Nonlinear Vibration Analysis of Cracked Structures

The dynamics of cracked structures feature non-smooth nonlinearity due to the repetitive opening and closing of the crack faces. Accurate prediction of resonant frequencies and response shapes of such structures is very important for practical applications such as damage detection and structural health monitoring. However, traditional linear and nonlinear vibration analysis tools that are typically employed with FE models fail to accurately predict such phenomena. In our research, highly efficient and accurate methods have been developed for predicting such phenomena, and successfully applied to problems with realistic complexity, such as turbine engine blades with cracks. We also develop models which account for fluid-structure interactions which affect localization and high-cycle fatigue.

Vibration Analysis of Multi-stage Turbine Engine Rotors

Turbine engine rotors have multiple stages of bladed disks without special symmetry. Vibration of stages is fully coupled and shows complicated dynamics. In our research, characteristics of such phenomena have been investigated, and an efficient computational method has been developed for model-based vibration prediction. The method uses only a single segment per stage and enables us to predict the vibration response of the entire multi-stage turbine engine rotors.

Nonlinear Parametric Reduced Order Models

Structural analyses based on finite element models (FEMs) are often used to predict vibration responses, stresses, and other structural characteristics to support design processes. As computing power increases, numerical simulations continue to replace experiments for testing new designs. However, the complexity of the designs can make the computational analysis very slow when many component changes are needed during the design process. This issue is particularly important in industrial FEMs which require extremely accurate structural response data, and therefore contain millions of degrees of freedom (DOFs). The large computational cost of direct analyses on these large FEMs detrimentally affects the design cycle, especially when it is necessary to evaluate the effects of parametric variability and damages on the structural response. Additionally, when the structure has a crack, it is well known that system-level response characteristics of cracked structures differ from their healthy counterparts. In general, a nonlinear analysis is needed to predict the vibration response of a cracked structure because the periodic opening and closing of the crack surfaces leads to a nonlinear response. This nonlinear analysis is complex and is computationally expensive. To alleviate these issues, we developed efficient approaches for reduced order modeling of complex cracked structures such as parametric reduced order models (PROMs), component mode synthesis with static mode compensation (SMC-CMS), bilinear frequency approximation (BFA), and bilinear mode approximation (BMA).

PROMs have been developed for fast reanalysis in the presence of structural variations. These models are able to handle simultaneously with very high efficiency both parametric variability and damage. In addition, for geometric variations (dents), the SMC-CMS has been developed. For SMC-CMS, a set of basis vectors can be established using a combination of normal modes of the pristine structure compensated by static modes. The key advantage of SMC-CMS is when the dent shapes are changed, normal modes of the dented structure do not need to be reconstructed because the normal mode is easily obtained by calculating the static mode from the new dent. Furthermore, for the cracked structure analysis, BFA and BMA have been developed. Although the generalized BFA and BMA cannot capture the effects of gradual opening and closing of the cracks, they can provide excellent approximate values for the resonant frequencies and response of complex cracked structures. The BFA and BMA are linear analyses, so the calculation time to obtain the dynamic response of cracked structures is much less than that of the nonlinear analyses.