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Research Papers

Free Vibration Analysis of Thin-Walled Cylinders Reinforced With Longitudinal and Transversal Stiffeners

[+] Author and Article Information
E. Carrera

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

E. Zappino

e-mail: enrico.zappino@polito.it

M. Filippi

e-mail: matteo.filippi@polito.it
Department of Aeronautic and Space Engineering, Politecnico di Torino,
Corso Duca degli Abruzzi 24,
10129 Torino, Italy

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received March 6, 2012; final manuscript received July 13, 2012; published online February 4, 2013. Assoc. Editor: Marco Amabili.

J. Vib. Acoust 135(1), 011019 (Feb 04, 2013) (11 pages) Paper No: VIB-12-1057; doi: 10.1115/1.4007559 History: Received March 06, 2012; Revised July 13, 2012

This paper deals with the dynamic analysis of reinforced thin-walled structures by means of refined one-dimensional models. Complex reinforced structures are considered which are built by using different components: skin, ribs, and stringers. Higher-order one-dimensional model based on the Carrera unified formulation (CUF) are used to model panels, stringer, and ribs by referring to a unique model. The finite element method (FEM) is used to provide a solution that deals with any boundary condition configuration. The structure is geometrically linear and the materials are isotropic and elastic. The dynamic behavior of a number of reinforced thin-walled cylindrical structures have been analyzed. The effects of the reinforcements (ribs and stringers) are investigated in terms of natural frequencies and modal-shapes. The results show a good agreement with those from commercial codes by reducing the computational costs in terms of degrees of freedom (DOFs).

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Figures

Grahic Jump Location
Fig. 1

Reference frame of the model

Grahic Jump Location
Fig. 2

Reference system and geometries of the different models. Model 1: only skin; model 2: skin and stringers; model 3: skin and ribs; model 4: skin, stringers, and ribs.

Grahic Jump Location
Fig. 3

Flexural normal modes of Table 1 obtained with the theory N = 10 (a) f = 46.590 Hz (b) f = 106.500 Hz (c) f = 177.589 Hz

Grahic Jump Location
Fig. 4

Torsional normal modes of Table 1 obtained with the theory N = 10 (a) f = 105.874 Hz (b) f = 211.747 Hz (c) f = 317.261 Hz

Grahic Jump Location
Fig. 5

Shell-like modal shapes with different values of M and L. (a) M = 2, L = 1 (b) M = 3, L = 2 (c) M = 4, L = 3.

Grahic Jump Location
Fig. 6

Flexural normal modes of Table 6 obtained with the theory N = 10 (a) f = 296.048 Hz (b) f = 324.025 Hz (c) f = 365.126 Hz

Grahic Jump Location
Fig. 7

Shell-like normal modes of Table 7 relative to the theory N = 28, M = 2, Lb = 1 (a) f = 85.526 Hz (b) y = 0 m (c) y = 3.75 m (d) y = 7.50 m (e) y = 11.25 m (f) y = 15 m

Grahic Jump Location
Fig. 8

Shell-like normal modes of Table 7 relative to the theory N = 28, M = 2, Lb = 1 (a) f = 102.981 Hz, (b) y = 0 m, (c) y = 3.75 m (d) y = 7.50 m (e) y = 11.25 m (f) y = 15 m

Grahic Jump Location
Fig. 9

Shell-like normal modes of Table 7 relative to the theory N = 28, M = 2, Lb = 1 (a) f = 111.835 Hz (b) y = 0 m (c) y = 3.75 m (d) y = 7.50 m (e) y = 11.25 m (f) y = 15 m

Grahic Jump Location
Fig. 10

Shell-like normal modes of Table 7 relative to the theory N = 28, y0 = L/9, M = 3, Lb = 2 (a) f = 118.628 Hz (b) y = 0 (c) y = y0 (d) y = 2y0 (e) y = 4y0 (f) y = 5y0 (g) y = 7y0 (h) y = 8y0 (i) y = 9y0

Grahic Jump Location
Fig. 11

Shell-like normal modes of Table 7 relative to the theory N = 28, y0 = L/9, M = 3, Lb = 2 (a) f = 121.170 Hz (b) y = 0, (c) y = y0 (d) y = 2y0 (e) y = 4y0 (f) y = 5y0 (g) y = 7y0 (h) y = 8y0 (i) y = 9y0

Grahic Jump Location
Fig. 12

Shell-like normal modes of Table 7 relative to the theory N = 28, y0 = L/9, M = 3, Lb = 2 (a) f = 126.894 Hz (b) y = 0 (c) y = y0 (d) y = 2y0(e) y = 4y0 (f) y = 5y0 (g) y = 7y0 (h) y = 8y0 (i) y = 9y0

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