In modern turbo machines such as aircraft jet engines, contact between the casing and bladed disks may occur through a variety of mechanisms: coincidence of vibration modes, thermal deformation of the casing, rotor imbalance, etc. These nonlinear interactions may result in severe damage to both structures and it is important to understand the physical mechanisms that cause them and under what circumstances they occur. In this study, we focus on the phenomenon of interaction caused by modal coincidence. Simple two-dimensional models of the casing and bladed disk structures are introduced in order to predict the occurrence of contact and the rotation speeds at which response becomes dangerous. Each structure is represented in terms of its two $n_d$-nodal diameter vibration modes, which are characteristic of axi-symmetric structures and allow for travelling wave motion. These two pairs of nodal diameter modes are made to interact through direct contact and the equations of motion are solved using an explicit time integration scheme in conjunction with the Lagrange multiplier method on the one hand. On the other hand, the Harmonic Balance Method is used for a better understanding of the solutions found by the time integration method. Both methods generally agree well and exhibit two distinct zones of completely different behaviors of the system.