electrostatic Actuator with Extended Digital Range via Tailored Topology
A Vertical Electrostatic Actuator with Extended Digital Range via Tailored Topology Yanhang Zhang and Martin L. Dunn Department of Mechanical Engineering University of Colorado at Boulder Boulder, CO 80309
More informationModule I Module I: traditional test instrumentation and acquisition systems. Prof. Ramat, Stefano
Preparatory Course (task NA 3.6) Basics of experimental testing and theoretical background Module I Module I: traditional test instrumentation and acquisition systems Prof. Ramat, Stefano Transducers A
More informationME 475 Modal Analysis of a Tapered Beam
ME 475 Modal Analysis of a Tapered Beam Objectives: 1. To find the natural frequencies and mode shapes of a tapered beam using FEA.. To compare the FE solution to analytical solutions of the vibratory
More informationMechatronics II Laboratory EXPERIMENT #1: FORCE AND TORQUE SENSORS DC Motor Characteristics Dynamometer, Part I
Mechatronics II Laboratory EXPEIMENT #1: FOCE AND TOQUE SENSOS DC Motor Characteristics Dynamometer, Part I Force Sensors Force and torque are not measured directly. Typically, the deformation or strain
More informationE05 Resonator Design
POLITECNICO DI MILANO MSC COURSE - MEMS AND MICROSENSORS - 2018/2019 E05 Resonator Design Giorgio Mussi 16/10/2018 In this class we will learn how an in-plane MEMS resonator handles process variabilities,
More informationSelf-reciprocating radioisotope-powered cantilever
JOURNAL OF APPLIED PHYSICS VOLUME 92, NUMBER 2 15 JULY 2002 Self-reciprocating radioisotope-powered cantilever Hui Li and Amit Lal a) SonicMEMS Laboratory, Department of Electrical and Computer Engineering,
More informationDESIGN AND SIMULATION OF UNDER WATER ACOUSTIC MEMS SENSOR
DESIGN AND SIMULATION OF UNDER WATER ACOUSTIC MEMS SENSOR Smitha G Prabhu 1, Nagabhushana S *2 1 Dept. Of Electronics and communication, Center for Nano Materials and MEMS, 2 Dept. of Electronics and Communication,
More informationMEMS Tuning-Fork Gyroscope Mid-Term Report Amanda Bristow Travis Barton Stephen Nary
MEMS Tuning-Fork Gyroscope Mid-Term Report Amanda Bristow Travis Barton Stephen Nary Abstract MEMS based gyroscopes have gained in popularity for use as rotation rate sensors in commercial products like
More informationModule 3 : Equilibrium of rods and plates Lecture 15 : Torsion of rods. The Lecture Contains: Torsion of Rods. Torsional Energy
The Lecture Contains: Torsion of Rods Torsional Energy This lecture is adopted from the following book 1. Theory of Elasticity, 3 rd edition by Landau and Lifshitz. Course of Theoretical Physics, vol-7
More informationCOUPLED FIELD ANALYSIS OF PIEZOELECTRIC CANTILEVER BEAM
COUPLED FIELD ANALYSIS OF PIEZOELECTRIC CANTILEVER BEAM Kunal Ganpati Rajdeep Department Of Mechanical Engineering, Solapur University / Fabtech Technical Campus & Research, Sangola, India ABSTRACT Electromechanical
More informationPiezoelectric Resonators ME 2082
Piezoelectric Resonators ME 2082 Introduction K T : relative dielectric constant of the material ε o : relative permittivity of free space (8.854*10-12 F/m) h: distance between electrodes (m - material
More informationPIEZOELECTRIC TECHNOLOGY PRIMER
PIEZOELECTRIC TECHNOLOGY PRIMER James R. Phillips Sr. Member of Technical Staff CTS Wireless Components 4800 Alameda Blvd. N.E. Albuquerque, New Mexico 87113 Piezoelectricity The piezoelectric effect is
More informationMET 487 Instrumentation and Automatic Controls. Lecture 13 Sensors
MET 87 nstrumentation and utomatic Controls Lecture Sensors July 6-9, 00 Stress and Strain Measurement Safe Load Level monitoring Force (indirect measurement by measuring strain of a flexural element Pressure
More informationChapter 2 Surface Acoustic Wave Motor Modeling and Motion Control
Chapter 2 Surface Acoustic Wave Motor Modeling and Motion Control 1 Abstract For miniaturization of ultrasonic transducers, a surface acoustic wave device has an advantage in rigid mounting and high-power-density
More informationEE C247B / ME C218 INTRODUCTION TO MEMS DESIGN SPRING 2014 PROBLEM SET #1
Issued: Thursday, Jan. 30, 2014 PROBLEM SET #1 Due (at 9 a.m.): Wednesday Feb. 12, 2014, in the EE C247B HW box near 125 Cory. This homework assignment is intended to give you some early practice playing
More informationEE C245 ME C218 Introduction to MEMS Design Fall 2012
EE C245 ME C218 Introduction to MEMS Design Fall 2012 Prof. Clark T.-C. Nguyen Dept. of Electrical Engineering & Computer Sciences University of California at Berkeley Berkeley, CA 94720 Lecture EE C245:
More informationME 237: Mechanics of Microsystems : Lecture. Modeling Squeeze Film Effects in MEMS
ME 237: Mechanics of Microsystems : Lecture Squeeze Film Effects in MEMS Anish Roychowdhury Adviser : Prof Rudra Pratap Department of Mechanical Engineering and Centre for Nano Science and Engineering
More information