Research Papers

Accurate Nonlinear Dynamics and Mode Aberration of Rotating Blades

[+] Author and Article Information
M. Filippi

Mul2 Group,
Department of Mechanical and
Aerospace Engineering,
Politecnico di Torino,
Turin 10129, Italy
e-mail: matteo.filippi@polito.it

A. Pagani, E. Carrera

Mul2 Group,
Department of Mechanical and
Aerospace Engineering,
Politecnico di Torino,
Turin 10129, Italy

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 9, 2018; final manuscript received June 26, 2018; published online July 24, 2018. Assoc. Editor: Ahmet S. Yigit.

J. Appl. Mech 85(11), 111004 (Jul 24, 2018) (7 pages) Paper No: JAM-18-1269; doi: 10.1115/1.4040693 History: Received May 09, 2018; Revised June 26, 2018

Nonlinear dynamics and mode aberration of rotating plates and shells are discussed in this work. The mathematical formalism is based on the one-dimensional (1D) Carrera unified formulation (CUF), which enables to express the governing equations and related finite element arrays as independent of the theory approximation order. As a consequence, three-dimensional (3D) solutions accounting for couplings due to geometry, material, and inertia can be included with ease and with low computational costs. Geometric nonlinearities are incorporated in a total Lagrangian scenario and the full Green-Lagrange strains are employed to outline accurately the equilibrium path of structures subjected to inertia, centrifugal forces, and Coriolis effect. A number of representative numerical examples are discussed, including multisection blades and shells with different radii of curvature. Particular attention is focused on the capabilities of the present formulation to deal with nonlinear effects, and comparison with s simpler linearized approach shows evident differences, particularly in the case of deep shells.

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Grahic Jump Location
Fig. 7

Equilibrium curves of the (a) shallow and (b) deep shells. “△”: nonlinear TE3 model; “□”: nonlinear L9 model; “dashed lines”: linearized approach; “−⋄−”: Shell FEM [15].

Grahic Jump Location
Fig. 1

Sketch of the multisection prismatic blade

Grahic Jump Location
Fig. 2

Frequency evolutions versus the rotational speed for multisection beams: (a) L=0.9525, Lh=0.0635 m, ρ1=ρ2=ρ0; (b) L=0.9525, Lh=0.0635 m, ρ1=0.5ρ0 and ρ2=1.5ρ0; (c) L=0.4318, Lh=0.5842 m, ρ1=0.5ρ0 and ρ2=1.5ρ0. “△”: NL TE3 model; “□”: NL 2L9 model; “○”: NL shell element [13]; “solid lines”: NL beam element [13].

Grahic Jump Location
Fig. 3

Sketch of fan blades

Grahic Jump Location
Fig. 4

Mode shapes of the (a) shallow and (b) deep shells

Grahic Jump Location
Fig. 5

Frequency evolutions versus the rotational speed for fan blades: (a) linearized and (b) nonlinear approach for the shallow shell. “△”: NL TE6 model; “□”: NL L9 model; “−⋄−”: Shell FEM [15].

Grahic Jump Location
Fig. 6

Frequency evolutions versus the rotational speed for fan blades: (a) linearized and (b) nonlinear approach for the deep shell. “□”: NL L9 model; “−⋄−”: Shell FEM [15].



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