Vibration Suppression of a Micropipe Conveying Fluid via Sliding Mode Technique

In this article, derivation of a nonlinear model and nonlinear controller design for a micropipe conveying fluid, which is excited with a piezoelectric actuator, are accomplished. The governing equations are derived by using Hamilton’s principle. The difference between the equations in micro-scales and macro-scales is established by using the modified couple stress theory. Unlike the classical Timoshenko beam theory, this new theorem includes a material length scale parameter which could help capturing the size effect. In addition, for thin members, so long as the deformation in the order of thickness, they do not remain in the elastic zone. Therefore, the linear theorem produces error in predicting in-plane movement of the member. In this way, the nonlinear terms are considered in the equations by applying mid-plane stretching theory. After this derivation, a frequency analysis is performed on the model. In addition, the effective parameters on the peak value of the response are studied as well. Finally, a sliding mode controller for the input voltage of the system is designed. It has been observed that by using this type of nonlinear controller, the behavior of the system could be improved significantly.