In this paper, a mathematical model is newly developed to investigate the dynamic stability of aspirating pipe induced by solid-liquid two phase flow. Slip model is introduced to describe the slip characteristics of solid-liquid two phase flow. Harmonic differential quadrature method (HDQ) and eigenvalue analysis method are used to solve the pipe governing equation. The effects of solid particle concentration and size, pipe mass ratio and gravity coefficient are discussed. These parameters on pipe stability, critical velocity and critical frequency are analyzed.


Pipe vibration caused by internal fluids has been widely studied in many fields, such as nuclear power, marine mining, chemical engineering, heat exchanger and mechanical engineering (Païdoussis et al., 2020; Dai et al., 2020). At present, many achievements have been made in the study of elastic instability behavior of flexible pipes subjected to internal single-phase (liquid or gas) flow. Among them, the main contributor, Païdoussis has successively studied the vibration characteristics of horizontal pipes (Païdoussis, 1966) and vertical pipes (Païdoussis, 1970).

The problem of how to solve the governing equations of pipe vibration effectively is discussed. Païdoussis used Galerkin method in his works. Langthjem (1995) develops finite element method to solve the governing equations. And Yang (2007) uses generalized differential quadrature method to analyze the free vibration of functionally graded piezoelectric material beams. In addition, there are many methods about solving the governing equations, such as differential quadrature (Wang and Ni, 2008), power series method (Wang et al., 2000), differential transformation method (Ni et al., 2011) and variational iteration method (Li, 2017). In particular, Ma et al. (2023) adopted harmonic differential quadrature method (HDQ) to solve pipe vibration problems, which has achieved high calculation accuracy and efficiency compared with other above methods. Most of the above research methods are analyzed by solving the eigenvalues of discrete governing equations, which belongs to the study of pipe stability in frequency domain, while the vibration characteristics of pipeline in time domain are lacking in analysis and research in this way.

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