Sensitivity Analysis of the Non-Linear Deflection of Non-Straight AFM Micro-Cantilever

Changizi, M. Amin; Stiharu, Ion

doi:10.1166/jamr.2012.1099

Cited by 4 publications

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An experimental validation of one beam pull-in to a rigid substrate was carried out in the laboratory and the result show that the model is accurate within 96% [13]. It is expected that the two beam model that used same constitutive formulation would yield similar accuracy range as same assumptions were made in the modeling.…”

Section: Discussionmentioning

confidence: 99%

Nonlinear Analysis of Pull-In Voltage of Twin Micro-Cantilever Beams

Changizi¹,

Stiharu²

2017

IJMEM

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Discussionmentioning

confidence: 99%

Nonlinear Analysis of Pull-In Voltage of Twin Micro-Cantilever Beams

Changizi¹,

Stiharu²

2017

IJMEM

Self Cite

View full text Add to dashboard Cite

show abstract

“…For a curved AFM beam, a point force at the tip can be considered as illustrated in figure 2 [16]. The moment at any cross section of the beam can be written as: The boundary conditions can be defined as following:…”

Section: Formulation Of the Large Deflection Of The Not-straight Beammentioning

confidence: 99%

“…Large deflection of a non-uniform spring-hinged cantilever beam under a follower point force at the tip was formulated and numerically solved [15]. Large deflection of curved beams under a tip load was studied analytically by the Lie symmetry method in [16].…”

Section: Introductionmentioning

confidence: 99%

A Closed Form Solution for Non-Linear Deflection of Non-Straight Ludwick Type Beams Using Lie Symmetry Groups

2018

IJOMAM

View full text Add to dashboard Cite

Micro Electro Mechanical Systems (MEMS) have found a large range of applications over the recent years. One of the prodigious application of micro-cantilever beams that is in use is represented by AFM probes (Atomic Force Microscopy). The AFM principle is based on the realtime measurement of the deflection of a micro-beam while following a surface profile. Hence, the prior knowledge of the deflection of beams has been of great interest to designers. Although both analytical and numerical solutions have been found for specific type of loads, there is no general solution specifically formulated for micro-cantilever beams that are not geometrically perfectly straight. Hence, the problem has not been specifically considered so far. The current work presents an analytical method based on Lie symmetry groups. The presented method produces an exact analytical solution for the deflection of Ludwick type beams subjected to any point load for nonstraight beams. The Lie symmetry method is used to reduce the order of the Ordinary Differential Equation (ODE) and formulate an analytical solution of the deflection function. The result is compared with an analytical solution for a particular case that is available in the open literature. It was found that the two results coincide.

show abstract