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Bimodal atomic force microscopy (AFM) provides both topographical and material composition of a material with a single-pass experiment. Based on the rectangular beam theory, the cantilever's second to first eigenmode frequency is 6.27. Due to the fact that they are not multiple integers, there are irregular taps over the surface during an experiment. This can cause nonlinear vibrations in the cantilever in addition to the fact that the probe does not interact with each pixel similarly. Therefore, exciting the cantilever with higher harmonics instead of the eigenmodes in multifrequency AFM mechanisms and its advantages are discussed. Based on this theoretical discussion, this study provides the guideline to select the correct harmonic. It is found that the ratio of second to first eigenmode frequency heavily depends on the geometry of the cantilever. Additionally, it is found that cantilevers with lower eigenmode frequency ratios, excited with the first eigenmode frequency and higher harmonic, can provide higher phase contrasts. Numerical studies are done on a polystyrene (PS) and gold (Au) sample system. Based on this study, first one needs to minimize f2/f1. Second, the second excitation frequency should be the closest n-th harmonic to f2/f1 (i.e., one needs to minimize |n−f2f1|). Experimentally, a bimodal AFM scheme with an external function generator is used to image PS and low-density polyethylene polymer blend. The highest 2nd eigenmode phase contrast is observed with a cantilever that has a lower f2/f1 and is excited with its first eigenmode frequency and 6th harmonic (i.e., the nearest harmonic to the second eigenmode).

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In the present paper, radial and hoop thermal and mechanical stress analysis of a rotating disk made of functionally graded material (FGM) with variable thickness is carried out by using finite element method (FEM). To model the disk by FEM, one-dimensional twodegree elements with three nodes are used. It is assumed that the material properties, such as elastic modulus, Poisson's ratio and thermal expansion coefficient, are considered to vary using a power law function in the radial direction. The geometrical and boundary conditions are in the shape of two models including thermal stress (model-A) and mechanical stress (model-B). In model-A there exists no pressure in both external and internal layers, and there is a temperature distribution considered as a second order function in the radial direction of the rotating disk. In this case, the temperature dependency of the material properties is considered and a hyperbolic type is assumed for the geometry of the disk. In model-B, there is a constant pressure only on the internal layer and a pressure on the internal layer of the disk without temperature distribution but with different types of surface profiles. Furthermore, the displacements and stresses for various power law indices (N) and angular velocities are calculated and compared to other results in the literature. The effect of varying thicknesses and dependency of material properties on temperature distribution is investigated.