The suggested analytical solution of the pipe dynamic vibration response with and without crack effect by using a damper-spring support

Purpose The problem of controlling the vibration produced by the flow of fluids within the pipes is discussed. This paper aims to study the pipe vibration response because of the addition of a spring and damper as a method of fixing the pipe and observe the effect of this addition on the deflection response of these pipes. Design/methodology/approach The effect of the crack on the vibration of the pipes in various regions and dimensions of the crack was investigated. The results of this study were obtained by deriving the differential equations of the pipes with and without cracks and for the different types of fixations (cantilever and fixed from one edge and spring and damper from the other edges). Findings The natural frequency and mode response of the pipes are analytically determined. To conclude, the results show that the addition of damping decreases the amount of vibration response of the pipes, which leads to a significant increase in the stability of the pipes during the flow. Practical implications The research helps improve pipe structural integrity and encourages innovation in design, thereby improving safety and maintenance. Originality/value After adding the spring damper, the pipe response reduces the vibration by 46%, 38% and 40% for pressures (5,10,15) bar, respectively.