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In this paper, the effect of the crack on the vibration behavior of a thick-walled cracked pipe conveying fluid is investigated. The presence of a crack on the pipe introduces considerable local flexibility at the crack location. This flexibility is modeled by the fracture mechanics approach. The accuracy of the model is validated through the experimental data reported in the literature. Then, by using the mentioned model, the vibration analysis of the cracked pipe conveying fluid has been accomplished. Moreover, in order to solve the equation governing the vibration of the cracked pipe conveying fluid, a new analytical technique based on the power series method is proposed. Then, by applying the boundary conditions and the compatibility conditions at the crack location, the frequency equation is obtained. The results are presented by appropriate curves showing the variation of the natural frequency of the cracked pipe conveying fluid in terms of the crack depth and the fluid flow velocity. Also, the results show that for a cracked pipe with a given depth and location for the crack, by increasing the fluid flow velocity, the natural frequencies of the pipe decrease. Also, as the fluid velocity approaches to a certain value, the fundamental natural frequency approaches zero and instability occurs.

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This paper investigates the vibration behavior of fluid conveying viscoelastic pipe rested on non-uniform elastic Winkler foundation. The Kelvin-Voigt model is employed to consider the viscoelastic behavior of the pipe. Using the Galerkin’s method, the eigenvalue problem for the simply supported fluid conveying viscoelastic pipe is extracted. The effects of the fluid velocity, the viscoelastic constants and the foundation parameters on the complex eigenvalues and the divergence and the flutter instability of the fluid conveying viscoelastic pipe are studied and discussed. It is found that including the viscoelastic behavior to the pipe material alters the trend of the instability of the fluid conveying pipe, i.e., the first and the second modes divergence and the coupled mode flutter for the elastic pipe change to the first mode divergence, the second mode flutter and the second mode divergence for the viscoelastic pipe, respectively. The structural damping causes the velocity of the divergence instability at the higher modes to be increased. Also, because the viscoelasticity of the pipe affects the different vibration modes in different manner, therefore, the pipe dose not exhibit a coupled-mode flutter. Moreover, the non-uniformity of the foundation stiffness alters the first divergence velocity. The results are verified through comparing them with those reported in the literature.

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The fluid induced vibration in fluid conveying pipes can cause fatigue and failure in the system. Therefore, controlling these unwanted vibrations and suppressing the vibrations of the fluid conveying pipe is important. In this paper by considering the passive vibration absorber for the fluid conveying pipe, the influence of the vibration absorber parameters on the dynamic behavior of the system is investigated. The governing equations of motion are obtained via the Newton’s second law, and analytical solutions for the characteristic equation and mode shapes of the system are obtained through the power series method. After verifying the obtained results, the effect of the vibration absorber parameters and the fluid flow velocity on the vibration behavior of the fluid conveying pipe have been investigated. Results show that by increasing the absorber mass, the effect of absorber on decreasing the oscillations amplitude is diminished. At different fluid velocities, the oscillation amplitude of the system can be reduced considerably by specifying proper values of the absorber parameters. At velocities near the critical velocity, where the oscillation amplitude reaches a maximum value, using a suitable vibration absorber may reduce the maximum oscillations amplitude of the system by 98%. The method presented in current study can be easily generalized to design passive vibration absorber for fluid conveying pipes with different boundary conditions.