Vibration Control of Smooth and Discontinuous Oscillator via Negative Derivative Feedback

Abstract Purpose The desired of this study is to decrease the vibrations of smooth and discontinuous (SD) oscillator using negative derivative feedback (NDF) controller. Methods The system has been analyzed approximately employing the method of multiple scales to derive the solution up to the first approximation. Conclusion The impact of negative derivative feedback (NDF) controller on smooth and discontinuous (SD) oscillator has been investigated under the condition of a simultaneous resonance $$(\Omega=\omega_1, \omega_1=\omega_2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Ω</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> .The influence of various parameters has been elucidated numerically using MATLAB. The results demonstrate a strong agreement between the approximate solution and the numerical solution.