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Technical Brief

Superharmonic Resonance of Cross-Ply Laminates by the Method of Multiple Scales

[+] Author and Article Information
Hadj Youzera

Laboratoire des Structures et Matériaux Avancés dans le
Génie Civil et Travaux Publics,
Université de Sidi Bel Abbes,
Sidi Bel Abbes 22000, Algérie;
Department of Civil Engineering,
Université Mustapha Stambouli of Mascara,
Mascara 29000, Algeria

Sid Ahmed Meftah

Laboratoire des Structures et Matériaux Avancés dans le
Génie Civil et Travaux Publics,
Université de Sidi Bel Abbes,
Sidi Bel Abbes 22000, Algérie

El Mostafa Daya

Laboratoire d'Etude des Microstructures et de Mécanique
des Matériaux (LEM3),
Université de Lorraine,
UMR CNRS 7239,
Ile du Saulcy,
Metz Cedex 01 F-57045, France
e-mail: meftahs@yahoo.com; daya@univ-metz.fr

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 24, 2015; final manuscript received May 23, 2017; published online June 16, 2017. Assoc. Editor: Mohammad Younis.

J. Comput. Nonlinear Dynam 12(5), 054503 (Jun 16, 2017) (9 pages) Paper No: CND-15-1451; doi: 10.1115/1.4036914 History: Received December 24, 2015; Revised May 23, 2017

General differential equations of motion in nonlinear forced vibration analysis of multilayered composite beams are derived by using the higher-order shear deformation theories (HSDT's). Viscoelastic properties of fiber-reinforced plastic composite materials are considered according to the Kelvin–Voigt viscoelastic model for transversely isotropic composite materials. The method of multiple scales is employed to perform analytical frequency amplitude relationships for superharmonic resonance. Parametric study is conducted by considering various geometrical and material parameters, employing HSDT's and first-order deformation theory (FSDT).

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Figures

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Fig. 1

Laminated composite beam geometry under uniform distributed load q(t)

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Fig. 2

Nonlinear amplitude frequency responses of the stacking sequence (−45 deg/45 deg/−45 deg/45 deg/−45 deg/45 deg/−45 deg/45 deg) composite beam when ω is near ωl/3, according to different kinematical models

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Fig. 3

Nonlinear amplitude frequency responses with Reddy model when ω is near ωl/3 according to the different stacking sequences of the composite beams

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Fig. 4

Nonlinear amplitude frequency responses of the stacking sequence (−45 deg/45 deg/−45 deg/45 deg/−45 deg/45 deg/−45 deg/45 deg) composite beam with Reddy model when ω is near ωl/3 for different amplitude of excitation F

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Fig. 5

Nonlinear amplitude frequency responses of the stacking sequence (−45 deg/45 deg/−45 deg/45 deg/−45 deg/45 deg/−45 deg/45 deg) composite beam with Reddy model when ω is near ωl/3 for different values of loss factor η1

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