Structural optimization with an automatic mode identification method for tracking the local vibration mode

Traditional optimization methods, which take a specific order of modal frequency as the design constraint, could fail to obtain the desired solution because of modal substitution. An improved optimization model with continuous sizing variables is established to solve this problem, in which the minimum weight and a given local modal frequency are considered as the objective and the constraint. To capture accurately the expected mode of vibration, a local mode identification technique is proposed based on the strain energy ratio between the local area and the whole structure. With that scheme, an optimization system is developed, in which the local mode can be effectively identified and the constraint can be updated with it in the iteration process. Two numerical examples, of a reinforced plate and a satellite structure, are applied to illustrate the effectiveness and efficacy of the proposed method.