Mistuning phenomena exist in the bladed disk due to the inevitable deviations among blades' properties, e.g., stiffness, mass, geometry, etc., leading to localization and response amplification. The dynamic performance of mistuned bladed disk is sensitive to the arrangement of blades. The blade arrangement optimization aims to obtain the optimal arrangement that minimizes the influence of mistuning. In this paper, a framework of high efficiency is raised to deal with the challenge of high computational cost this optimization. It comprehensively utilizes mixed-dimensional finite element model (MDFEM), Gaussian process (GP) regression, and genetic algorithm (GA). The MDFEM can perform mistuned modal analysis efficiently and provides the training set of GP regression rapidly. The GP model, as a surrogate model, predicts the desired dynamic performance directly without calculating the numerical model and can function as fitness function in optimization. GA has the capability to deal with combinatorial problems and is a good option for problems with large search domains and several local maxima/minima. The techniques and processes of three methods are illustrated in detail. Case studies, based on a real turbine, are concretely presented in a gradually progressive manner to test and verify the effectiveness, accuracy, and efficiency of methods and entire framework step by step. The results show the satisfactory optimal arrangement for a randomly chosen set of mistuned blades, and the influence of mistuning is reduced indeed. The time cost of the optimization has been reduced several orders of magnitude. This framework can be a promising approach for the blade arrangement optimization problem.

Acoustic metamaterials with unit cells that are integrated with piezoelectric transducer circuitry exhibit interesting band gap behaviors that can be used for wave/vibration manipulation. This research reports the evaluation of uncertainty effects to a typical piezoelectric metamaterial, where uncertainties in geometry/configuration and in circuitry elements are taken into consideration. Monte Carlo-type analysis is performed to assess the band gap features under these uncertainties. In order to facilitate tractable computation in uncertainty analysis, order-reduced modeling of the electromechanically integrated system is formulated. The component mode synthesis-based order-reduced modeling increases the computational efficiency significantly while maintaining good accuracy. Results show that the band gap behavior is generally less sensitive to configuration uncertainty but can be greatly affected by circuitry parameter uncertainty. These results can be used to guide the design and synthesis of piezoelectric metamaterials, and the method developed can be applied to the uncertainty quantification of other types of metamaterials.

In this paper, a novel and efficient modal analysis method is raised to work on blisk structures based on mixed-dimension finite element model (MDFEM). The blade and the disk are modeled separately. The blade model is figured by 3D solid elements considering its complex configuration and its degrees-of-freedom (DOFs) are condensed by dynamic substructural method. Meanwhile, the disk is structured by 2D axisymmetric element developed specially in this paper. The DOFs of entire blisk are tremendously reduced by this modeling approach. The key idea of this method is derivation of displacement compatibility to different dimensional models. Mechanical energy equivalence and summation further contribute to the model synthesis and modal analysis of blade and disk. This method has been successfully applied on the modal analysis of blisk structures in turbine, which reveals its effectiveness and proves that this method reduces the computational time expenses while maintaining the precision performances of full 3D model. Though there is limitation that structure should have proper coverage of blades, this method is still feasible for most blisks in engineering practice.