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Resonant Frequency and Sensitivity of a Caliper Formed With Assembled Cantilever Probes Based on the Modified Strain Gradient Theory

Published online by Cambridge University Press:  10 September 2014

Mohammad Abbasi  and
Seyed E. Afkhami
Mohammad Abbasi*
Affiliation:
School of Mechanical Engineering, Shahrood Branch, Islamic Azad University, Daneshgah Blvd., 36199-43189 Shahrood, Iran
Seyed E. Afkhami
Affiliation:
School of Mechanical Engineering, Shahrood Branch, Islamic Azad University, Daneshgah Blvd., 36199-43189 Shahrood, Iran
*
*Corresponding author. m.abbasi28@yahoo.com
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Abstract

The resonant frequency and sensitivity of an atomic force microscope (AFM) with an assembled cantilever probe (ACP) is analyzed utilizing strain gradient theory, and then the governing equation and boundary conditions are derived by a combination of the basic equations of strain gradient theory and Hamilton’s principle. The resonant frequency and sensitivity of the proposed AFM microcantilever are then obtained numerically. The proposed ACP includes a horizontal cantilever, two vertical extensions, and two tips located at the free ends of the extensions that form a caliper. As one of the extensions is located between the clamped and free ends of the AFM microcantilever, the cantilever is modeled as two beams. The results of the current model are compared with those evaluated by both modified couple stress and classical beam theories. The difference in results evaluated by the strain gradient theory and those predicted by the couple stress and classical beam theories is significant, especially when the microcantilever thickness is approximately the same as the material length-scale parameters. The results also indicate that at the low values of contact stiffness, scanning in the higher cantilever modes decrease the accuracy of the proposed AFM ACP.

Keywords

atomic force microscopeassembled cantilever probestrain gradient theoryresonant frequencysensitivity
Type
Technology and Software Development
Information
Microscopy and Microanalysis , Volume 20 , Issue 6 , December 2014 , pp. 1672 - 1681
Copyright
© Microscopy Society of America 2014 

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