Journal of Mechanical Science and Technology 25 (11) (2011) 2769~2774 www.springerlink.com/content/1738-494x DOI 10.1007/s12206-011-0813-1 Vibration localization of a mistuned rotating multi-packet blade system undergoing external cyclic harmonic force † Seung Min Kwon and Hong Hee Yoo * Department of Mechanical Engineering, Hanyang University, Seoul, 133-791, Korea (Manuscript Received June 20, 2011; Revised July 21, 2011; Accepted July 31, 2011) ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract A multi-packet blade system consists of several blades which are attached to a disk and connected through shrouds. The blades of a multi-packet blade system are usually assumed to be identical. However, there always exists small, random mistuning among the blades due to manufacturing tolerance, in-operation wear and environmental changes. Such mistuning may cause significant increase in the forced vibration responses of some blades in the multi-packet blade system. Critical fatigue problems often occur in mistuned systems since the forced vibration response of a mistuned system is often significantly larger than that of a tuned system. Therefore, it is very important to predict the maximum blade response. In this study, blades are idealized as cantilever beams and the flexibilities of the disk and shrouds are idealized as discrete springs. Equations of motion are derived using the hybrid deformation variable method. To realize vibration localization with random mistuning, transient analysis is carried out for a multi-packet blade system excited by multiple nozzle jet forces. Keywords: Forced vibration response; Multi-packet blade system; Random mistuning; Transient analysis; Vibration localization ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction Rotating multi-packet blade systems designed to be cycli- cally periodic are widely used in several turbo machineries, such as turbine generators, turbo engines, turbo fans and rotor craft wings. These periodic structures are comprised of several blades which are attached to a disk and grouped in packets by shrouds. Since the disk and the shroud possess flexibilities, they create stiffness coupling effects between blades. The blades of a multi-packet blade system are usually assumed to be identical. However, there always exists small and random discrepancies among blades due to manufacturing tolerance, operation wear and environmental change. The discrepancy is often called mistuning, which can cause a significant increase in the forced vibration responses of some blades. The increase of stress in a blade can lead to premature failure of the blade. Vibration energy is concentrated to some blades of the mis- tuned system. This is often called the vibration localization of the mistuned system. In order to avoid unexpected premature failure of the system, the effect of mistuning on the vibration localization should be investigated thoroughly. The maximum forced response amplitudes of blades in a mistuned multi-blade system are generally much larger than those of blades in a tuned system [1-3]. Ewins showed that the maximum forced response increases with the increasing of mistuning up to certain level, but increasing the level of mis- tuning beyond this level leads to a decrease in maximum forced response [4]. Ottarsson and Pierre demonstrated this remarkable effect of random mistuning in an analytical study [5]. A study of mode localization in mistuned bladed disks was performed using transfer matrices [6]. Kruse and Pierre carried out a case study for an industrial rotor [7]. In order to decrease the maximum forced response and reduce the ad- verse effects of random mistuning, intentional mistuning could be implemented into the design of a multi-blade system. To overcome the adverse effects of random mistuning, multi- packet blade system design in which blades are grouped into packets was introduced [8]. Thus, multi-packet design intro- duces a form of mistuning which provides a successful detun- ing effect. Castanier and Pierre proposed the intentional mis- tuning of blades in order to reduce the forced response ampli- tudes of turbomachinery rotors [9]. Intentional mistuning was introduced into the model by changing the nominal blade stiffness in rotationally periodic patterns. In this paper, several effects of random mistuning on the statistics of the forced response are investigated. The uncer- tainty effects of blade’s material properties and dimensions for the forced vibration response of a multi-packet blade system † This paper was recommended for publication in revised form by Editor Yeon June Kang * Corresponding author. Tel.: +82 2 2220 0446, Fax.: +82 2 2293 5070 E-mail address: hhyoo@hanyang.ac.kr © KSME & Springer 2011