Research Papers

Free Vibration Response of Thin and Thick Nonhomogeneous Shells by Refined One-Dimensional Analysis

[+] Author and Article Information
Alberto Varello

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

Erasmo Carrera

Professor of Aerospace Structures and
Aeroelasticity Department of Mechanical and
Aerospace Engineering,
Politecnico di Torino,
Corso Duca degli Abruzzi 24,
Torino 10129, Italy;
School of Aerospace, Mechanical and
Manufacturing Engineering,
RMIT University,
Melbourne VIC 3083, Australia
e-mail: erasmo.carrera@polito.it

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 21, 2013; final manuscript received July 24, 2014; published online August 20, 2014. Assoc. Editor: Marco Amabili.

J. Vib. Acoust 136(6), 061001 (Aug 20, 2014) (12 pages) Paper No: VIB-13-1173; doi: 10.1115/1.4028127 History: Received May 21, 2013; Revised July 24, 2014

The free vibration analysis of thin- and thick-walled layered structures via a refined one-dimensional (1D) approach is addressed in this paper. Carrera unified formulation (CUF) is employed to introduce higher-order 1D models with a variable order of expansion for the displacement unknowns over the cross section. Classical Euler–Bernoulli (EBBM) and Timoshenko (TBM) beam theories are obtained as particular cases. Different kinds of vibrational modes with increasing half-wave numbers are investigated for short and relatively short cylindrical shells with different cross section geometries and laminations. Numerical results of natural frequencies and modal shapes are provided by using the finite element method (FEM), which permits various boundary conditions to be handled with ease. The analyses highlight that the refinement of the displacement field by means of higher-order terms is fundamental especially to capture vibrational modes that require warping and in-plane deformation to be detected. Classical beam models are not able to predict the realistic dynamic behavior of shells. Comparisons with three-dimensional elasticity solutions and solid finite element solutions prove that CUF provides accuracy in the free vibration analysis of even short, nonhomogeneous thin- and thick-walled shell structures, despite its 1D approach. The results clearly show that bending, radial, axial, and also shell lobe-type modes can be accurately evaluated by variable kinematic 1D CUF models with a remarkably lower computational effort compared to solid FE models.

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Fig. 1

Cross sections geometry for the one-layer and three-layer cylinders. (a) One-layer cylinder and (b) three-layer cylinder.

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Fig. 2

Procedure to build the element structural stiffness matrix KEL of a B3 element with N = 2

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Fig. 3

Cross section deformation for different lobe-type modes

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Fig. 4

Dimensionless frequency parameter for different 1D models. Bending modes.

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Fig. 5

Dimensionless frequency parameter for different 1D models. Two-lobe modes.

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Fig. 6

Dimensionless frequency parameter for different 1D models. Three-lobe modes.

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Fig. 7

Dimensionless frequency parameter for different 1D models. Four-lobe modes.

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Fig. 8

Third bending modal shape (b.3). (a) Present 1D model and (b) NASTRAN solid model.

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Fig. 9

Second radial modal shape (r.2). (a) Present 1D model and (b) NASTRAN solid model.

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Fig. 10

First axial modal shape (a.1). (a) Present 1D model and (b) NASTRAN solid model.

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Fig. 11

Fifth two-lobe modal shape (2.5). (a) Present 1D model and (b) NASTRAN solid model.

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Fig. 12

Fourth three-lobe modal shape (3.4). (a) Present 1D model and (b) NASTRAN solid model.

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Fig. 13

Second four-lobe modal shape (4.2). (a) Present 1D model and (b) NASTRAN solid model.




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