Analysis of Effect of Internal Pressure on Natural Frequencies of Bending Vibrations of a Straight Pipe with Fluid

Three computational methods were compared to evaluate the correctness of determining the natural frequencies of bending vibrations of a straight pipe with a fluid. Natural frequencies of bending vibrations of a pipe were computed by the finite element method using ANSYS Mechanical, module Modal Acoustic, and ACT Acoustic. Using ANSYS Mechanical, the estimation of changes in the internal volume of a straight pipe is received depending on the internal pressure. To solve this problem, Shell and Solid elements for the pipe and Solid, Fluid, and Hydrostatic Fluid for fluid are used. Using ANSYS Mechanical, the natural frequencies are obtained for the pipe with the fluid depending on the density and internal pressure. In this case, the density of the fluid is taken into account in the equivalent density of the tube material. In accordance with the results of calculations, the paper proposes an analytical dependence of the first natural frequency of the tube bending vibrations and fluid density, taking into account the internal pressure and the change in the internal volume. The obtained dependences makes it possible to determine with high accuracy, the density of the fluid by the magnitude of its natural frequency and internal pressure, including taking into account the change in the internal volume of the tube. As it is discussed in the paper, the computational method can be extended to a curved tube Coriolis meter in calculating the fluid density based on the experimental natural frequency.