Vibration Analysis of Composite Beams With End Effects via the Formal Asymptotic Method

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Jun-Sik Kim ◽  
K. W. Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Asymptotic Expansion ◽  
Cross Section ◽  
Asymptotic Method ◽  
Vibration Analysis ◽  
Expansion Method ◽  
Composite Beams ◽  
Asymptotic Expansion Method ◽  
Element Method

Vibration analysis of composite beams is carried out by using a finite element-based formal asymptotic expansion method. The formulation begins with three-dimensional (3D) equilibrium equations in which cross-sectional coordinates are scaled by the characteristic length of the beam. Microscopic two-dimensional and macroscopic one-dimensional (1D) equations obtained via the asymptotic expansion method are discretized by applying a conventional finite element method. Boundary conditions associated with macroscopic 1D equations are considered to investigate the end effect. It is then described how one could form and solve the eigenvalue problems derived from the asymptotic method beyond the classical approximation. The results obtained are compared with those of 3D finite element method and those available in the literature for composite beams with solid cross section and thin-walled cross section.

Vibration Analysis of Composite Beams With End Effects via the Formal Asymptotic Method

2009 ◽  
Author(s):  
Jun-Sik Kim ◽  
K. W. Wang
Keyword(s):  
Finite Element ◽  
Asymptotic Expansion ◽  
Cross Section ◽  
Asymptotic Method ◽  
Vibration Analysis ◽  
Eigenvalue Problems ◽  
Free Vibration Analysis ◽  
Expansion Method ◽  
Composite Beams ◽  
Asymptotic Expansion Method

Free vibration analysis of composite beams is carried out by using a finite element-based formal asymptotic expansion method. The formulation begins with three-dimensional equilibrium equations in which cross-sectional coordinates are scaled by the characteristic length of the beam. Microscopic 2D and macroscopic 1D equations obtained via the asymptotic expansion method are discretized by applying a conventional finite element method. Boundary conditions associated with macroscopic 1D equations are also considered in order to investigate the end effect. We then describe how to form and solve the eigenvalue problems derived from the asymptotic method beyond the classical approximation. The results obtained are compared to those of 3D FEM and those available in literature for composite beams with solid cross-section and thin-walled cross-section.

scholarly journals Forced Vibration Analysis of Laminated Composite Shells Reinforced with Graphene Nanoplatelets Using Finite Element Method

2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
Trung Thanh Tran ◽  
Van Ke Tran ◽  
Pham Binh Le ◽  
Van Minh Phung ◽  
Van Thom Do ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Thermal Environments ◽  
Forced Vibration Analysis ◽  
Laminated Composite Shells ◽  
Element Method

This paper carries out forced vibration analysis of graphene nanoplatelet-reinforced composite laminated shells in thermal environments by employing the finite element method (FEM). Material properties including elastic modulus, specific gravity, and Poisson’s ratio are determined according to the Halpin–Tsai model. The first-order shear deformation theory (FSDT), which is based on the 8-node isoparametric element to establish the oscillation equation of shell structure, is employed in this work. We then code the computing program in the MATLAB application and examine the verification of convergence rate and reliability of the program by comparing the data of present work with those of other exact solutions. The effects of both geometric parameters and mechanical properties of materials on the forced vibration of the structure are investigated.

Free Vibration Analysis for Tapered Cross-Section Steel-Concrete Composite Material Beam

2017 ◽  
Vol 893 ◽  
pp. 380-383
Author(s):  
Jun Xia ◽  
Z. Shen ◽  
Kun Liu
Keyword(s):  
Finite Element ◽  
Composite Material ◽  
Cross Section ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Composite Beams ◽  
Shear Connection ◽  
The Common ◽  
Interlayer Slip

The tapered cross-section beams made of steel-concrete composite material are widely used in engineering constructions and their dynamic behavior is strongly influenced by the type of shear connection jointing the two different materials. The 1D high order finite element model for tapered cross-section steel-concrete composite material beam with interlayer slip was established in this paper. The Numerical results for vibration nature frequencies of the composite beams with two typical boundary conditions were compared with ANSYS using 2D plane stress element. The 1D element is more efficient and economical for the common tapered cross-section steel-concrete composite material beams in engineering.

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