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Investigation of dynamics of discrete framed structures by a numerical wave-based method and an analytical homogenization approach

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Chinese Journal of Aeronautics 2017年第1期30卷 66-74页

作者： Zhou Changwei Sun Xiangkun Mohamed Ichchou Abdel-Malek Zine Jean-Pierre Lainé Stephane Hans Claude Boutin Laboratory of Tribology and Systems Dynamics Ecole Centrale de Lyon Ecully 69134 France Institut Camille Jordan Ecole Centrale de Lyon Ecully 69134 France Laboratory of Tribology and Systems Dynamics Ecole Nationale des Travaux Publics de l'Etat Vaulx-en-Velinx 69518 France

In this article, the analytical homogenization method of periodic discrete media（HPDM）and the numerical condensed wave finite element method（CWFEM） are employed to study the longitudinal and transverse vibrations of framed structures. The valid frequency range of the HPDM is re-evaluated using the wave propagation feature identified by the CWFEM. The relative error of the wavenumber by the HPDM compared to that by the CWFEM is illustrated in functions of frequency and scale ratio. A parametric study on the thickness of the structure is carried out where the dispersion relation and the relative error are given for three different thicknesses. The dynamics of a finite structure such as natural frequency and forced response are also investigated using the HPDM and the CWFEM.

关键词： framed structures Homogenization method Periodic structures Wave finite element method Wave propagation

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A New Non-uniform Beam Element and Its Application to Buckling Analysis for framed structures

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Journal of Donghua University(English Edition) 2012年第2期29卷 111-114页

作者：陆念力王佳 School of Mechatronics Engineering Harbin Institute of Technology

The non-uniform beam components are commonly used in engineering,while the method to analyze such component is not too satisfactory yet. A new non-uniform beam element with high precision was developed based on the non-linear analysis and the static condensation. Based on the interpolation theory, the displacement fields of the three-node non-uniform Euler-Bernoulli beam element were constructed at first: the quintic Hermite interpolation polynomial was used for the lateral displacement field and the quadratic Lagrange interpolation polynomial for the axial displacement field. Then,based on the basic assumptions of non-uniform Euler-Bernoulli beam whose section properties were continuously varying along its centroidal axis, the linear and geometric stiffness matrices of the three-node non-uniform beam element were derived according to the nonlinear finite element theory. Finally,the degrees of freedom ( DOFs) of the middle node of the element were eliminated using the static condensation method, and a new two-node non-uniform beam element including axial-force effect was obtained. The results indicate that each bar needs to be meshed with only one element could get a fairly accurate solution when it is applied to the stability analyses.

关键词： non-uniform beam element finite element method structural buckling framed structures static condensation

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