The unbalanced rotating cylinder partially filled with fluid; multiple scales analysis of a forced Korteweg–de Vries–Burgers equation

The paper is concerned with an unbalanced cylindrical rotor containing a small amount of fluid, spun out to form a thin layer on the inner surface of the cylinder. The main interest is in the possibility of this fluid layer to counterbalance an unbalanced point mass. By such an application, the system is often called a ‘fluid balancer.’ The paper considers the case where the fluid is not locked-in to the forcing frequency dictated by the unbalanced mass, but is, with the rotor, in a state of asynchronous whirl. This will imply an inherent slow drift away from a balanced condition. Another main interest of the paper is the derivation of approximate analytical solutions to the nonlinear, forced equation that governs the fluid layer thickness perturbation. This equation is of the forced Korteweg–de Vries–Burgers type, and the analysis is based on the method of multiple scales. The leading-order solution is capable of giving a qualitative explanation of the balancing effect of the fluid, in other words, to explain the mechanics of the fluid balancer. Good agreement between theoretical and experimental results is found.