Nonlinear linear dynamics and numerical analysis of a sloshing tank

Resumo

Sloshing motion in liquids refers to the phenomenon of oscillation or agitation that occurs when a liquid is subjected to movement or disturbance. This can happen in containers, tanks, ships, or any other object that contains liquid and is subject to movement, such as acceleration, deceleration, turning or tilting. These oscillations can be caused by several factors, such as sudden changes in speed, changes in the direction of movement, winds, waves, or even internal movements of the liquid due to its own inertia. Sloshing can have significant effects in different contexts, such as naval engineering, liquid cargo transportation, storage tank projects, among others. Therefore, the study of sloshing is important to ensure the safety and stability of structures that contain moving liquids, as the forces resulting from these oscillations can affect structural integrity and even lead to accidents if they are not properly considered and controlled. Mathematical models and computer simulations are often used to predict and mitigate the effects of sloshing in different applications. Thus, this work investigates a mathematical model that describes a tank coupled to an electric motor, and therefore we determine the parameter space of the Lyapunov Exponent, basins of attraction, bifurcation diagrams and phase maps. These numerical analyzes are important to determine the range of parameters that diagnose chaos in the system.