NONLINEAR VIBRATIONS OF THE IMMERSED DAGGER-SHAPED ATOMIC FORCE MICROSCOPE CANTILEVER IN DIFFERENT LIQUIDS STUDIED BY EX
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NONLINEAR VIBRATIONS OF THE IMMERSED DAGGER-SHAPED ATOMIC FORCE MICROSCOPE CANTILEVER IN DIFFERENT LIQUIDS STUDIED BY EXPERIMENTAL AND THEORETICAL METHODS A. H. Gholizadeh Pasha and A. Sadeghi∗
UDC 539.3; 544.2
Abstract: In this paper, the nonlinear dynamic behavior of an immersed dagger-shaped atomic force microscope cantilever in different liquids has been investigated for the first time. The Timoshenko beam theory, which considers rotatory inertia and shear deformation effects, has been used for modeling the cantilever. The nonlinear tip-sample interaction force has been modeled by using the Hertzian contact theory. Water, methanol, acetone, and carbon tetrachloride are considered as the immersion environments. In most cases, the softening behavior has been observed for the cantilever. The resonant frequency is found to decrease with an increase in the liquid viscosity. The experimental results have been compared with the theoretical predictions and are found to be in good agreement. Keywords: atomic force microscope, dagger-shaped cantilever, damping effect, Timoshenko beam theory, immersion in liquid. DOI: 10.1134/S0021894420040197
INTRODUCTION Binning et al. [1] developed the atomic force microscope (AFM) for analyzing various materials. In the AFM, the tip is attached near one end. The radius of the contact size is as small as around 10 nm, and the contact load can be several nano-Newtons. The damage to the material in the contact region is sufficiently small. In the last few years, many researchers have shown a growing interest in investigating the dynamic behavior of the AFM cantilever. There are, however, still important unsolved problems regarding the disagreement between experimental measurements and theoretical investigations of the contact stiffness. Turner and Wiehn [2] studied the sensitivity of the vibration modes of the AFM cantilever in air and derived a closed-form expression. They assumed that the cantilever is parallel to the sample surface. Chang [3] studied the sensitivity of vibration modes of the AFM cantilever, taking into account the angle between the cantilever and the surface without considering the tip dimensions. Sadeghi [4] studied linear vibrations of the double tapered atomic force microscope cantilever by using the Timoshenko beam theory. He considered the effect of various parameters on the resonant frequency, but ignored the effects of nonlinear terms on the contact stiffness. Sedighi and Shirazi [5] performed an accurate investigation of lateral vibrations of a quintic nonlinear beam on an elastic foundation, using an exact formulation of the beam curvature. Wang and Fang [6] investigated vibrations in an elastic beam with nonlinear supports at
Islamic Azad University, Damavand, Iran; [email protected]; ∗ a [email protected]. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 61, No. 4, pp. 174–183, July–August, 2020. Original article submitted December 2, 2019; revision submitted February 28, 2020; accepted for publication March 30, 2020. ∗ Corresponding
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