FREE VIBRATION ANALYSIS OF CROSS-PLY LAYERED COMPOSITE BEAMS WITH FINITE LENGTH ON ELASTIC FOUNDATION

2008 ◽  
Vol 05 (01) ◽  
pp. 21-36 ◽  
Author(s):  
RAMAZAN-ALI JAFARI-TALOOKOLAEI ◽  
MOHAMMAD-HOSSEIN KARGARNOVIN ◽  
MOHAMMAD-TAGHI AHMADIAN
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Cross Section ◽  
Finite Length ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Free Vibration Analysis ◽  
Composite Beams ◽  
Layered Composite

In this paper, free vibration analysis of cross-ply layered composite beams (LCB) with finite length and rectangular cross-section rested on an elastic foundation is investigated by finite element method. Based on the Timoshenko beam theory which includes the shear deformation and rotary inertia, the stiffness and mass matrices of a LCB are obtained using the energy method. Then, the natural frequencies are calculated by employing eigenvalue technique. The obtained results are verified against existing data in the literatures for a LCB with no foundation and uniform cross-section. Good agreements are observed between these cases. In the same way, the natural frequencies of a specific case, i.e. the stepped beam are calculated and finally, free vibrations of a symmetric and non-symmetric LCB are compared with each others.

Analytical and Experimental Free Vibration Analysis of Uniform Cracked Thick Beam on Two-Parameter Elastic Partial Foundation

Volume 1 ◽  
2004 ◽  
Author(s):  
Ali Bahc¸ıvan ◽  
Vedat Karadag˘
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Cross Section ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Beam Element ◽  
Thick Beam ◽  
Two Parameter

In this study, the analytical and experimental free vibration analysis of rectangular cross-section uniform cracked thick beam on two-parameter vibration and noise isolating elastic foundation, considering shear deformation and rotatory inertia is made by the finite element method. The beam element in our study is a recently introduced 4 degrees of freedom thick beam element and has two nodes with two degrees of freedom at each node such as transverse displacements and cross-section rotations. Two kinds of end conditions, i.e. clamped-clamped and clamped-free ends are considered in this study. Axial displacement of the beam is also considered. For axial displacement of the beam, linear finite elements are used. The elastic foundation is idealized as a constant two-parameter model characterized by two moduli, i.e. the Winkler foundation modulus k and the shear foundation modulus kG. In the case kG = 0, this model reduces to the Winkler model, i.e. the elastic foundation is idealized as a constant one-parameter model. The effects of foundation stiffness parameters, partial elastic foundation and crack changing its depth on the natural frequencies of the beam are examined. The effect of partial elastic foundation on the natural frequencies of the beam is examined for only half of the beam length. The crack is in the middle of the beam and only on one side of the beam having a form of open crack. In the analytical analysis, the spring coefficients of the crack are calculated in the computer program and then directly added to the stiffness matrix. The crack model used in this study is mentioned as a linear spring model in the literature. The crack modeled is in the middle of the beam and the related spring constants of rotational and extensional springs, which will be used, are added to the global matrix in the process. In the experimental analysis, steel and hard plastic beam are used as the beam material. Moreover, sponge and glass wool, which are manufactured by Petkim Ltd., are used as the isolating elastic foundation material. The results obtained from the analytical and experimental studies are presented by showing in tables and graphs and their importance in design is discussed. The analytical and experimental results and comparisons show the efficiency and effectiveness of the proposed method.

Use of trigonometric series functions in free vibration analysis of laminated composite beams

2020 ◽  
Vol 6 (2) ◽  
pp. 61
Author(s):  
Muhittin Turan ◽  
Volkan Kahya
Keyword(s):  
Free Vibration ◽  
Trigonometric Series ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Composite Beams ◽  
Layered Composite ◽  
End Conditions

In this study, free vibration analysis of layered composite beams is performed by using an analytical method based on trigonometric series. Based on the first-order shear deformation beam theory, the governing equations are derived from the Lagrange’s equations. Appropriate trigonometric series functions are selected to satisfy the end conditions of the beam. Navier-type solution is used to obtain natural frequencies. Natural frequencies are calculated for different end conditions and lamina stacking. It was seen that the slenderness, E11/E22 and fiber angle have a significant effect on natural frequency. The results of the study are quite compatible with the literature.

Free Vibration Analysis of Cracked Composite Beams Subjected to Coupled Bending-Torsion Loads Based on a First Order Beam Theory

2013 ◽  
Vol 325-326 ◽  
pp. 1318-1323 ◽  
Author(s):  
A.R. Daneshmehr ◽  
D.J. Inman ◽  
A.R. Nateghi
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Order Theory ◽  
Composite Beams ◽  
First Order ◽  
First Order Theory

In this paper free vibration analysis of cracked composite beams subjected to coupled bending-torsion loads are presented. The composite beam is assumed to have an open edge crack. A first order theory is applied to count for the effect of the shear deformations on natural frequencies as well as the effect of coupling in torsion and bending modes of vibration. Local flexibility matrix is used to obtain the additional boundary conditions of the beam in the crack area. After obtaining the governing equations and boundary conditions, GDQ method is applied to solve the obtained eigenvalue problem. Finally, some numerical results are given to show the efficacy of the method. In addition, to count for the effect of coupling on natural frequencies of the cracked beams, different fiber orientations are assumed and studied.

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.

Free‐Vibration Analysis of Composite Beams

1991 ◽  
Vol 36 (3) ◽  
pp. 36-47 ◽  
Author(s):  
Dewey H. Hodges ◽  
Ali R. Atilgan ◽  
Mark V. Fulton ◽  
Lawrence W. Rehfield
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Composite Beams

Uncertain Structural Free Vibration Analysis With Non-Probabilistic Spatially Varying Parameters

2019 ◽  
Vol 5 (2) ◽  
Author(s):  
Jinwen Feng ◽  
Qingya Li ◽  
Alba Sofi ◽  
Guoyin Li ◽  
Di Wu ◽  
...  
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Spatial Dependency ◽  
The Finite Element Method ◽  
Engineering Structures ◽  
Spatially Varying ◽  
Computational Strategy ◽  
Bounded System

The uncertain free vibration analysis of engineering structures with the consideration of nonstochastic spatially dependent uncertain parameters is investigated. A recently proposed concept of interval field is implemented to model the intrinsic spatial dependency of the uncertain-but-bounded system parameters. By employing the appropriate discretization scheme, evaluations of natural frequencies for engineering structures involving interval fields can be executed within the framework of the finite element method. Furthermore, a robust, yet efficient, computational strategy is proposed such that the extreme bounds of natural frequencies of the structure involving interval fields can be rigorously captured by performing two independent eigen-analyses. Within the proposed computational analysis framework, the traditional interval arithmetic is not employed so that the undesirable effect of the interval overestimation can be completely eliminated. Consequently, both sharpness and physical feasibility of the results can be guaranteed to a certain extent for any discretized interval field. The plausibility of the adopted interval field model, as well as the feasibility of the proposed computational scheme, is clearly demonstrated by investigating both academic-sized and practically motivated engineering structures.

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