Tuning a Vibrating Blade Dynamic Vibration Absorber by using Ant Colony Optimization and Finite Element Modeling

Abstract

The present contribution deals with the optimal tuning of a vibrating blade dynamic vibration absorber (VBDVA). To achieve this aim, the natural optimization technique named Ant Colony Optimization (ACO) is applied to the finite element model of the system. Dynamic vibration absorbers (DVAs) are systems constituted by mass, spring and damping elements (secondary structure), which are coupled to a mechanical system (primary structure). The main idea behind the DVAs is the generation of a force, which has the same intensity of the excitation force but in the opposite phase [1]. This phenomenon is known as anti-resonance. The tuning of the DVAs is the procedure that sets the anti-resonance frequency to a given value by changing the DVA parameters (mass, spring and damping values). VBDVA was studied in this work, which is composed by a blade that is subjected to an initial tension and fixed lumped mass. These three parameters (the mass value and its position and the initial tension) are responsible for the VBDVA tuning [2]. Supported by this theory, the optimization problem is described as the minimization of the objective function that relates the difference between the resonance frequencies of the primary system and the VBDVA. The optimum tuning defines the minimum difference respecting the design constraints. To solve the optimization problem it was used ACO [3]. This population-based technique is inspired in the behavior of real ants and their communication scheme by using pheromone trail. A moving ant lays some pheromone on the ground, thus marking the path. The collective behavior that emerges from the participating agents is a form of positive feedback where the more the ants follow a trail, the more attractive that trail becomes for being followed. In the early nineties, when the Ant Colony algorithm was first proposed, it was used as an approach for the solution of combinatorial optimization problems, such as the traveling salesman problem. However, the extension for continuous variables is recent and it is still under development. In this context, this paper presents an engineering application of a continuous domain problem of ACO. Numerical results are reported, illustrating the success of using the methodology presented, as applied to mechanical systems.