On the Equivalence of Acoustic Impedance and Squeeze Film Impedance in Micromechanical Resonators

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Charanjeet Kaur Malhi ◽  
Rudra Pratap
Keyword(s):  
Finite Element ◽  
Acoustic Impedance ◽  
Entire Range ◽  
Microelectromechanical Systems ◽  
Acoustic Analysis ◽  
Computational Cost ◽  
Squeeze Film ◽  
Frequency Range ◽  
Element Analysis ◽  
Structural Dynamic

In this work, we address the issue of modeling squeeze film damping in nontrivial geometries that are not amenable to analytical solutions. The design and analysis of microelectromechanical systems (MEMS) resonators, especially those that use platelike two-dimensional structures, require structural dynamic response over the entire range of frequencies of interest. This response calculation typically involves the analysis of squeeze film effects and acoustic radiation losses. The acoustic analysis of vibrating plates is a very well understood problem that is routinely carried out using the equivalent electrical circuits that employ lumped parameters (LP) for acoustic impedance. Here, we present a method to use the same circuit with the same elements to account for the squeeze film effects as well by establishing an equivalence between the parameters of the two domains through a rescaled equivalent relationship between the acoustic impedance and the squeeze film impedance. Our analysis is based on a simple observation that the squeeze film impedance rescaled by a factor of jω, where ω is the frequency of oscillation, qualitatively mimics the acoustic impedance over a large frequency range. We present a method to curvefit the numerically simulated stiffness and damping coefficients which are obtained using finite element analysis (FEA) analysis. A significant advantage of the proposed method is that it is applicable to any trivial/nontrivial geometry. It requires very limited finite element method (FEM) runs within the frequency range of interest, hence reducing the computational cost, yet modeling the behavior in the entire range accurately. We demonstrate the method using one trivial and one nontrivial geometry.

scholarly journals Nonlinear Structural Dynamic Finite Element Analysis Using Ritz Vector Reduced Basis Method

1996 ◽  
Vol 3 (4) ◽  
pp. 259-268 ◽  
Author(s):  
M.S. Yao
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Finite Amplitude ◽  
Basis Vector ◽  
Reduced Basis ◽  
Ritz Vector ◽  
Element Analysis ◽  
Structural Dynamic ◽  
Nonlinear Equations Of Motion

The large number of unknown variables in a finite element idealization for dynamic structural analysis is represented by a very small number of generalized variables, each associating with a generalized Ritz vector known as a basis vector. The large system of equations of motion is thereby reduced to a very small set by this transformation and computational cost of the analysis can be greatly reduced. In this article nonlinear equations of motion and their transformation are formulated in detail. A convenient way of selection of the generalized basis vector and its limitations are described. Some illustrative examples are given to demonstrate the speed and validity of the method. The method, within its limitations, may be applied to dynamic problems where the response is global in nature with finite amplitude.

Simplified Dynamic Finite-Element Analysis for Three-Dimensional Pile-Grouped-Raft-High-Rise Buildings

2008 ◽  
Vol 400-402 ◽  
pp. 613-619
Author(s):  
Hui Xiong ◽  
Shou Ping Shang ◽  
Liang Huang
Keyword(s):  
Finite Element ◽  
Structural Engineering ◽  
Computational Cost ◽  
Time History ◽  
Pile Group ◽  
Element Analysis ◽  
Structural Dynamic ◽  
Shell Elements ◽  
High Rise ◽  
Mass Spring

Combined with the respective advantages in S-R(Sway-Rocking) impedance concept and finite-element method, a simplified 3D structural dynamic FEM considering composite pile-group-soil effects is presented. The structural members including piles are modeled by spacial beam or shell elements, and raft-base is divided into thick-shell elements with its spring-dashpot boundary coefficient obtained by impedance backcalculated. The mass-spring elements for soil between piles are set to simulate vertical, horizontal pile-group effects by strata-equivalent approach. The soil beside composite body is separated into near-field and far-field parts. The former is modeled by nonlinear spring-dashpot elements based on Winkler’s hypothesis, while the latter is modeled by a series of linear mass-spring-dashpots. With the effects of boundary track forces and energy radiation, the presented model enables researchers to conduct the time-domain nonlinear analysis in a relatively simple manner which avoids sophisticated boundary method and solid-element mesh bringing with tremendous computational cost. The seismic effect on dynamic interaction of pile-soil-complicated structures would be efficiently annotated from two structural engineering and geotechnical engineering aspects and the numerical calculation effort would be drastically decreased too. The complete procedure is mainly performed using the parametric design language assembled in the Finite Element Code Ansys. With the dynamic analysis of foundation and superstructure for a pile-supported 15-storey building, the influence of the participant effect on structural dynamic response will be depicted by various dynamic parameters of pile-soil-raft foundation in detail. Not only do the results have an agreement with some conclusions drawn by the general interaction theory, but also certain of phenomena which would be disagree with that by general analysis is involved. Even with the finite-element meshes for 68 piles, the time-history analysis procedure for PGSS (Pile-Group-Soil-Superstructure) system and the qualitative evaluation with various SSI parameters can be also fulfilled efficiently and rapidly by presented means. These results may be of help to the designers to quickly assess the significance of interaction effect for the high-rise buildings resting on any type or layout of pile-group foundation.

Bond Thickness Effects upon Dynamic Behaviour in Adhesive Joints

2010 ◽  
Vol 97-101 ◽  
pp. 3920-3923 ◽  
Author(s):  
Xiao Cong He
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Dynamic Behaviour ◽  
Adhesive Layer ◽  
Adhesive Joints ◽  
Response Functions ◽  
Frequency Range ◽  
Element Analysis ◽  
Cantilevered Beam ◽  
Different Thickness

The influence of adhesive layer thickness on the dynamic behaviour of the single-lap adhesive joints is investigated in this paper. The ABAQUS finite element analysis (FEA) software was used to predict the frequency response functions (FRFs) of the single-lap adhesive joints of different thickness of the adhesive layer. As a reference, the FRFs of a cantilevered beam without joint were investigated as well. It is clear that the FRFs of the four beams are close to each other within the frequency range 0~1000 Hz. It is also found that the composite damping of the single-lap adhesive joint increases as the thickness of the adhesive layer increases.

scholarly journals Coulomb-actuated microbeams revisited: experimental and numerical modal decomposition of the saddle-node bifurcation

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Anton Melnikov ◽  
Hermann A. G. Schenk ◽  
Jorge M. Monsalve ◽  
Franziska Wall ◽  
Michael Stolz ◽  
...  
Keyword(s):  
Finite Element ◽  
Microelectromechanical Systems ◽  
Dynamic Range ◽  
Dynamic Performance ◽  
Major Step ◽  
Element Analysis ◽  
Electrostatic Actuators ◽  
Voltage Range ◽  
Drive Voltage ◽  
Depth Analysis

AbstractElectrostatic micromechanical actuators have numerous applications in science and technology. In many applications, they are operated in a narrow frequency range close to resonance and at a drive voltage of low variation. Recently, new applications, such as microelectromechanical systems (MEMS) microspeakers (µSpeakers), have emerged that require operation over a wide frequency and dynamic range. Simulating the dynamic performance under such circumstances is still highly cumbersome. State-of-the-art finite element analysis struggles with pull-in instability and does not deliver the necessary information about unstable equilibrium states accordingly. Convincing lumped-parameter models amenable to direct physical interpretation are missing. This inhibits the indispensable in-depth analysis of the dynamic stability of such systems. In this paper, we take a major step towards mending the situation. By combining the finite element method (FEM) with an arc-length solver, we obtain the full bifurcation diagram for electrostatic actuators based on prismatic Euler-Bernoulli beams. A subsequent modal analysis then shows that within very narrow error margins, it is exclusively the lowest Euler-Bernoulli eigenmode that dominates the beam physics over the entire relevant drive voltage range. An experiment directly recording the deflection profile of a MEMS microbeam is performed and confirms the numerical findings with astonishing precision. This enables modeling the system using a single spatial degree of freedom.

scholarly journals Explicit Dynamic Finite Element Method for Failure with Smooth Fracture Energy Dissipations

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jeong-Hoon Song ◽  
Thomas Menouillard ◽  
Alireza Tabarraei
Keyword(s):  
Finite Element ◽  
Fracture Energy ◽  
Computational Cost ◽  
Quadrature Rule ◽  
Dynamic Failure ◽  
Structural Dynamic ◽  
Integration Schemes ◽  
Hourglass Control ◽  
Quadrilateral Finite Element ◽  
Explicit Dynamic

A numerical method for dynamic failure analysis through the phantom node method is further developed. A distinct feature of this method is the use of the phantom nodes with a newly developed correction force scheme. Through this improved approach, fracture energy can be smoothly dissipated during dynamic failure processes without emanating noisy artifact stress waves. This method is implemented to the standard 4-node quadrilateral finite element; a single quadrature rule is employed with an hourglass control scheme in order to decrease computational cost and circumvent difficulties associated with the subdomain integration schemes for cracked elements. The effectiveness and robustness of this method are demonstrated with several numerical examples. In these examples, we showed the effectiveness of the described correction force scheme along with the applicability of this method to an interesting class of structural dynamic failure problems.

Interval Finite Element Analysis of Structural Dynamic Problems

2015 ◽  
Vol 8 (2) ◽  
pp. 382-389 ◽  
Author(s):  
Naijia Xiao ◽  
Rafi L. Muhanna ◽  
Francesco Fedele ◽  
Robert L. Mullen
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Dynamic Problems ◽  
Element Analysis ◽  
Structural Dynamic

Fabrication and finite element analysis of vibrating parallel film actuator made with cellulose acetate for potential haptic application

2016 ◽  
Vol 230 (15) ◽  
pp. 2720-2727 ◽  
Author(s):  
Md Mohiuddin ◽  
Asma Akther ◽  
Eun Byul Jo ◽  
Hyun Chan Kim ◽  
Jaehwan Kim
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Cellulose Acetate ◽  
Vibration Characteristics ◽  
Experimental Results ◽  
Vibration Velocity ◽  
Frequency Range ◽  
Actuation Frequency ◽  
Element Analysis ◽  
Wide Range

The present study investigates a film actuator made with dielectric cellulose acetate films separated by narrow spacers as a means of electrostatic actuation for potential haptic application. Fabrication process for the actuator is explained along with experiments conducted over a wide frequency range of actuation frequency. A valid finite element simulation of the actuator is made on the quarter section of the actuator by using full 3D finite elements. Vibration characteristics such as fundamental natural frequency, mode shape and output velocity in the frequency range for haptic feeling generation are obtained from the finite element analysis and compared with the experimental results. Experimental results demonstrate that the finite element model is practical and effective enough in predicting the vibration characteristics of the actuator for haptic application. The film actuator shows many promising properties like high transparency, wide range of actuation frequency and high vibration velocity for instance.

Finite Element Analysis of SiCp/Al Model of Unit Cell during Ultrasonic Vibration Scratching

2016 ◽  
Vol 693 ◽  
pp. 1022-1029
Author(s):  
G.Q. Liang ◽  
Ping Fa Feng ◽  
Jian Fu Zhang
Keyword(s):  
Finite Element ◽  
Maximum Amplitude ◽  
Element Model ◽  
Ultrasonic Frequency ◽  
Frequency Range ◽  
Element Analysis ◽  
Scale Modeling ◽  
Sic Particles ◽  
Significant Damage ◽  
Extent Of Damage

In this paper, finite element model of SiCp /Al single cell body and single diamond particles were established by cross-scale modeling method. The results shows that the extent of damage of SiC particles increased with the increase of amplitude and frequency; The integrity of SiC particles are still better under the ultrasonic frequency 20000 Hz and the maximum amplitude 5um,so the optimal frequency range of ultrasonic scratch is (20000-30000)Hz. As for 22000 Hz, the integrity of SiC particles was better under the amplitude 4um,while the SiC particles have a significant damage in the border area under the amplitude 5um,so the best frequency and amplitude for ultrasonic scratches are: 22000 Hz and 4 um.

A Determination of Material Properties of Flexible Structures Using EMA and FEM Analysis

2014 ◽  
Vol 693 ◽  
pp. 293-298 ◽  
Author(s):  
Rastislav Duris
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Low Cost ◽  
Flexible Structures ◽  
Fem Analysis ◽  
Element Analysis ◽  
Structural Dynamic ◽  
Vibration Data ◽  
Complex Interactions ◽  
Applied Forces

Dynamic behavior of mechanical structures results from complex interactions between applied forces and the stiffness properties of the structure. Currently, many problems of structural dynamic analysis are solved using Finite Element Method (FEM). However, in recent years, the implementation of the Fast Fourier Transform (FFT) in low cost computer-based signal analyzers has provided a powerful tool for acquisition and analysis of vibration data. This article discusses combination of two approaches to structural dynamics testing; the experimental part which is referred to as Experimental Modal Analysis (EMA), respectively the analytical part, which is realized by Finite Element Analysis (FEA). Main goal of the paper is calculation of material properties from experimentally determined modal frequencies.

Sign in / Sign up

Export Citation Format

Share Document