Effect of aspect ratio on the dynamic response of a fluid-conveying pipe using the Timoshenko beam model

Abstract

The effect of aspect ratio of length to diameter on the dynamic response of a fluid-conveying pipe has been studied using the Timoshenko beam model. The coupled partial differential equations are solved by generalized integral transform technique. A comparison between the numerical results based on the Timoshenko beam model and the Euler–Bernoulli beam model was conducted to evaluate the effect of aspect ratio on the dynamic response of a fluid-conveying pipe. The limits of applicability of the Euler–Bernoulli beam theory were studied. By using generalized integral transform technique, the effect of aspect ratio on different mode dynamics was studied. The results indicate that the natural frequencies decrease with the increasing of internal fluid velocity, and its values are closer to the ones from Euler–Bernoulli beam model with a larger aspect ratio and lower mode. When the mode is higher, the natural frequency is decreasing more dramatically with the decreasing of aspect ratio. The critical velocity decreases with the decreasing of aspect ratio. Meanwhile with internal flow velocity increasing, the maximum vibration deflection is increasing faster with smaller aspect ratio, which means that a pipe conveying fluid will lose stability more easily with a smaller aspect ratio at a specific internal flow velocity.