On antiresonance in the forced response of mistuned bladed disks

Mistuning in bladed disks usually increases the maximum local forced response leading to shortened component life in turbine engines. This paper investigates mistuning using a transfer function approach where the frequency response functions (FRFs) are described by natural frequencies and antiresonant frequencies. Using this approach, antiresonant frequencies are shown to be a critical factor in determining the maximum local response. Two insights are gained by formulating antiresonant frequencies as the eigenvalues of reduced system matrices: 1) Mistuning a particular blade has no affect on that blade's antiresonant frequencies. 2) Engine orders N and N/2, where N is the number of blades on the disk, tend to produce the highest maximum local response. Numerical examples are given using a lightly damped spring mass oscillator model of a bladed disk. Pole-zero loci of mistuned bladed disks show that increased maximum response is often due to the damping of antiresonant frequencies. An important conclusion is that antiresonant frequencies can be arranged such that a mistuned bladed disk has a lower maximum response than a tuned bladed disk.