Research Papers

Component-Wise Method Applied to Vibration of Wing Structures

[+] Author and Article Information
E. Carrera

Professor of Aerospace Structures and Aeroelasticity
e-mail: erasmo.carrera@polito.it

A. Pagani

Ph.D. student
e-mail: alfonso.pagani@polito.it

M. Petrolo

Research Assistant
e-mail: marco.petrolo@polito.it
Department of Mechanical and Aerospace Engineering,
Politecnico di Torino,
Corso Duca degli Abruzzi 24,
10129 Torino, Italy

1Corresponding author.

Manuscript received May 18, 2012; final manuscript received October 15, 2012; accepted manuscript posted October 22, 2012; published online May 16, 2013. Assoc. Editor: Marc Geers.

J. Appl. Mech 80(4), 041012 (May 16, 2013) (15 pages) Paper No: JAM-12-1198; doi: 10.1115/1.4007849 History: Received May 18, 2012; Revised October 15, 2012; Accepted October 22, 2012

This paper proposes advanced approaches to the free vibration analysis of reinforced-shell wing structures. These approaches exploit a hierarchical, one-dimensional (1D) formulation, which leads to accurate and computationally efficient finite element (FE) models. This formulation is based on the unified formulation (UF), which has been recently proposed by the first author and his coworkers. In the study presented in this paper, UF was used to model the displacement field above the cross-section of reinforced-shell wing structures. Taylor-like (TE) and Lagrange-like (LE) polynomial expansions were adopted above the cross-section. A classical 1D FE formulation along the wing's span was used to develop numerical applications. Particular attention was given to the component-wise (CW) models obtained by means of the LE formulation. According to the CW approach, each wing's component (i.e. spar caps, panels, webs, etc.) can be modeled by means of the same 1D formulation. It was shown that Msc/Patran® can be used as pre- and postprocessor for the CW models, whereas Msc/Nastran® DMAP alters can be used to solve the eigenvalue problems. A number of typical aeronautical structures were analyzed and CW results were compared to classical beam theories (Euler-Bernoulli and Timoshenko), refined models (TE) and classical solid/shell FE solutions from the commercial code Msc/Nastran®. The results highlight the enhanced capabilities of the proposed formulation. In fact, the CW approach is clearly the natural tool to analyze wing structures, since it leads to results that can only be obtained through 3D elasticity (solid) elements whose computational costs are at least one-order of magnitude higher than CW models.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Fig. 1

Coordinate frame of the beam model

Grahic Jump Location
Fig. 2

Cross-section L-elements in natural geometry: (a) four-point element, L4; (b) nine-point element, L9

Grahic Jump Location
Fig. 3

Two assembled L9 elements in actual geometry

Grahic Jump Location
Fig. 4

From a 3D problem to 1D CUF finite elements, TE and LE approaches

Grahic Jump Location
Fig. 5

Differences between the TE and LE models

Grahic Jump Location
Fig. 6

Component-wise approach to simultaneously model panels, stringers and ribs

Grahic Jump Location
Fig. 7

Three-stringer spar modeled with L9 elements

Grahic Jump Location
Fig. 10

Frequencies and vibration modes versus beam models in the case of the two-stringer spar

Grahic Jump Location
Fig. 9

L9 distributions above the cross-section, LE models of the two-stringer spar: (a) 3 L9, (b) 4 L9

Grahic Jump Location
Fig. 11

Shell-like ninth mode of the two-stringer spar: (a) 3 L9 model (14.97 Hz), (b) 4 L9 model (12.70 Hz), (c) SOLID model (11.58 Hz)

Grahic Jump Location
Fig. 12

MAC values between the CW models and the SOLID model, two-stringer spar: (a) 3 L9 CW model, (b) 4 L9 CW model

Grahic Jump Location
Fig. 13

Three-stringer spar

Grahic Jump Location
Fig. 14

MAC values, three-stringer spar

Grahic Jump Location
Fig. 15

Local modes, 5 L9 (LE) model of the three-stringer spar: (a) mode 12, f12 = 31.21 Hz, (b) mode 21, f21 = 84.66 Hz, (c) mode 29, f29 = 104.99 Hz

Grahic Jump Location
Fig. 16

Local modes, Msc/Nastran® solid models of the three-stringer spar: (a) mode 12, f12 = 29.69 Hz, (b) mode 19, f19 = 58.24 Hz

Grahic Jump Location
Fig. 17

Rectangular wing boxes

Grahic Jump Location
Fig. 18

Natural frequencies values versus structural model. Comparison between the ribbed and the rib-free configuration.

Grahic Jump Location
Fig. 19

A bending and a differential–bending modal shape. Seventh order (N = 7) TE model of the wing box without the rib: (a) mode 2, f2 = 60.39 Hz, (b) mode 3, f3 = 63.49 Hz.

Grahic Jump Location
Fig. 20

Shell-like modes, LE models of the rectangular wing boxes: (a) mode 7, f7 = 13.38 Hz, (b) mode 14, f14 = 30.28 Hz, (c) mode 51, f51 = 135.74 Hz

Grahic Jump Location
Fig. 21

Local modes, Msc/Nastran® solid models of the rectangular wing boxes: (a) mode 7, f7 = 12.58 Hz, (b) mode 22, f22 = 28.75 Hz, (c) mode 62, f62 = 66.16 Hz

Grahic Jump Location
Fig. 22

Cross-section of the wing, dimensions in millimeters

Grahic Jump Location
Fig. 23

Shell-like modes of the wing (configuration A) evaluated with the CW model: (a) mode 10 (89.35 Hz), (b) mode 26 (142.91 Hz)

Grahic Jump Location
Fig. 24

Shell-like modes of the wing (configuration A) evaluated with the CW model. Midspan cross-section: (a) mode 8 (86.36 Hz), (b) mode 9 (88.94 Hz), (c) mode 54 (246.70 Hz).

Grahic Jump Location
Fig. 25

Shell-like modes of the wing (configuration A) evaluated with the SOLID model. Midspan cross-section: (a) mode 10 (75.13 Hz), (b) mode 8 (73.85 Hz), (c) mode 51 (218.63 Hz).

Grahic Jump Location
Fig. 26

MAC values between the CW models and the SOLID model, complete aircraft wing (configuration A)




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In