A new investigation for double tapered atomic force microscope cantilevers by considering the damping effect

The resonant frequency of flexural vibration for a double tapered atomic force microscope (AFM) cantilever has been investigated by considering the damping effect. In this paper the effects of the contact position, contact stiffness, height of the tip, thickness of the beam, the height and breadth taper ratios of cantilever, the angle between the cantilever and the sample surface and damping parameter based on Timoshenko beam theory on the non-dimensional frequency and sensitivity have been studied. The differential Quadrature method (DQM) is employed to solve the nonlinear differential equations of motion. The results show that the resonant frequency decreases when Timoshenko beam parameter or cantilever thickness increases and high order modes are more sensitive to it. The first frequency is sensitive only in the lower range of contact stiffness, but the higher order modes are sensitive to the contact stiffness in a larger range. Increasing the tip height increases the sensitivity of the vibrational modes in a limited range of normal contact stiffness. Increasing the lateral contact stiffness increases the sensitivity to the normal contact stiffness after critical normal contact stiffness, but when the normal contact stiffness is lower than critical normal contact stiffness, the situation is reversed. By increasing the lateral damping parameter, the resonant frequency and sensitivity to the contact stiffness decrease. Furthermore, by increasing the breadth taper ratio, the frequency increases. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim