Action of pendulum in transient fluid flow

Abstract

The work is dedicated to the authors' latest research on the interaction of moving inflexible objects when subjected to non-constant velocity fluid flow (air, water) without the use of work-intensive space-time programming methods. In the first part of the study, the differential equation of the plane pendulum motion is derived using the novel approach of fluid-rigid body interaction phenomenon, in this equation, the moment caused by the fluid interaction is simplified by ignoring the flow viscosity. This makes it possible to obtain the usual second-order differential equation of pendulum motion, which contains components of relative velocity in a simplified way, instead of the partial differential equations in a continuous mathematical space. The application of the obtained equation is further used in solving specific tasks of engineering importance. The first task analyzes the pendulum swing motion in a still airflow. Here, the equation described above is numerically integrated and the results are compared with an experiment in a natural environment. The comparison resulted in a drag interaction factor that was further used in other more complex cases. The second task analyzes the pendulum motion when fluid flow velocities are a decreasing function of time in a harmonic behavior. In addition, in this case, the possibilities of applying the developed theory to other forms of flow rate change, such as pulse or poly harmonic forms, are considered. In the third task, the synthesis of motion control in a mechatronic system was performed. In this case, the possibility of regulating the additional resistance torque arising from the rotary damping generator is considered. The work is illustrated with graphical results. The outcomes obtained in the work can be used in the analysis of the interaction of existing moving objects with the fluid flow, as well as in the synthesis of new technological processes, for example, for obtaining energy from vibrating objects immersed in fluid flow.