Sloshing dynamics in tanks: Nonlinear numerical analysis approach

Authors

  • Mauricio Aparecido Ribeiro Department of Electronics, Federal University of Technology - Parana, Doutor Washington Subtil Chueire Street, Ponta Grossa, Parana, 84017-220, Brazil
  • Jose Manoel Balthazar Department of Electronics, Federal University of Technology - Parana, Doutor Washington Subtil Chueire Street, Ponta Grossa, Parana, 84017-220, Brazil\\ Department of Mechanical, Sao Paulo State University, Av. Eng. Luiz Edmundo C. Coube Street, Bauru, Sao Paulo, 610101, Brazil
  • Maria Aline Gonçalves Department of Mechanical, Sao Paulo State University, Av. Eng. Luiz Edmundo C. Coube Street, Bauru, Sao Paulo, 610101, Brazil
  • Angelo Marcelo Tusset Department of Electronics, Federal University of Technology - Parana, Doutor Washington Subtil Chueire Street, Ponta Grossa, Parana, 84017-220, Brazil
  • Jeferson J. Lima Department of Electronics, Federal University of Technology - Parana, Doutor Washington Subtil Chueire Street, Ponta Grossa, Parana, 84017-220, Brazil
  • Raphaela C. Machado Faculdade de Engenharia de Guaratinguetá, Universidade de São Paulo- UNESP Avenida Doutor Ariberto Pereira da Cunha, Portal das Colinas, 12516410, São Paulo, Brazil

Abstract

Sloshing describes the oscillatory displacement of liquids inside containers subjected to motion. It occurs in various scenarios, including ships, tanks, and other vessels undergoing acceleration, deceleration, or changes in direction. Factors such as sudden changes in speed, wind, waves, and the liquid's own inertia can trigger sloshing. Sloshing has significant implications in fields such as marine engineering and liquid transportation. The forces generated by these oscillations can impact structural integrity and even cause accidents. This research investigates a mathematical model of a tank coupled to an electric motor, our goal is to determine the parameter space of the Lyapunov Exponent, analyze bifurcation diagrams and generate phase maps, and an analysis of the initial conditions to ascertain the basins of attraction formed by the system. These numerical analyses are crucial to identify the parameter ranges that induce chaotic behavior within the system.

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Published

05/31/2025

Issue

Vol. 16 No. 2 (2025): Mathematics in Engineering, Science and Aerospace (MESA)

Section

Articles