Investigating Transverse Vibrations of Free-Free Beam on the Frictional Substrate and Validation with Test Results

Document Type : Research Article

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Abstract

In the present paper, the transverse vibrations of the Euler–Bernoulli beam along with the strong dry friction at the boundary conditions have been investigated. With  special attention to the force of frictionon theboundary 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 is also a function of other parameters. The calculation of the beam frequencies as well as proper modeling of boundary conditions have been interesting for researchers and scientists. In the present study, the force of friction at substrates is investigated through the friction force modeling by using the nonlinear elastic-plastic Valanis model and also by the Classical Model of Coulomb friction. The assumed modes method for solving is used and the resulting equations by using the Fourth Runge-Kutta numerical method are solved. These two models are compared and the results of modal testing are used for the validation. Finally, according to Valanis parameters, it is shown that this model has a positive relation with the findings. The hardening effect of the frequency response-curves is also observed.

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References

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Amirkabir Journal of Mechanical Engineering
Volume 45, Issue 2 - Serial Number 2
December 2013
Pages 43-51

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