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Studying the effect of thermal radiation on the mechanical behavior of FGM microbeams

Number of pages: 77 File Format: word File Code: 32290
Year: Not Specified University Degree: Master's degree Category: Facilities - Mechanics
Tags/Keywords: Electrostatic excitation - MEMS - Micro beam FGM - micro shot - Pull-in voltage - Stress theory - thermal moment - Thermal radiation
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  • Summary of Studying the effect of thermal radiation on the mechanical behavior of FGM microbeams

    Dissertation of Master's degree in mechanical engineering, applied design

    Abstract

     

    Microelectromechanical systems are generally classified based on the type of their excitation mechanism. In addition to electrostatic excitation, which is considered as one of the most important excitation mechanisms, thermal excitation is widely used in multi-layer microelectromechanical systems and variable function. In the last two decades, there has been a great transformation in the production of a wide range of electronic and mechanical equipment. The widespread use of these systems, especially in sensors and actuators, has caused the studies of many researchers to focus on their static and dynamic behavior.

    The main goal of this thesis is to study the mechanical behavior of a microbeam made of functionally variable materials exposed to nonlinear electrostatic force and temperature changes related to radiation and thermal displacement based on the modified Couple stress theory. It has been assumed that the functionally variable beam is made of metal and ceramic and the properties of the material in it change exponentially in the direction of thickness. By changing the ceramic percentage of the bottom surface, five different types of microbeams have been investigated and their static and dynamic tensile instability voltages, which are also exposed to heat, have been obtained. Also, tensile instability temperatures in the presence of electrostatic forces have been determined for five different types of microbeams. Due to the micro dimensions of the beam, it is first assumed that the temperature changes uniformly in the beam and any kind of temperature gradient is ignored. Secondly, it has been shown that not considering the component of the Couple stress theory will lead to incorrect results.

    Introduction

    In recent years, with the development of the industry and the possibility of manufacturing equipment on a micro scale, the use of systems in micro dimensions known as micro-electromechanical systems [1] have gained great importance. Micro-electromechanical systems are capable of performing complex operations in micro dimensions and with great precision. The widespread use of these systems in industries makes the need for more theoretical and practical studies in this field clearer.

    In recent decades, extensive efforts have been made by researchers to analyze and design new materials. Due to extensive industrial developments, it is possible to use these materials in advanced industries. Therefore, creating models for more accurate prediction of the behavior of these materials is very important. One of these categories of new materials is functionally graded materials [2]. Research on these materials has expanded greatly in the last two decades. FG materials have variable physical or mechanical properties as a continuous function of location and can exhibit desired and in some cases contradictory properties that cannot be found in a homogeneous material. One of the characteristics of these materials is the absence of specific internal boundaries in the material, which prevents the concentration of stress and the onset of failure due to interface stresses. Due to such unique features, new ideas about these materials and their new applications are being researched, among these applications, the design and construction of FG micro beams can be mentioned. In addition, since many microbeams are used in sensors to measure temperature, the thermomechanical analysis of these materials and the effect of their properties on the static and dynamic behavior of microbeams should be further investigated. has been developed. This model includes a material characteristic length parameter [5] as one of the material properties (in addition to the Lame coefficients), which considers the effect of material size in the structural equations.In this theory, the material's potential energy is a function of bending [6] in addition to strain, which leads to the introduction of a new term in the structural equation. This theory (revised theory of Couple stress) was proposed by Yang[7] [1] in 2002. It is based on the fact that the Couple stress tensor is symmetric and only one characteristic length of the material is considered in the equations. In static conditions, the mechanical and electrostatic force and moment are equal and the micro actuator is in a stable condition. Gradually, with the increase in voltage, the electrostatic force increases and establishes a new balance with mechanical force and torque in each static position, but this increase in electrostatic force continues until there is no more tolerance for the mechanical member to deal with the incoming electrostatic force, and the static balance is upset and it enters an unstable non-linear dynamic condition, in which it is not possible to calculate the position of the micro-beam in this state, and suddenly the micro-beam collides with a fixed lower surface. The voltage for which the micro-beam is placed in a situation where with a very low voltage increase, the electrostatic force exceeds the mechanical force and the static balance is disturbed, has been named Pull-in voltage correction. It should be mentioned that to solve the obtained nonlinear equations, step-by-step linearization method [8] has been used, which is a fast and reliable method in investigating the relationship between transverse displacement and voltage in micro-beam.

    Single-headed beams are the most widely used structures in MEMS, which are usually made of Si, SiN or polymers. A beam is a girder with one end fixed and fixed and the other end free and suspended, which carries the load at a fixed and fixed point. Today, microwire [9] is one of the integral components in MEMS, which is widely used in sensors, switches, etc. is used.

    In some cases, the loads imposed on the system cause a linear rise in the beam. Temperature changes are one of the most basic types of stimuli that can directly change the system. The thermal actuator is known for its ability to produce large linear displacements. This mechanism can usually be achieved by using two layers (or multiple layers) or FGM beams with different thermal expansion coefficients. FGM microbeams are of special importance in the MEMS industry and are considered key components. Such beams are known to be used in thermal applications, for example, as actuators in thermostats.

    Given that the sizes are on a micro scale, the classical elastic theory is not able to accurately predict the behavior of the material [1]. In this research, by using the modified theory of Couple's stress, which is one of the non-classical elastic theories, the equation of the displacement governing the FG single-ended microbeam under electrostatic and thermal loads has been obtained using Hamilton's principle[10]. The thermal boundary conditions are assumed to be that the micro-beam is heated from the top by radiation by a heat source and has thermal transfer conditions with the surrounding environment from the bottom.

    In this thesis, using MCST, the static and dynamic stability of a capacitive micro-beam made of functionally variable materials, subjected to electrostatic field stimulation and temperature changes (related to radiation and thermal transfer) is investigated. In order to check the stability, first, the static pull-in voltages and temperatures have been determined separately for five different types of FGM micro-beams to check the effect of increasing the ceramic percentage. In the following, the static stability is checked by applying heat and voltage simultaneously, and finally, the effect of step voltage on the dynamic stability of the FGM micro-beam bent by temperature changes is studied. In each part, the obtained results are compared with the results obtained from the classical theory.

  • Contents & References of Studying the effect of thermal radiation on the mechanical behavior of FGM microbeams

    List:

    List of figures ..

    D

    List of tables ..

    C

    Introduction ..

    1

    Chapter one: Concepts and generalities.

    6

    1-1 Microelectromechanical systems.

    6

    1-1-1 introduction.

    6

    1-1-2 classification of microelectromechanical systems.

    9

    1-1-3 types of microelectromechanical actuators.

    10

    1-1-3-1 magnetic stimulation.

    10

    1-1-3-2 stimulation by piezoelectric materials. 11 1-1-3-3 thermal stimulation. 11 1-3-4 stimulation by memory alloys. 11 1-1-3-5 electrostatic stimulation. 11 1-1-4 electrostatic micro-actuators. .

    12

    1-1-5 common phenomena in microelectromechanical systems .

    13

    1-1-5-1 damping of the compressed fluid layer .

    13

    1-1-5-2 thermoelastic damping .

    13

    1-1-5-3 instability Tensile.

    14

    1-2 functionally variable materials.

    15

    1-2-1 introduction.

    15

    1-2-2 history of functionally variable materials.

    16

    1-2-3 application of functionally variable materials.

    17

    1-2-4 functional variable material modeling.

    18

    1-2-4-1 Radi model.

    19

    1-2-4-2 exponential model.

    19

    1-2-4-3 power model.

    19

    1-3 Couple stress theory or Elastic strain gradient.

    20

    1-3-1 Introduction.

    20

    1-3-2 History of the Couple stress theory.

    20

    Chapter Two: Review of the work done.

    22

    2-1 Study of the effect of temperature changes in systems 2-2 study of the effect of electrostatic forces in microelectromechanical systems. 23 2-3 study of Couple stress theory in microelectromechanical systems. 25 2-4 study of the behavior of beams and FGM structures.

    27

    2-5 The purpose and necessity of conducting the research.

    29

    Chapter three: Presentation of the studied model and derivation of the governing equations.

    31

    3-1 Introduction of the studied system.

    31

    3-2 Mathematical and mathematical modeling and derivation of equations to achieve beam rise.

    33

    3-2-1 Heat conduction equation.

    33

    3-2-2 Formulation of FGM microbeam equations based on MCST.

    34

    Chapter four: Methods of solving equations under different loadings.

    41

    4-1 Static equation.

    41

    4-1-1 effect of voltage.

    41

    4-1-2 effect of temperature change.

    42

    4-1-3 simultaneous effect of temperature change and gradual application of electrostatic force.

    43

    4-2 dynamic equation.

    43

    Chapter five: Numerical results .

    46

    5-1 Introduction ..

    46

    5-2 Effect of gradual application of electrostatic force (in the absence of temperature changes) .

    49

    5-3 Effect of gradual application of temperature (in the absence of electrostatic force) .

    50

    5-4 Simultaneous effect of temperature changes and Gradual application of electrostatic force.

    52

    5-5 Effect of applying step DC voltage on FGM microbeam.

    57

    5-6 Effect of application of step DC voltage on bent FGM microbeam due to temperature changes.

    59

    Chapter six: Summary.

    61

    6-1 Conclusion.

    61

    6-1 Suggestions for future work.

    62

    References ..

    63

    Abstract ..

    68

    Source:

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    [2] Nathanson, H.C., Newell W.E., Wickstrom R.A. and Davis J.R. (1967). The Resonant Gate Transistor, IEEE Trans. on Electron Devices, (14) 117-133.

    [3] Walkers J.A. (2000). The future of MEMS in telecommunications networks, Journal of Micromechanics and Microengineering (10) 1-7.

    [4] Zavaracky P.M., Majumber S., McGrur E. (1997).Micromechanical switches fabricated using nickel surface micromachining, Journal of Microelectromech Systems 6 3-9.

    [5] Younis M.I. (2011). MEMS linear and nonlinear statics and dynamics, Springer New York Dordrecht Heidelberg London

    [6] Rezazadeh, Gh., Tahmasebi A., Zubtsov M., (2006). Application of Piezoelectric Layers in Electrostatic MEM Actuators: Controlling of Pull-in Voltage. J Microsystem Technologies 12(12):1163-70.

    [7] Jia, X.L., Yang J., Kitipornchai S., (2010). Characterization of FGM micro-switches under electrostatic and Casimir forces. Materials Science and Engineering 10:012178.

    [8] Epps J., Chandra R. (1997). Shape memory alloy actuation for active tuning of composite beams. Smart Material Structures (6) 251-264. [9] Bever M.B., Duwez P.F. (1972). (1999). Functionally graded materials: design, processing and applications. Kluwer academic publishers.

    [11] Daniel, I. M. and O. Ishai. Engineering Mechanics of Composite Materials. Oxford University Press, New York, NY, second edition, 2006. [12] Reddy J.N. (2000). Analysis of functionally graded plates. John Wiley & Sons, Ltd.

    [13] Fleck N.A., Muller G.M., Ashby M.F. (1994). Strain gradient plasticity: theory and experiment, Acta Metallurgica et Materialia 42, 475–487

    [14] Lam D.C.C., Yang F., Chong A.C.M., Wang J., Tong P. (2003). Experiments and theory in strain gradient elasticity, J. Mech. Phys Solids, 51:1477–508.

    [15] E. Cosserat, F. Cosserat (1909). Theorie des corps deformables.  Hermann et Fils, Paris.

    [16] Toupin, R.A., (1962). Elastic materials with couple stresses. Arch. Ration. Mech. Anal. 11, 385–414.

    [17] Mindlin, R.D., Tiersten, H.F., (1962), effects of couple-stresses in linear elasticity. Arch. Ration. Mech. Anal 11: 415–448.

    [18] Lafontan, X., Pressecq, F., Beaudoin, F., Rigo, S., Dardalhon, M., Roux, J. L., Schmitt, P., Kuchenbecker, J., Baradat, B., Lellouchi, D., Le-Touze, C., Nicot, J.-M. (2003). The advent of MEMS in space. Microelectronics Reliability 43, 1061-1083.

    [19] Zhu Y., D. Espinosa H. (2004). Effect of temperature on capacitive RF MEMS switch performance a coupled-field analysis. Journal of micromechanics and micro engineering, (14) 1270.

    [20] Fleck NA., Hutchinson JW. J. Mech Phys Solids 41(12):1825 Livage J (2003) Nat Mater 2:297, (1993).

    [21] Cleveringa, HHM., E. Van der Giessen, (1997). Needleman A, Acta Mater 45:3163.

    [22] Emery R.D., Lenshek DX., Behin B., Gherasimova M., Povirk GL., (1997). MRS Symp Proc Polycryst Thin Films 361–366.

    [23] Leung O. S., Ph.D. dissertation, Stanford, 2001.

    [24] Espinosa HD., Prorok BC., Fischer M., Journal of Mechanics and Physics of Solids 51:47–67, 2003.

    [25] Emery R.D., Povirk G.L. (2003). Tensile behavior of free-standing gold films. Part I. Coarse-grained films. Acta Mater 51:2067–2078.

    [26] Zhang Y., Zhao Y., (2006). Numerical and analytical study on the pull-in instability of micro-structure under electrostatic loading. Joutnal of Sensors and Actuators A, Physics. 127:366-7.

    [27] Rezazadeh Gh., Khatami F., Tahmasebi A., (2007). Investigation of the Torsion and Bending effects on Static Stability of Electrostatic Torsional Micromirrors. Journal of Microsystem Technologies 13(7):715-22.

    [28] Puers, R. and Lapadatu D., 1996. Electrostatic forces and their effects on capacitive mechanical sensors, Journal Sensors Actuators A 56 203-10.

    [29] Nguyen, C.T.C., Katehi L.P.B., Rebeiz G.M., (1998). Micromachined Devices for Wireless Communications, Proc. IEEE 86:1756-68.

    [30] Younis, M. I., 2004. Modeling and Simulation of Microelectromechanical Systems in Multi-Physics Fields.

Studying the effect of thermal radiation on the mechanical behavior of FGM microbeams
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