Corresponding Author


Document Type

Original Article

Subject Areas

Mathematics and Statistics


Frequency response; Micro- beam; Perturbation technique; PPF controller; Resonance; Stability


This manuscript displays the vibrations reduction of a clamped- clamped micro-beam subjected to an excitation external force via applying the positive position feedback (PPF) controller. The approximate solutions of the whole system are obtained up to the second order approximation with the help of the multiple scale perturbation technique (MSP). The Stability analysis is studied by utilizing the frequency response equations near the simultaneous condition .Time histories and response curves figures before and after control of the whole system are examined numerically using Rung-Kutta Fourth-order method (Maple(16) software and Matlab 7.7(R2014) software. Numerical results of the influences of different parameters and the whole system behavior are investigated at the worst resonance case to display the optimum conditions of decreasing the vibrations. The acquired results revealed that PPF controller plays a significant role in reducing the studied system oscillations. The effectiveness of the controller was about 162, means that the controller reduced the vibration to about 99.40%. A comparison between the numerical and approximate solutions is presented to appear the validity of the results.