Dynamics of pumping effect in 1 pipe-2 tanks flow configuration with periodic excitation

Abstract

This paper is dedicated to analyzing the pumping effect in rigid 1 pipe-2 tanks flow configuration proposed by G. Propst. Our main purpose is to study the dynamic behaviors of the periodic solutions of the governing differential equation, as the periodic solution will result in the periodically forced pump in the configuration. We establish a sufficient condition for the existence of the harmonic solution by applying the topological degree theory. Additionally, we utilize the regular perturbation method and averaging method to examine the stability of the harmonic solution, as well as the existence and stability of the second-order subharmonic solution of the equation. Through numerical bifurcation analysis, we present the bifurcation diagrams of the periodic solutions, which reveal that higher-order subharmonic solutions with varying stability can be generated through period-doubling bifurcation of the periodic solutions.