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Technical Brief

Layerwise Analyses of Compact and Thin-Walled Beams Made of Viscoelastic Materials

[+] Author and Article Information
Matteo Filippi

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

Erasmo Carrera

Professor of Aerospace Structures and Aeroelasticity
Department of Mechanical and Aerospace Engineering,
Politecnico di Torino,
Torino 10129, Italy
e-mail: erasmo.carrera@polito.it

Andrea M. Regalli

Department of Mechanical and Aerospace Engineering,
Politecnico di Torino,
Torino 10129, Italy
e-mail: andreamariaregalli@yahoo.it

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 7, 2016; final manuscript received June 23, 2016; published online July 19, 2016. Assoc. Editor: Mahmoud Hussein.

J. Vib. Acoust 138(6), 064501 (Jul 19, 2016) (9 pages) Paper No: VIB-16-1010; doi: 10.1115/1.4034023 History: Received January 07, 2016; Revised June 23, 2016

This paper evaluates the vibration characteristics of structures with viscoelastic materials. The mechanical properties of viscoelastic layers have been described with the complex modulus approach. The equations of motion are derived using the principle of virtual displacement (PVD), and they are solved through the finite element method (FEM). Higher-order beam elements have been derived with the Carrera Unified Formulation (CUF), which enables one to go beyond the assumptions of the classical one-dimensional (1D) theories. According to the layerwise approach, Lagrange-like polynomial expansions have been adopted to develop the kinematic assumptions. The complex nonlinear dynamic problem has been solved through an iterative technique in order to consider both constant and frequency-dependent material properties. The results have been reported in terms of frequencies and modal loss factors, and they have been compared with available results in the literature and numerical three-dimensional (3D) finite element (FE) solutions. The proposed beam elements have enabled bending, torsional, shell-like, and coupled mode shapes to be detected.

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Figures

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Fig. 1

Coordinates mapping between coordinate systems

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Fig. 2

Dimensions of rectangular cross section beam

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Fig. 3

Root loci related to the first six torsional mode shapes of the asymmetric structure

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Fig. 4

Frequencies (a) and modal loss factors and (b) related to the first torsional mode shape of the orthotropic beam [θ/core/−θ]. ηc = 0.6

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Fig. 5

Frequencies and modal loss factors related to the first mode shapes of the orthotropic beam [θ/core/θ]. ηc = 1.5. “—”: 3D FE, “– – –”: 3L16 (a) bending frequencies, (b) bending loss factors, (c) torsional frequencies, and (d) torsional loss factors.

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Fig. 6

Dimensions (mm) and numerical models for the I-beam damper: (a) LE9 model (5475DOFs) and (b) solid model (56,400DOFs)

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Fig. 7

Mode shapes, frequencies, and modal loss factors of the cantilevered I-beam damper: ηc = 1.5 (a) f = 90.774 Hz, η = 0.0626, f = 90.955 Hz, η = 0.0626, (b) f = 102.643 Hz, η = 0.0242, f = 105.409 Hz, η = 0.0284, (c) f = 391.10 Hz, η = 0.0926, f = 402.815 Hz, η = 0.0903, (d) f = 407.67 Hz, η = 0.0101, f = 408.954 Hz, η = 0.0124, (e) f = 427.01 Hz, η = 0.174, f = 428.394 Hz, η = 0.175, (f) f = 437.722 Hz, η = 0.0124, f = 443.777 Hz, η = 0.0143, (g) f = 480.01 Hz, η = 1.012, f = 419.294 Hz, η = 1.388, (h) f = 554.236 Hz, η = 0.0349, f = 566.047 Hz, η = 0.0354, (i) f = 597.675 Hz, η = 0.802, f = 550.543 Hz, η = 0.971, and (j) f = 68.150 Hz, η = 0.0002, f = 68.341 Hz, η = 0.0002

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