---

In this study, the nonlinear vibration behavior of a dynamic atomic force microscope (DAFM) in the tapping mode is investigated. First, the governing differential equation of motion and boundary conditions for dynamic analysis are obtained by a combination of the basic equations of the modified couple stress theory and Hamilton principle. Regarding the nonlinear dynamics of the probe, perturbation technique has been used to solve the nonlinear equations. Afterwards, closed-form expressions for nonlinear frequency and effective nonlinear damping factor are derived. The effect of connection position of the tip on the vibration behavior of the microcantilever are also analyzed. The results obtained by couple stress theory are compared with those of classical beam theory. The results show that the nonlinear frequency and effective nonlinear damping factor are size dependant. According to the results, an increase in the equilibrium separation between the tip and the surface sample reduces the overall effect of van der Waals forces on the nonlinear frequency, but its effect on the effective nonlinear damping factor is negligible. The results also indicate that the change in the distance between tip and cantilever free end has a significant effect on the accuracy of the DAFM.

---

Hybrid joints (Metal–Composite) is being used more and more in aerospace industry due to their low weight and high strength. Dynamic study of this joint, owing to limitation of increase in screw’s preload in composite substructure, has certain importance. Effective factors on nonlinear behavior of the joint are low preload of the screw and high excitation force amplitude on the structure. Layer Element Model has been used to better the description of joint’s behavior in recent years. In this study effects of nonlinear behavior of joint on the structure has been investigated using 2D layer element theory in two divisions: increase of damping and decrease of stiffness which result in nonlinearity. Stiffness characteristics of the joint was modeled with normal stiffness and damping characteristics of the joint with structural damping in shear direction. Nonlinear frequency response function for two preload and two excitation force was extracted and nonlinear finite element model for stiffness and damping of the joint is suggested by High-order polynomial approximation in terms of response amplitude. Effects of increase of excitation force amplitude and decrease of screw’s preload on increase of nonlinearity was extracted by this finite element model. Results indicate that presented nonlinear finite element model corresponds closely to nonlinear vibration tests.