Nonlinear Vibrations of the Partially Tensioned System Taking into Account the Asymmetry of the Stiffness of Supports
2019
scientific article
english
- slender nonlinear systems
- free vibrations
- Euler's load
EN The nonlinear vibrations of the partially tensioned slender column are presented in this paper. The considered system is subjected to Euler’s load, which direction of action is consistent with the non-deformed axis of the column. The magnitude of the external load is variable and its application point is located at different heights between the upper and lower supports. In addition, the longitudinal displacement and rotation of both of the system ends are limited by the discrete elements in the form of translational and rotational springs. This nonlinear system is based on the screw drive used in the vertical lift platform for disabled people or cargo lift equipped with an engine room located in the lower part of the frame. The boundary problem of free vibrations of the mentioned system has been formulated on the basis of Bernoulli – Euler theory and due to nonlinear expressions the solution of the problem was conducted with small parameter method. The results of numerical simulations are concern on linear and nonlinear component of vibrations in relation to the location of external load application and influence of asymmetric value of supports stiffness on the free vibration frequency.
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