Dynamic stiffness analysis for free vibrations of axially loaded laminated composite beams

2008 ◽  
Vol 84 (1) ◽  
pp. 87-98 ◽  
Author(s):  
Jun Li ◽  
Hongxing Hua ◽  
Rongying Shen
Keyword(s):  
Dynamic Stiffness ◽  
Laminated Composite ◽  
Composite Beams ◽  
Free Vibrations ◽  
Stiffness Analysis ◽  
Axially Loaded ◽  
Laminated Composite Beams

Geometrically Nonlinear Free Vibrations of Laminated Composite Beams: An Effective Formulation

2011 ◽  
Vol 105-107 ◽  
pp. 1681-1684 ◽  
Author(s):  
Khalid El Bikri ◽  
El Bekkaye Merrimi ◽  
Rhali Benamar
Keyword(s):  
Spectral Analysis ◽  
Laminated Composite ◽  
Composite Beams ◽  
Free Vibrations ◽  
Axial Stiffness ◽  
Geometrically Nonlinear ◽  
Nonlinear Frequency ◽  
Simple Formulation ◽  
Laminated Composite Beams ◽  
Good Agreement

The purpose of the present paper is to show that the problem of geometrically non linear free vibration of symmetrically and asymmetrically laminated composite beams with immovable ends can be reduced to that of isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters. This simple formulation is developed using the governing axial equation of the beam in which the axial inertia and damping are ignored. The theoretical model is based on Hamilton’s principle and spectral analysis. Iterative form solutions are presented to calculate the fundamental nonlinear frequency parameters which are found to be in a good agreement with the published results. The non-dimensional curvatures associated to the fundamental mode are also given in the case of clamped-clamped symmetrically and asymmetrically laminated composite beams.

Spectral Element Model for the PZT-Bonded Laminated Composite Beams

2012 ◽  
Vol 249-250 ◽  
pp. 838-841 ◽  
Author(s):  
Usik Lee ◽  
Il Wook Park ◽  
In Joon Jang
Keyword(s):  
Frequency Domain ◽  
Dynamic Stiffness ◽  
Laminated Composite ◽  
Element Model ◽  
Spectral Element ◽  
Composite Beams ◽  
Dft Theory ◽  
Shape Functions ◽  
Laminated Composite Beams ◽  
Dynamic Shape

This paper presents a spectral element model for the laminated composite beams with a surface-bonded PZT layer. The spectral element model represented by exact dynamic stiffness matrix is derived in the frequency-domain by using the frequency-dependent dynamic shape functions which are formulated from the free wave solutions satisfying the governing differential equations transformed into the frequency-domain by using the DFT theory. The performance of the present spectral element model is then evaluated by comparing its solutions with those obtained by using the conventional finite element model

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