comsol MEMS模块简易教程

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comsol MEMS模块简易教程,指导comsol MEMS模拟仿真
CONTENT S Preface Solving electro-Thermo-Mechanical Problems Microresistor Beam ntroduction Model definition Results and discussion Modeling in COMSOL Multiphysics Modeling Using the Graphical U 7 Solving piezoelectric Problems 22 A Piezoelectric shear actuated beam 23 Introduction ..,23 Model definitie 23 Results Modeling in Comsol Multiphysics Referen 27 Modeling Using the Graphical User Interface 27 Eigenfr y Analysis .32 Frequency-Response Analysis 33 Appendix: Geometry Modeling 35 Low-Voltage Electroosmotic Micropump 38 Introducti Model definition 4 Results and discussion Modeling in comsol Multiphysics 45 Refe Modeling Using the Graphical User Interface 46 Appendix--Geometry Modeling ii CoNTeNTS MeMs Module minicourse Preface Mathematical modeling has become a very important part of the research and development work in engineering and science. Retaining a competitive edge requires a fast path between ideas and prototypes, and in this regard mathematical modeling and simulation provide a valuable shortcut for understanding both qualitative and quantitative aspects of scientific and engineering design This minicourse gives you an introduction into the modeling of microscale systems using COmsOL Multiphysics and the mems module. It takes you though several fields of science commonly encountered when modeling MEMs: clectrical and structural problems, piezoelectricity, and microfluidics. You do not require any prior expertise in mathematical modeling or CoMsOL Multiphysics in order to find it rewarding Enjoy your modeling The comsol team 2 MEMS MODULE MINICOURSE Solving Electro-Thermo-Mechanica Problems Electro-mechanical actuators and sensors constitute the backbone of the whole mems area. The mechanical movement they provide differentiate mems devices from onventional microclcctronics whcrc thc mechanics is designed to bc fixcd and onl electric(wanted)and heat currents(side effect)are observed The MEms Module contains several example models of mems actuators and sensors such as cantilever beams、 comb drives、 micromirrors、 resonators、 thermomechanical microvalves, pressure sensors, and accelerometers. You can make a quick 3d analysis of thc electrostatic ficld and calculatc capacitance valucs bascd on that using Electrostatic application mode alone. Or you can model pure continuum mechanics, like how residual stresses affect on the resonant frequencies, by using Structural Mechanics application modes USing Moving Mesh application Inode you can accurately combine movements and gcomctry changes in your own modcls. Lastly you can create fully electro-thermo-Structural couplings, like in the following example of a microresistor beam. The application in this example is to move the structure b conducting a current through conductive layers and generate a tenperature increase that lcads to a displacement through thcrmal expansion MEMS MODULE MINICOURSE 3 Microresistor beam Introduction This example illustrates the ability to couple thermal, electrical, and structural analysis in one model. This particular application moves a beam by passing a current through it; the current generates heat, and the temperature increase leads to displacement through theral expansion. The model estimates how much current and increase in temperature are necessary to displace the beam Although the model involves rather simple 3D geometry and straightforward physics it provides a good example of multiphysics modeling because it contains several appli cation modes addcd incrementally to thc modcl. Notc that this modcl of a microrcsis tor beam also appears in the companion MEMS Module model library in the Actuators models folder under the name micro beam 3d Model definition 0 Figure 1: Microbeam geometry A coppcr microbeam has a length of 13 um plus a height and width of l um Fcct at both end bond it rigidly to a su bstrate. An electrical potential of 0.2 V applied between the feet induces an electric current. due to the material's resistivity the current heats up the structure. Because the beam operates in the open, the generated heat dissipates into the air. The thermally induccd stress loads the matcrial and deforms the bcam 4 MEMS MODULE MINICOURSE As a first approximation, assume the electrical conductivity is constant. However,a conductor's resistivity increases with temperature. In the case of copper, the relationship between resistivity and temperature is approximately linear over a wide range of temperatures po(1∞(TTo) You obtain the conductor's temperature dependency from the relationship that defines electrical resistivity; conductivity is simply its reciprocal (o= lip) Results and discussion Thc ncxt two figurcs comparc thc microbcam's dcformation givcn constant and then temperature-dependent conductivity, respectively. The maximum displacement for onstant conductivity is 88 nm(8.79e-8) whereas for the temperature-dependent case the displacement is 48 nm(4.83e-8). The plots scale the deformation by 20 to emphasize the difference Boundary: Total displacement [m] Deformation: Displacement [m] MaX:8.797e8 4 Min:0 Figure 2: Microbeam deformation with constant electrical conductivity MEMS MODULE MINICOURSE 5 Boundary: Total displacement Im] Deformation: Displacement lml Max:4.836e8 0.5 Min: 0 Figure 3: Microbeam deformation with temperature-dependent electrical conductivity Modeling in COmsol Multiphysics This example creates the 3D geometry from two 2D work planes; the first one views the geometry from above, and the second does so from the side. To draw the 2D work geometries you use the line tool with specific axes and grid settings, then extrude the work geometries into 3D. The final step is to create a composite geometry of the extruded objects. You can also skip the step-by-step instructions for the geometry creation and import the ready-made geometry directly from the model library In this model three application modes describe the physics: Heat Transfer by Conduction from ComsoL Multiphysics, and two from the mems module, specifically the Solid Strain-Stress and Conductive Media DC application modes. For modeling the material, this example takes copper from the mems module's materials library The overall modeling approach is as follows: In the Conductive Media dc application mode, all boundaries-except the two bases where you apply the potential difference- are insulated. You then enter the resistive-heating subdomain variable, Q emdc, into the heat-source term of the heat Transfer by Conduction application mode. Next set the base boundaries facing the substrate to a constant temperature of 323 K. You model the convective air cooling in other boundaries using heat flux boundary conditions with a heat transfer coefficient, h, of5W/m/ K and external temperature Tinf, of 298 K. You then obtain the thermally induced stress by including a 6 MEMS MODULE MINICOURSE

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