Analysis of sensitivity and optimization for mistuned bladed disk forced response using high-fidelity models

An effective method is developed for efficient calculations of the sensitivity of the maximum forced response levels for mistuned bladed disks with respect to blade frequency mistuning. The expressions for 1st and 2nd order sensitivity coefficients are derived in an analytical form which provides high accuracy and computational efficiency. Then, the optimization methods are used for searching the best and worst mistuning patterns of bladed disks. Two major types of the mistuning optimization problems are considered: (i) a continuous optimization problem when the blade mistuning can take any values from a prescribed range and (ii) a combinatorial optimization problem, when the set of mistuned blades is given and the optimization can be achieved by blade re-arrangement in a disk. For the first type of the optimization problem a set of sensitivity-based optimization algorithms is applied and for the second type a variant of a genetic algorithm is developed. The analysis of mistuning sensitivity coefficients and results of optimization searching are shown on an example of a realistic turbine bladed disk