Nyquist's theorem in active vibration control system of conservative and non conservative pipes conveying fluid.

Fluid conveying pipes are used in all hydraulic systems and enter in all industrial fields, such as water, petroleum products and gases of all kinds. In spite of this widespread and critical importance of fluid conveying pipes, they suffer from major problems. One of these problems is the problem of vibrations that cause the collapse of the systems completely and cause significant economic losses if not avoided. For this reason, the researchers have dealt with this issue in all years, but the problem is not over. This research will highlight the problem of controlling the vibrations resulting from fluid flow inside the pipes, in addition to the study of reducing the vibrations of these pipes. Therefore, after investigation the control and stability for pipe with various methods, with previous papers, presenting in this paper investigation for active control for pipe by using Nyquist's method. There, the research has studied the response and the natural frequency; the dynamic behavior of conservative and non- conservative pipes conveying fluid using Nyquist's Theorem in the presence with no hydraulic damping (active control); and monitoring the response and stability of each case of stabilization. This study is carried out by deriving differential equations for pipes and for different types of fixation. Where, the analytical solution included drive the general equation of motion for pipe conveying fluid and then solving its equation by using Galerkin's technique, and then, calculating the stability by using Nyquist's techniques. [ABSTRACT FROM AUTHOR]