IN-PLANE AND OUT OF PLANE FREE VIBRATION OF U-SHAPED AFM PROBES BASED ON THE NONLOCAL ELASTICITY

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GHADIRI M.; HOSSEINI S.A.H.; KARAMI M.; NAMVAR M.

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Journal Paper

Paper Information

Journal: JOURNAL OF SOLID MECHANICS Year:2018 | Volume:10 | Issue:2 Page(s): 285-299

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Title

IN-PLANE AND OUT OF PLANE FREE VIBRATION OF U-SHAPED AFM PROBES BASED ON THE NONLOCAL ELASTICITY

Author(s)

GHADIRI M. | HOSSEINI S.A.H. | KARAMI M. | NAMVAR M. | Issue Writer Certificate

Keywords

U-SHAPED PROBE

AFM

NONLOCAL ELASTICITY THEORY

EULER–BERNOULLI BEAM THEORY

VIBRATION ANALYSIS

Abstract

Atomic force microscope (AFM) has been developed at first for topography imaging; in addition, it is used for characterization of mechanical properties. Most researches have been primarily focused on rectangular single-beam probes to make vibration models simple. Recently, the U-shaped AFM probe is employed to determine sample elastic properties and has been developed to heat samples locally. In this study, a simplified analytical model of these U-shaped AFM is described and three beams have been used for modelling this probe. This model contains two beams are clamped at one end and connected with a perpendicular cross beam at the other end. The beams are supposed only in bending flexure and twisting, but their coupling allows a wide variety of possible dynamic behaviors. In the present research, the natural frequency and sensitivity of flexural and torsional vibration for AFM probes have been analyzed considering influence of scale effect. For this purpose, governing equations of dynamic behavior of U-shaped AFM probe are extracted based on Eringen's theory using EULER–BERNOULLI BEAM THEORY and an analytical method is employed to solve these equations. The results in this paper have been extracted for different values of nonlocal parameters; it is shown that for a special case, there is a good agreement between reported results in available references and our results. The obtained results show that the frequencies of U-shaped AFM decrease with increasing the nonlocal parameter.

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APA: Copy

GHADIRI, M., HOSSEINI, S.A.H., KARAMI, M., & NAMVAR, M.. (2018). IN-PLANE AND OUT OF PLANE FREE VIBRATION OF U-SHAPED AFM PROBES BASED ON THE NONLOCAL ELASTICITY. JOURNAL OF SOLID MECHANICS, 10(2), 285-299. SID. https://sid.ir/paper/319547/en

Vancouver: Copy

GHADIRI M., HOSSEINI S.A.H., KARAMI M., NAMVAR M.. IN-PLANE AND OUT OF PLANE FREE VIBRATION OF U-SHAPED AFM PROBES BASED ON THE NONLOCAL ELASTICITY. JOURNAL OF SOLID MECHANICS[Internet]. 2018;10(2):285-299. Available from: https://sid.ir/paper/319547/en

IEEE: Copy

M. GHADIRI, S.A.H. HOSSEINI, M. KARAMI, and M. NAMVAR, “IN-PLANE AND OUT OF PLANE FREE VIBRATION OF U-SHAPED AFM PROBES BASED ON THE NONLOCAL ELASTICITY,” JOURNAL OF SOLID MECHANICS, vol. 10, no. 2, pp. 285–299, 2018, [Online]. Available: https://sid.ir/paper/319547/en

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