Approximate symplectic approach for mistuned bladed disk dynamic problem

A blade disk system plays a crucial role in the energy conversion efficiency of turbomachinery. Generally, a bladed disk is designed as a tuned system, which implies that the dynamic behaviors of all the blades are identical. In practice, there are some differences between the blades, known as mistuning, that can result in localized vibration. Thus, in this study, an approximate symplectic method developed to reproduce the vibration localization in a mistuned bladed disk system, that can provide guidance for designing vibration control strategies for the system. Considering the morphological characteristics of the interface roughness and the dynamic/stickiness characteristics of the sliding joint surface, an improved dry friction model is established to describe the coupling effects between the blades. Considering the micro-dynamic behaviors of the multi-joint surfaces, the dynamic problem of the entire bladed disk system is formulated as a set of ordinary differential equations (ODEs). An approximate symplectic method is developed in the Hamiltonian framework to simulate the vibration of each blade in the mistuned bladed disk system. From the numerical results reported, the phenomenon of vibration localization in the mistuned bladed disk system is reproduced in the comparison with the results in the tuned bladed disk system. In addition, the influences of the initial positive pressure, contact angle, and roughness of the surfaces on the strength of the vibration localization are revealed in detail in the numerical simulations.