چكيده انگليسي :
101 Analysis of Nonlinear Vibrations of a Pipe with Breathing Crack Using Perturbation Method Majid Talebian m talebian@me iut ac ir Date of Submission 2014 12 20 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisor Mostafa Ghayour Ghayour@cc iut ac irAbstract The dynamic behavior of long pipelines due to the wide applications in power plants refineries petrochemical plants oil rigs and offshore structures are allocated to a special place One of the mostcommon defects in structures is crack that can have dangerous effect on the structural behavior which maycause it to damage Fatigue cracks often exist in structural members that are subjected to repeated loading The crack models analyses fall largely into two categories 1 open crack models and 2 open and closedor breathing crack models Most researchers have used open crack models in their studies and have claimedthat the change in natural frequency might be a parameter used to detect the presence of crack However theassumption that crack is always open in vibration is not realistic because compressive loads may close thecrack In open crack model it is assumed that the crack in the vibration of the beam always remains open Several studies have been conducted over the last two decades shows that fatigue crack in the vibration ofthe structure can be opened and closed It causes stiffness change when system vibration the most importanteffect is influenced of the harmonic components in the dynamic response of the system Furthermore thebreathing crack due to decrease in the natural frequency is lower than the one predicted by open crackmodel This means that using open crack model show that fatigue crack depth is less than the actual one Inthis thesis free vibrations of breathing crack pipe is investigated by using perturbation methods For thispurpose the transverse vibrations of the simply supported beam and pipe in the first mode is modeled as asingle degree of freedom SDOF system by using equivalent mass stiffness and damping In this model due to the opened and closed form of the crack during vibration it is assumed that the equivalent stiffness ofthe system is varying as a harmonic function The spring stiffness of the beam is obtained analytically andfor the pipe is compared with the experimental values Then the nonlinear vibration equations are solved byusing the Lindstedts Poincare perturbation method and for validation the results are compared with theresults obtained by the Runge Kutta fourth order method Moreover the effects of crack depth and locationon the natural frequency and the displacement of the beam and pipe are studied Super harmonicscomponent is observed in the system response which is due to the nonlinearity of the system The increasingof the non linear effects which are due to the change in the crack parameters causes some changes to thesuper harmonics amplitudes By investigating of the results it is concluded that damping value is not aconstant amount and it increases with increasing the crack depth and position It is proved that the opencrack model shows lower amounts of crack depth in comparison with the actual predict Keywords Crack pipe Breathing crack Perturbation method Natural frequency
