Instability of Internally Damped Curved Pipes

Abstract

The equation of motion of a fulid‐conveying pipe that includes the effect of damping is derived on the basis of Hamilton's principle. Depending upon the constraint conditions on the ends of the pipe, the induced or applied end forces may be classified as being either conservative or nonconservative. It is shown that when internal damping is taken into consideration, the conservative system could be subjected to a flutter type of instability. In certain cases, the capacity of the curved pipe to sustain flow is greatly affected by the internal damping factor. Under increasing fluid velocity, the pipes with an angle of bend less than 90° yield natural frquencies that do not follow the pattern of the pipe bends with angles of bend greater than 90°. Numerical results are presented for a wide range of parameters, including fluid velocity, damping parameter, and angle of the pipe bend.