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<p>In this paper, the effect of the stiffness and the mass distribution of the foundation on the natural frequencies of the fluid-conveying pipe are studied. Assuming the fluid to be non-compressible, using the Euler-Bernoulli theory and applying the Hamilton’s principle, the equation governing the transverse vibration of the fluid conveying pipe resting on elastic foundation is derived. A semi-analytical method which is named homotopy perturbation method (HPM) is used to solve the equation. One of the advantages of the HPM is the capability of the method to determine the natural frequencies at the higher fluid velocities. Based on the results, both the stiffness and the mass distribution of the foundation influence the fluid-conveying pipe natural frequencies and the corresponding fluid critical velocities. Moreover, neglecting the mass distribution of the foundation, especially at high frequencies, leads to inaccurate results.</p>

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On the Effect of Mass and Stiffness Distribution of an Elastic Foundation on the Critical Velocity of the Fluid-Conveying Pipe Using Homotopy Perturbation Method

  • 期刊论文

  • 发表日期：

    2026年5月26日

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  • Mousa Rezaee,
  • Reza Azmi,
  • Reza Fathi

摘要

In this paper, the effect of the stiffness and the mass distribution of the foundation on the natural frequencies of the fluid-conveying pipe are studied. Assuming the fluid to be non-compressible, using the Euler-Bernoulli theory and applying the Hamilton’s principle, the equation governing the transverse vibration of the fluid conveying pipe resting on elastic foundation is derived. A semi-analytical method which is named homotopy perturbation method (HPM) is used to solve the equation. One of the advantages of the HPM is the capability of the method to determine the natural frequencies at the higher fluid velocities. Based on the results, both the stiffness and the mass distribution of the foundation influence the fluid-conveying pipe natural frequencies and the corresponding fluid critical velocities. Moreover, neglecting the mass distribution of the foundation, especially at high frequencies, leads to inaccurate results.