Vibration Modeling of Beam with Poor Friction on the Two-Point Contact and Validation with the Modal Test Results

In the present paper، the transverse vibrations of Euler – Bernoulli beam along with the poor dry friction at the boundary conditions has been investigated. With special attention to the force of friction on the boundary conditions which plays a role as one non-linear factor and brings out nonlinear response، Natural frequencies also change despite the linear systems and these natural frequencies become a function of the force of friction and the force of friction in substrates also is a function of other parameters. The Calculation of the beam frequencies and the proper modeling of boundary conditions have been interesting for the researchers and scientists. Under present study، the force of friction at substrates is investigated through the friction force modeling by using nonlinear elastic - plastic Valanis model and also by the Classical Model of Coulomb friction. The assumed modes method for solving was used and the resulting equations by using Fourth Runge-Kutta numerical method have been solved. These two models have been compared and the results of modal testing were used for the validation. Finally، according to Valanis parameters، it was shown that this model has a positive relation with findings. Due to the weak of force of friction on the substrate، the softening effect of the frequency response-curves was observed.