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.

Force Vibration Analysis of Thick Beams on Two Parameter Elastic Foundation by Finite Element Method

2002 ◽  
Author(s):  
Ali Bahcivan ◽  
Vedat Karadag
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Cross Section ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Beam Element ◽  
Thick Beam ◽  
Two Parameter

In the present work, the free vibration analysis of rectangular cross-section uniform beams on two-parameter elastic foundation, considering shear deformation and rotatory inertia is made by the finite element method. In this analysis, two different thick beam elements are used. The first 4 degrees of freedom thick beam element has two nodes with two degrees of freedom at each node such as transverse displacements and cross-section rotations. In the second beam element, the nodal variables are the transverse displacement, the cross-section rotation and shear deformation. 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. Axial displacement of the beam is also considered. Three kinds of end conditions, i.e., simply-supported, clamped-clamped and clamped-free ends are considered in this study. The effects of axial force, foundation stiffness parameters and partial elastic foundation on the natural frequencies of the beam are examined. In this analysis, the vibration calculation results are presented in the tables and their importance in design are discussed. The numerical results obtained from this analysis are compared with the exact or available solutions, wherever possible. Numerical results and comparisons show the effectiveness of the proposed method.

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.

scholarly journals Free Vibration Analysis Of The Moderately Thick Laminated Composite Rectangular Plate On Two-Parameter Elastic Foundation With Elastic Boundary Conditions

2016 ◽  
Vol 1 (1) ◽  
pp. 190 ◽  
Author(s):  
H. Zhang ◽  
D.Y. Shi ◽  
Q.S. Wang
Keyword(s):  
Fourier Series ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Elastic Foundation ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Two Parameter

<p>An improved Fourier series method is presented for the free vibration analysis of the moderately thick laminated composite rectangular plate with general elastic supports and point supports resting on an elastic foundation. The approach is based on the first order shear deformation theory and foundation effect using two-parameter Pasternak foundation model. The displacement and rotation functions are generally sought, regardless of boundary conditions, as Fourier series and supplementary functions. All the series expansion coefficients are determined using the Rayleigh-Ritz technique. The excellent accuracy of the current results is validated by comparing them with existing results.</p>

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.

scholarly journals Phononic Band Gap and Free Vibration Analysis of Fluid-Conveying Pipes with Periodically Varying Cross-Section

2021 ◽  
Vol 11 (21) ◽  
pp. 10485
Author(s):  
Hao Yu ◽  
Feng Liang ◽  
Yu Qian ◽  
Jun-Jie Gong ◽  
Yao Chen ◽  
...  
Keyword(s):  
Free Vibration ◽  
Band Gap ◽  
Cross Section ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Critical Parameters ◽  
Mode Shapes ◽  
Beam Model ◽  
The Impact ◽  
Fluid Conveying Pipes

Phononic crystals (PCs) are a novel class of artificial periodic structure, and their band gap (BG) attributes provide a new technical approach for vibration reduction in piping systems. In this paper, the vibration suppression performance and natural properties of fluid-conveying pipes with periodically varying cross-section are investigated. The flexural wave equation of substructure pipes is established based on the classical beam model and traveling wave property. The spectral element method (SEM) is developed for semi-analytical solutions, the accuracy of which is confirmed by comparison with the available literature and the widely used transfer matrix method (TMM). The BG distribution and frequency response of the periodic pipe are attained, and the natural frequencies and mode shapes are also obtained. The effects of some critical parameters are discussed. It is revealed that the BG of the present pipe system is fundamentally induced by the geometrical difference of the substructure cross-section, and it is also related to the substructure length and fluid–structure interaction (FSI). The number of cells does not contribute to the BG region, while it has significant effects on the amplitude attenuation, higher order natural frequencies and mode shapes. The impact of FSI is more evident for the pipes with smaller numbers of cells. Moreover, compared with the conventional TMM, the present SEM is demonstrated more effective for comprehensive analysis of BG characteristics and free vibration of PC dynamical structures.

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