Transverse vibrations of curved beams are investigated. Different curvatures are considered. The beam is simply supported and resting on a nonlinear elastic foundation. The method of multiple scales is used in the analysis. A three-to-one internal resonance case is studied. It is possible when one of the mode numbers is three times the other mode. Amplitude and phase modulation equations are obtained. Steady state solutions and stability are discussed. A three-to-one internal resonance is possible for all types of curvatures under the assumptions in the article.
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The increase in vehicle speed, unsuitable road conditions and comfort demand have resulted in extensive research on vibration control of vehicle systems. In this paper, firstly, a specific passenger car (with a conventional suspension system) was considered including the vertical body displacements for sinusoidal road functions. Secondly, passive and active vibration control cases are studied to eliminate the body deflections. Thirdly, a new calculation method, namely artificial neural networks (ANN), for control force values was proposed for the active suspension system. In ANN application, feed-forward, multi-layer perceptron and back-propagation algorithm are used. By training calculated control values the required values were obtained by using ANN application. The analysis is performed in frequency domain.
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