The Effect of Squeeze-Film Damping on the Shock Response of Clamped-Clamped Microbeams

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Hadi Yagubizade ◽  
Mohammad I. Younis
Keyword(s):  
Element Model ◽  
Squeeze Film ◽  
Beam Equation ◽  
Mechanical Shock ◽  
Computationally Efficient ◽  
Reduced Order ◽  
Squeeze Film Damping ◽  
Nonlinear Finite Element Model ◽  
Euler Bernoulli Beam ◽  
Fully Coupled

This paper presents an investigation into the nonlinear effect of squeeze-film damping on the response of a clamped–clamped microbeam to mechanical shock. In this work, we solve simultaneously the nonlinear Reynolds equation, to model squeeze-film damping, coupled with a nonlinear Euler–Bernoulli beam equation. A Galerkin-based reduced-order model and a finite-difference method are utilized for the solid domain and fluid domain, respectively. Several results demonstrating the effect of gas pressure on the response of the microbeams are shown. Comparison with the results of a fully coupled multiphysics nonlinear finite-element model is presented. The results indicate that, for devices operating in air, squeeze-film damping can be used effectively to minimize the displacements of released microstructures during shock and impact. The results also indicate that squeeze-film damping has more significant effect on the response of microstructures in the dynamic shock regime compared to the quasi-static shock regime. A computationally efficient approach is proposed to model the fluidic-structural problem more efficiently based on a nonlinear analytical expression of the squeeze-film damping.

The Effect of Squeeze-Film Damping on Suppressing the Shock Response of MEMS

2009 ◽  
Author(s):  
Hadi Yagubizade ◽  
Mohammad I. Younis ◽  
Ghader Rezazadeh
Keyword(s):  
Reynolds Equation ◽  
Element Model ◽  
Squeeze Film ◽  
Beam Equation ◽  
Mechanical Shock ◽  
Shock Loads ◽  
Reduced Order ◽  
Squeeze Film Damping ◽  
Nonlinear Finite Element Model ◽  
Euler Bernoulli Beam

This paper presents an investigation into the response of a clamped-clamped microbeam to mechanical shock under the effect of squeeze-film damping (SQFD). In this work, we solve simultaneously the nonlinear Reynolds equation, to model squeeze-film damping, coupled with a nonlinear Euler-Bernoulli beam equation. A Galerkin-based reduced-order model and a finite-deference method (FDM) are utilized for the solid domain and for the fluid domain, respectively. Several results showing the effect of gas pressure on the response of the microbeams are shown. Comparison with the results of a multi-physics nonlinear finite-element model is presented. The results indicate that squeeze-film damping has more significant effect on the response of microstructures in the dynamic shock loads compared to the quasi-static shock loads.

Dynamic Finite Element Modeling of Electrostatically Actuated Micro Structures Considering Squeeze Film Damping Effect

2006 ◽  
Author(s):  
M. T. Ahmadian ◽  
Hoseinali Borhan ◽  
M. Moghimi Zand
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Dynamic Models ◽  
Dynamic Equilibrium ◽  
Element Model ◽  
Nonlinear Finite Element ◽  
Squeeze Film ◽  
Solution Technique ◽  
Squeeze Film Damping ◽  
Nonlinear Finite Element Model

Developing a transient fully-meshed model of coupled-domain microsystems is of paramount importance not only for accurate simulation and design but also for creating more accurate low-order or macro dynamic models. So in this paper, a complete nonlinear finite element model for coupled-domain MEMS devices considering electrostatic and squeeze film effects is presented. For this purpose, we use the Galerkin weighted-residual technique for developing the finite element model that capture the original microsystem's nonlinear behaviors, such as the structural dynamics, the squeeze-film damping, the electrostatic actuation and the geometric nonlinearity caused by inherent residual stresses. In addition, using the Newmark's nonlinear solution, technique, the extracted dynamic equilibrium equations are discretised and simulated. The system dynamic behavior is successfully modeled by using the developed nonlinear finite element model and finally some simulated results of electrostatic microactuator behaviors are verified with experimental findings and are in very good agreement.

Characterization of the Dynamical Response of a Micromachined G-Sensor to Mechanical Shock Loading

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Daniel Jordy ◽  
Mohammad I. Younis
Keyword(s):  
Element Model ◽  
Plane Motion ◽  
Squeeze Film ◽  
Dynamical Response ◽  
Mechanical Shock ◽  
Mems Devices ◽  
Squeeze Film Damping ◽  
Out Of Plane ◽  
Gap Width

Squeeze film damping has a significant effect on the dynamic response of microelectromechanical system (MEMS) devices that employ perforated microstructures with large planar areas and small gap widths separating them from the substrate. Perforations can alter the effect of squeeze film damping by allowing the gas underneath the device to easily escape, thereby lowering damping. By decreasing the size of the holes, damping increases and the squeeze film damping effect increases. This can be used to minimize the out-of-plane motion of the microstructures toward the substrate, thereby minimizing the possibility of contact and stiction. This paper aims to explore the use of the squeeze film damping phenomenon as a way to mitigate shock and minimize the possibility of stiction and failure in this class of MEMS devices. As a case study, the performance of a G-sensor (threshold accelerometer) employed in an arming and fusing chip is investigated. The effect of changing the size of the perforation holes and the gap width separating the microstructure from the substrate are studied. A multiphysics finite-element model built using the software ANSYS is utilized for the fluidic and transient structural analysis. A squeeze film damping model, for both the air underneath the structure and the flow of the air through the perforations, is developed. Results are shown for various models of squeeze film damping assuming no holes, large holes, and assuming a finite pressure drop across the holes, which is the most accurate way of modeling. It is found that the threshold of shock that causes the G-sensor to contact the substrate has increased significantly when decreasing the holes size or the gap width, which is very promising to help mitigate stiction in this class of devices, thereby improving their reliability.

Characterization of the Dynamical Response of a Micromachined G-Sensor to Mechanical Shock Loading

2007 ◽  
Author(s):  
Daniel E. Jordy ◽  
Mohammad I. Younis
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Squeeze Film ◽  
Dynamical Response ◽  
Mems Devices ◽  
Damping Coefficients ◽  
Squeeze Film Damping ◽  
Out Of Plane ◽  
Gap Width

Squeeze film damping has a significant effect on the dynamic response of MEMS devices that employ perforated microstructures with large planar areas and small gap widths separating them from the substrate. Perforations can alter the effect of squeeze film damping by allowing the gas underneath the device to easily escape, thereby lowering the damping. By decreasing the size of the holes, the damping increases and the squeeze film damping effect increases. This can be used to minimize the out-of-plane motion of the microstructures toward the substrate, thereby minimizing the possibility of contact and stiction. This paper aims to explore the use of the squeeze-film damping phenomenon as a way to mitigate shock and minimize the possibility of stiction and failure in this class of MEMS devices. As a case study, we consider a G-sensor, which is a sort of a threshold accelerometer, employed in an arming and fusing chip. We study the effect of changing the size of the perforation holes and the gap width separating the microstructure from the substrate. We use a multi-physics finite-element model built using the software ANSYS. First, a modal analysis is conducted to calculate the out-of-plane natural frequency of the G-sensor. Then, a squeeze-film damping finite-element model, for both the air underneath the structure and the flow of the air through the perforations, is developed and utilized to estimate the damping coefficients for several hole sizes. Results are shown for various models of squeeze-film damping assuming no holes, large holes, and assuming a finite pressure drop across the holes, which is the most accurate way of modeling. The extracted damping coefficients are then used in a transient structural-shock analysis. Finally, the transient shock analysis is used to determine the shock loads that induce contacts between the G-sensor and the underlying substrate. It is found that the threshold of shock to contact the substrate has increased significantly when decreasing the holes size or the gap width, which is very promising to help mitigate stiction in this class of devices, thereby improving their reliability.

scholarly journals Comparative Study of Blades Reduced Order Models With Geometrical Nonlinearities and Contact Interfaces

2020 ◽  
Author(s):  
Elise Delhez ◽  
Florence Nyssen ◽  
Jean-Claude Golinval ◽  
Alain Batailly
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Performance Indicator ◽  
Element Model ◽  
Reduced Order Models ◽  
Computationally Efficient ◽  
Reduced Order ◽  
Reduction Methods ◽  
Blade Tip ◽  
Reduced Space

Abstract This paper investigates the use of different model reduction methods accounting for geometric nonlinearities. These methods are adapted to retain physical degrees-of-freedom in the reduced space in order to ease contact treatment. These reduction methods are applied to a 3D finite element model of an industrial compressor blade (NASA rotor 37). In order to compare the different reduction methods, a scalar indicator is defined. This performance indicator allows to quantify the accuracy of the predicted displacement both locally (at the blade tip) and globally. The robustness of each method with respect to variations of the external excitation is also assessed. The performances of the reduction methods are then compared in the case of frictional contact between the blade tip and the surrounding casing. This work brings evidence that reduced order models provide a computationally efficient alternative to full order finite element models for the accurate prediction of the time response of structures with both distributed and localized nonlinearities.

Reduced Order Modeling of the Squeeze Film Damping in MEMS

2006 ◽  
Author(s):  
Aurelio Soma` ◽  
Guido Spinola ◽  
Alberto Ballestra ◽  
Alessandro Pennetta
Keyword(s):  
Finite Element ◽  
Coupled Model ◽  
Reduced Order Modeling ◽  
Squeeze Film ◽  
Design Parameters ◽  
Reduced Order ◽  
Equivalent Damping ◽  
Squeeze Film Damping ◽  
Numerical Finite Element ◽  
Micro Systems

In this work the effect of the Squeeze Film Damping on MEMS structures is studied. When a device is being designed, it is very important to preview with good approximation its dynamic behavior. However, as the simulation of the micro-systems involves different physical domains, the analysis with numerical methods can turn out remarkably onerous. Moreover the Reduced Order Modeling is preferable when, due to technological reasons, the membrane is built with several holes and the geometrical FEM coupled model will be computational heavy. Therefore Reduced Order Models allow to integrate in a total mathematical model the main parameters, obtained by the numerical analysis, considering the behavior of the structure analyzed in different physical domains. In the present work the non-linear coefficients of equivalent damping and stiffness by finite element models are investigated to be exported in a reduced order model. By means of numerical finite element calculation is studied the sensitivity analysis related to design parameters such as dimension of the plate and the presence, or lack, of holes.

Computationally Efficient Approaches to Simulate the Dynamics of Microbeams Under Mechanical Shock

2006 ◽  
Author(s):  
Mohammad I. Younis ◽  
Danial Jordy ◽  
James M. Pitarresi
Keyword(s):  
Hybrid Approach ◽  
Computational Cost ◽  
Nonlinear Behavior ◽  
Reduced Order Model ◽  
Beam Model ◽  
Mechanical Shock ◽  
Computationally Efficient ◽  
Order Model ◽  
Reduced Order ◽  
Dynamic Loading Conditions

We present computationally efficient models and approaches and utilize them to investigate the dynamics of microbeams under mechanical shock. We explore using a hybrid approach utilizing a beam model combined with the shock spectrum of a spring-mass-damper model. We conclude that this approach is computationally efficient and yields accurate results in both quasi-static and dynamic loading conditions. We utilize a reduced-order model based on the nonlinear Euler-Bernoulli beam model. We demonstrate that this model is capable of capturing accurately the dynamic behavior of microbeams under shock pulses of various amplitudes (low-g and high-g), in various damping conditions, structural boundaries (clamped-clamped and clamped-free), and can capture both linear and nonlinear behavior. We investigate high-g loading cases. We report significant increase in the computational cost of simulations when using traditional nonlinear finite-element models because of the activation of higher-order modes. We demonstrate that the developed reduced-order model can be very efficient in such cases.

Simulation of Squeeze-Film Damping of Microplates Actuated by Large Electrostatic Load

2007 ◽  
Vol 2 (3) ◽  
pp. 232-241 ◽  
Author(s):  
Mohammad I. Younis ◽  
Ali H. Nayfeh
Keyword(s):  
Electrostatic Force ◽  
Mode Shapes ◽  
Squeeze Film ◽  
Beam Equation ◽  
Beam Model ◽  
Static Deflection ◽  
Quality Factors ◽  
Squeeze Film Damping ◽  
Plate Equations ◽  
Analytical Expressions

We present a new method for simulating squeeze-film damping of microplates actuated by large electrostatic loads. The method enables the prediction of the quality factors of microplates under a limited range of gas pressures and applied electrostatic loads up to the pull-in instability. The method utilizes the nonlinear Euler-Bernoulli beam equation, the von Kármán plate equations, and the compressible Reynolds equation. The static deflection of the microplate is calculated using the beam model. Analytical expressions are derived for the pressure distribution in terms of the plate mode shapes around the deflected position using perturbation techniques. The static deflection and the analytical expressions are substituted into the plate equations, which are solved using a finite-element method. Several results are presented showing the effect of the pressure and the electrostatic force on the structural mode shapes, the pressure distributions, the natural frequencies, and the quality factors.

Reduced Order Modeling and Vibration Analysis of Mistuned Bladed Disk Assemblies With Shrouds

1999 ◽  
Vol 121 (3) ◽  
pp. 515-522 ◽  
Author(s):  
R. Bladh ◽  
M. P. Castanier ◽  
C. Pierre
Keyword(s):  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Reduced Order Modeling ◽  
Forced Response ◽  
Modeling Technique ◽  
Computationally Efficient ◽  
Bladed Disks ◽  
Reduced Order ◽  
Synthesis Approach

This paper presents important improvements and extensions to a computationally efficient reduced order modeling technique for the vibration analysis of mistuned bladed disks. In particular, this work shows how the existing modeling technique is readily extended to turbomachinery rotors with shrouded blades. The modeling technique employs a component mode synthesis approach to systematically generate a reduced order model (ROM) using component modes calculated from a finite element model (FEM) of the rotor. Based on the total number of degrees of freedom, the ROM is typically two or three orders of magnitude smaller than the FEM. This makes it feasible to predict the forced response statistics of mistuned bladed disks using Monte Carlo simulations. In this work, particular attention is devoted to the introduction of mistuning into the ROM of a shrouded assembly. Mistuning is modeled by projecting the mistuned natural frequencies of a single, cantilever blade with free shrouds onto the harmonic modes of the shrouded blade assembly. Thus, the necessary mistuning information may be measured by testing individual blades.

Sign in / Sign up

Export Citation Format

Share Document