A direct method of natural frequency analysis on pipeline conveying fluid with both ends supported

The natural frequency equations of fluid–structure interaction in pipeline conveying fluid with both ends supported is investigated by a direct method, and the direct method is derived from Ferrari's method which is used to solve quartic equations. The dynamic equation of pipeline conveying fluid with two variables is obtained by Hamilton's variation principle based on Euler–Bernoulli Beam theory. By using the separation of variables method and the derived method from Ferrari's method, the natural frequency equations and the critical flow velocity equations of pipeline conveying fluid with both ends supported are obtained in mathematical decoupling. Each order natural frequencies and critical flow velocities can be obtained by using numerical method. The first five order dimensionless critical flow velocities are obtained, and the results indicate that clamped–simply supported is less stable than clamped–clamped supported and more stable than simply–simply supported. All the conclusions can be applied to nuclear installations and other engineering fields of improving the vibration.

► A direct method which derived from Ferrari's method was used to solve quartic equations.
► Frequency equations of pipeline conveying fluid with both ends supported was studied.
► Each order natural frequencies can be obtained by using the direct method.
► The first five critical flow velocities were obtained by using numerical method.