Searching for the Optimal Arrangement of Mistuned Blades Based on Solving the Traveling Salesman Problem for Simple Mass-Spring Linear System

The article presents an approach to finding the optimal arrangement of blades in a bladed disk based on solving the traveling salesman problem using the ant colony algorithm. The solution to the problem is presented for an equivalent model of the bladed disk. The mistuning parameters are assumed as known — for example, from the data of geometric measurements for each blade from the set used for assembling the bladed disk — considering the influence of the rotation on the investigated resonance mode. Approaches have already been published for the construction of equivalent models and the use of combinatorial optimization methods, including solving the traveling salesman problem, to find the optimal arrangement of the blades. Therefore, this article focuses on demonstrating a simple program implementation of this method. This approach allows a quick assessment of the effect of the blade assembly in the bladed disk on the amplitudes of alternating stresses. It even considers several restarts of the algorithm to determine other possible configurations of the system.