Analysis of Microelectromechanical Systems (MEMS) Devices by the Meshless Point Weighted Least-squares Method

Wang, Q. X.; Li, Hua; Lam, Kwok‐Yan

doi:10.1007/s00466-006-0077-2

Cited by 17 publications

(11 citation statements)

References 27 publications

(35 reference statements)

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“…However, for higher voltage, i.e.Ṽ = 13.8, 14.2 and 15 V, solutions become unstable at 0.92, 1.13 and 1.68 ms, respectively. All these results are in very close agreement with the results reported by Wang et al [45].…”

Section: Example 2 (A Fixed-fixed Microswitch Wang Et Al [45])supporting

confidence: 95%

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A Kriging‐based error‐reproducing and interpolating kernel method for improved mesh‐free approximations

Shaw

Bendapudi

Roy

2007

Numerical Meth Engineering

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SUMMARYAn error-reproducing and interpolating kernel method (ERIKM), which is a novel and improved form of the error-reproducing kernel method (ERKM) with the nodal interpolation property, is proposed. The ERKM is a non-uniform rational B-splines (NURBS)-based mesh-free approximation scheme recently proposed by Shaw and Roy (Comput. Mech. 2007; 40(1):127-148). The ERKM is based on an initial approximation of the target function and its derivatives by NURBS basis functions. The errors in the NURBS approximation and its derivatives are then reproduced via a family of non-NURBS basis functions. The non-NURBS basis functions are constructed using a polynomial reproduction condition and added to the NURBS approximation obtained in the first step. In the ERKM, the interpolating property at the boundary is achieved by repeating the knot (open knot vector). However, for most problems of practical interest, employing NURBS with open knots is not possible because of the complex geometry of the domain, and consequently ERKM shape functions turn out to be non-interpolating. In ERIKM, the error functions are obtained through localized Kriging based on a minimization of the squared variance of the estimate with the reproduction property as a constraint. Interpolating error functions so obtained are then added to the NURBS approximant. While enriching the ERKM with the interpolation property, the ERIKM naturally possesses all the desirable features of the ERKM, such as insensitivity to the support size and ability to reproduce sharp layers. The proposed ERIKM is finally applied to obtain strong and weak solutions for a class of linear and non-linear boundary value problems of engineering interest. These illustrations help to bring out the relative numerical advantages and accuracy of the new method to some extent.

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Section: Example 2 (A Fixed-fixed Microswitch Wang Et Al [45])supporting

confidence: 95%

“…This microswitch may be modeled as a Timoshenko beam. The governing equations may be written as follows [45]:…”

Section: Example 2 (A Fixed-fixed Microswitch Wang Et Al [45])mentioning

confidence: 99%

A Kriging‐based error‐reproducing and interpolating kernel method for improved mesh‐free approximations

Shaw

Bendapudi

Roy

2007

Numerical Meth Engineering

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“…Kuang and Chen (2005) employed the Adomian decomposition method (ADM) to analyze the nonlinear pull-in behavior in electrostatic micro-actuators and showed that the ADM technique enabled the derivation of highly precise analytical solutions without the need for any simplifying assumptions regarding the nonlinear system. Wang et al (2007) analyzed MEMS devices using a meshless point weighted least-squares (PWLS) method and showed that the results were comparable with those obtained by other simulation approaches and experimental data.…”

Section: Introductionsupporting

confidence: 79%

Application of hybrid differential transformation/finite difference method to nonlinear analysis of micro fixed-fixed beam

Chen¹,

Lai²,

Liu³

2009

Microsyst Technol

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Analyzing the dynamic response of electrostatic devices is problematic due to the complexity of the interactions between the electrostatic coupling effect, the fringing field effect and the nonlinear electrostatic force. To resolve this problem, this study presents an efficient computational scheme in which the nonlinear governing equation of the electrostatic device is obtained in accordance with Hamilton's principle and is then solved using a hybrid differential transformation/finite difference method. The feasibility of the proposed approach is demonstrated by modeling the dynamic responses of two micro fixedfixed beams with lengths of 250 and 350 lm, respectively. The numerical results show that the pull-in voltage reduces as the beam length increases due to a loss in the structural rigidity. Furthermore, it is shown that the present results for the pull-in voltage deviate by no more than 0.75% from those derived in the literature using a variety of different schemes. Overall, the results presented in this study demonstrate that the proposed hybrid method represents a computationally efficient and precise means of obtaining detailed insights into the nonlinear dynamic behavior of micro fixed-fixed beams and similar micro-electromechanical systems (MEMS)-based devices.

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“…For wide prismatic microbeams, several researchers have incorporated Palmer's model (Palmer 1937) to account for the effect of fringing field capacitance (Osterberg and Senturia 1997;Pamidighantam et al 2002;Wang et al 2007). For narrow and thick microbeams, Batra et al (2006) demonstrated the effectiveness of an improved fringing model obtained by using the Method of Moments (MoM).…”

Section: Verification Of the Fringing Field Model And The Displacemenmentioning

confidence: 98%

“…For a prismatic beam having constant widthb, the expression for distributed electrostatic force using the Palmer's model of fringing field capacitance (Palmer 1937) is written as (Osterberg and Senturia 1997;Pamidighantam et al 2002;Batra et al 2006;Wang et al 2007)…”

Section: Introductionmentioning

confidence: 99%

Closed-form empirical relations to predict the static pull-in parameters of electrostatically actuated microcantilevers having linear width variation

Joglekar

Pawaskar

2010

Microsyst Technol

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We develop novel closed-form empirical relations to estimate the static pull-in parameters of electrostatically actuated tapered width microcantilever beams. A computationally efficient single degree-of-freedom model is employed in the setting of Ritz energy technique to extract the static pull-in parameters of the distributed electromechanical model that takes into account the effects of fringing field capacitance. The accuracy of this singledof model together with the variable-width equivalent of the Palmer's fringing model is established through a comparison with 3D finite element simulations. A unique surface fitting model is proposed to characterize the variations of both the pull-in displacement and pull-in voltage, over a realistically wide range of system parameters. Optimum coefficients of the proposed surface fitting model are obtained using nonlinear regression analysis. Empirical estimates of pull-in parameters are validated against finite element simulations, and available experimental and numerical data. An excellent agreement indicates that the proposed relationships are sufficiently accurate to be safely used for the electromechanical design of tapered microcantilever beams.

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Analysis of Microelectromechanical Systems (MEMS) Devices by the Meshless Point Weighted Least-squares Method

Cited by 17 publications

References 27 publications

A Kriging‐based error‐reproducing and interpolating kernel method for improved mesh‐free approximations

A Kriging‐based error‐reproducing and interpolating kernel method for improved mesh‐free approximations

Application of hybrid differential transformation/finite difference method to nonlinear analysis of micro fixed-fixed beam

Closed-form empirical relations to predict the static pull-in parameters of electrostatically actuated microcantilevers having linear width variation

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