Robust dynamic analysis of detuned-mistuned rotating bladed disks with geometric nonlinearities

Abstract

This work is devoted to the robust analysis of the effects of geometric nonlinearities on the nonlinear dynamic behavior of rotating detuned (intentionally mistuned) bladed disks in presence of unintentional mistuning (simply called mistuning). Mistuning induces uncertainties in the computational model, which are taken into account by a probabilistic approach. This paper presents a series of novel results of the dynamic behavior of such rotating bladed disks exhibiting nonlinear geometric effects. The structural responses in the time domain are analyzed in the frequency domain. The frequency analysis exhibits responses outside the frequency band of excitation. The confidence region of the stochastic responses allows the robustness to be analyzed with respect to uncertainties and also allows physical insights to be given concerning the structural sensitivity. The bladed disk structure is made up of 24 blades for which several different detuned patterns are investigated with and without mistuning.

A Table of patterns

Pattern number	Arrangement
${\mathcal {P}}_{0}$	24A
${\mathcal {P}}_{1}$	$(5A1B)_4$
${\mathcal {P}}_{2}$	$(AB)_{12}$
${\mathcal {P}}_{3}$	$(4A4B)_{3}$
${\mathcal {P}}_{4}$	4A2B3A2B5A2B3A2B
${\mathcal {P}}_{5}$	$(3A3B)_4$
${\mathcal {P}}_{6}$	$(4A2B)_4$
${\mathcal {P}}_{7}$	$AB2A2B(AB)_2 2A2B2AAB2B(AB)_2$
${\mathcal {P}}_{8}$	$2A BA 2B 2A 3B (AB)_{2} 2AB 3A 3B$
${\mathcal {P}}_{9}$	$(2A2B)_6$
${\mathcal {P}}_{10}$	$4A4B(2A2B)_{2}2A6B$
${\mathcal {P}}_{11}$	B4AB18A
${\mathcal {P}}_{12}$	12A12B
${\mathcal {P}}_{13}$	6B12A3B3A
${\mathcal {P}}_{14}$	3B15A3B3A
${\mathcal {P}}_{15}$	6A3B6A9B
${\mathcal {P}}_{16}$	$(3B6A)_23B3A$
${\mathcal {P}}_{17}$	3A6B3A12B
${\mathcal {P}}_{18}$	3B12A6B3A
${\mathcal {P}}_{19}$	18A6B
${\mathcal {P}}_{20}$	3B12A6B3A
${\mathcal {P}}_{21}$	6B9A6B3A
${\mathcal {P}}_{22}$	6A3B3A12B
${\mathcal {P}}_{23}$	9A3B6A6B
${\mathcal {P}}_{24}$	14A9B
${\mathcal {P}}_{25}$	3A3B3A15B
${\mathcal {P}}_{26}$	15B9A
${\mathcal {P}}_{27}$	3B6A12B3A
${\mathcal {P}}_{28}$	3A21B
${\mathcal {P}}_{29}$	$3A3B(3A6B)_2$
${\mathcal {P}}_{30}$	$(3A3B)_2 3A 9B$
${\mathcal {P}}_{31}$	$(6A6B)_2$
${\mathcal {P}}_{32}$	3B9A9B3A
${\mathcal {P}}_{33}$	3B21A
${\mathcal {P}}_{34}$	6A6B3A9B
${\mathcal {P}}_{35}$	18A6B
${\mathcal {P}}_{36}$	3B12A3B6A
${\mathcal {P}}_{37}$	3B6A3B3A6B3A
${\mathcal {P}}_{38}$	6A8B3A6B
${\mathcal {P}}_{39}$	9A3B3A9B
${\mathcal {P}}_{40}$	3B9A3B3A3B3A
${\mathcal {P}}_{41}$	3B6A6B3A3B3A
${\mathcal {P}}_{42}$	3B9A6B6A
${\mathcal {P}}_{43}$	$(3A3B)_4$
${\mathcal {P}}_{44}$	$(3A9B)_2$
${\mathcal {P}}_{45}$	$(9A3B)_2$