scholarly journals Integral Method for Flow Induced Transverse Vibrations Analysis of Flexible Pipes

2020 ◽  
Vol 12 (1) ◽  
pp. 3-11
Author(s):  
Viorel ANGHEL ◽  
Stefan SOROHAN
Keyword(s):  
Vibration Analysis ◽  
Integral Method ◽  
Free Vibration Analysis ◽  
Matrix Formulation ◽  
Beam Dynamic ◽  
Transverse Vibrations ◽  
Flexible Pipes ◽  
Fluid Velocities ◽  
Straight Beam ◽  
Good Agreement

This paper reviews some existing studies and numerical methods used for flow induced transverse vibrations analysis of flexible pipes. An integral method, based on the use of Green’s functions, already used for different straight beam dynamic analysis is adapted for the proposed subject. This approximate method leads to a matrix formulation and to an eigenvalue problem for free vibration analysis. The presented approach is able to estimate also the critical fluid velocities. Effects of boundary conditions and of elastic foundation characteristics, Coriolis terms and of other parameters on dynamic behavior of a pipe, can be included. Some numerical examples are also presented for comparisons with results obtained by FEM or with other data from literature. They show good agreement.

scholarly journals Numerical Methods for Transverse Vibration Analysis of Straight Euler and Timoshenko Beams

2019 ◽  
Vol 11 (3) ◽  
pp. 15-28 ◽  
Author(s):  
Viorel ANGHEL
Keyword(s):  
Numerical Methods ◽  
Vibration Analysis ◽  
Integral Method ◽  
Short Review ◽  
Timoshenko Beams ◽  
Matrix Formulation ◽  
Inertia Effects ◽  
Approximate Integral ◽  
Shear Effects ◽  
Good Agreement

This paper presents a short review of numerical methods used for lateral vibration analysis in the case of straight Euler and Timoshenko beams. A particular integral method is described with more details. This approximate integral method is based on the use of flexibility influence functions (Green’s functions). It leads to a matrix formulation and to an eigenvalue problem for vibration analysis. The presented approach is able to estimate separately the shear effects and the rotary inertia effects and also the combined effects. Simple numerical examples are also presented for comparisons with analytical and finite elements results. The results show good agreement.

scholarly journals Free Vibration Analysis of Fiber Metal Laminated Straight Beam

2018 ◽  
Vol 16 (1) ◽  
pp. 944-948 ◽  
Author(s):  
Sinan Maraş ◽  
Mustafa Yaman ◽  
Mehmet Fatih Şansveren ◽  
Sina Karimpour Reyhan
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
High Performance ◽  
Free Vibration Analysis ◽  
Vibration Characteristics ◽  
Numerical Results ◽  
Experimental Results ◽  
Hybrid Structures ◽  
Straight Beam ◽  
Fiber Metal

AbstractIn recent years, studies on the development of new and advanced composite materials have been increasing. Among these new technological products, Fiber Metal Laminates (FML), and hybrid structures made of aluminium, carbon, glass or aramid fiber, are preferred especially in the aircraft industry due to their high performance. Therefore, free vibration analysis is necessary for the design process of such structures. In this study, the vibration characteristics of FML for clamped-free boundary conditions were investigated experimentally and numerically. Firstly, numerical results were obtained using Finite Element Method (FEM) and then these results were compared with the experimental results. It was seen that the numerical results were in good agreement with the experimental results. As the theoretical model was justified, the effects of various parameters such as number of layers, fiber orientations, and aluminium layer thickness on the in-plane vibration characteristics of the FML straight beam were analysed using FEM. Thus, most important parameters affecting the vibration characteristics of the hybrid structures were determined.

scholarly journals Green’s function approach to frequency analysis of thin circular plates

2016 ◽  
Vol 64 (1) ◽  
pp. 181-188
Author(s):  
K.K. Żur
Keyword(s):  
Power Series ◽  
Free Vibration ◽  
Influence Function ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Thin Plates ◽  
Circular Plates ◽  
Natural Modes ◽  
Good Agreement ◽  
Analytical Frequency

Abstract The free vibration analysis of homogeneous and isotropic circular thin plates by using the Green’s functions is considered. The formulae for construction of the influence function for all nodal diameters are presented in a closed form. The limited independent solutions of differential Euler equations were expanded in the Neumann power series using the method of successive approximation. This approach allows to obtain the analytical frequency equations as power series rapidly convergent to exact eigenvalues for different number of nodal diameters. The first ten dimensionless frequencies for eight different natural modes of circular plates are calculated. A part of obtained results have not been presented yet in open literature for thin circular plates. The results of investigation are in good agreement with selected results obtained by other methods presented in literature.

scholarly journals FREE VIBRATION ANALYSIS OF LAMINATED STIFFENED CYLINDRICAL PANELS USING FINITE ELEMENT METHOD

2016 ◽  
Vol 54 (6) ◽  
pp. 771
Author(s):  
Trinh Anh Tuan ◽  
Tran Huu Quoc ◽  
Tran Minh Tu
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Shell Element ◽  
Cylindrical Panels ◽  
Parametric Studies ◽  
Shell Panel ◽  
Degenerated Shell Element ◽  
Good Agreement

A study on the free vibration analysis of stiffened laminated composite cylindrical shell is described in this paper. The eight-noded isoparametric degenerated shell element is developed to model both shell panel and stiffeners by using the degenerated solid concept based on Reissner-Mindlin assumptions which taking to account the shear deformation and rotatory effect. Numerical results are presented and comparison is made with the published results from the literature and the good agreement is found. Parametric studies considering different geometrical variables of shell and stiffeners have also been carried out.

Using Super Element and p-Approximation for Free Vibration Analysis of Composite Plates

2004 ◽  
Author(s):  
M. Sharafaty Zangeneh ◽  
M. T. Ahmadian ◽  
Seyed Reza Ghoreishi
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Thin Plates ◽  
Ansys Software ◽  
Thick Plates ◽  
Cubic Polynomial ◽  
Plane Direction ◽  
Good Agreement

Effective and efficient methods in computational mechanics have been of interest for the designers and engineers in the last decade. A 3D super elements is developed and implemented for the free vibration analysis of the composite plates. These new elements have been constructed by a 2D super elements in the plane direction and p-version finite element in the thickness direction. Results of 2D super elements are comparable to SHELL 63 and results of 3D super elements with cubic polynomial are comparable to SHELL 93. In the thin plates, 2D super element (or SHELL 63) and 3D super elements (or SHELL 93) have same results, but in the thick plates results change drastically. Natural frequencies of thick plates analyzed by one 3D super element in comparison with 25 conventional elements (SHELL 63 and SHELL 93) by ANSYS software indicate good agreement in the results with a maximum 4% deviation.

scholarly journals Vibration analysis of a circular disc backed by a cylindrical cavity

2001 ◽  
Vol 215 (11) ◽  
pp. 1303-1311 ◽  
Author(s):  
D G Gorman ◽  
J M Reese ◽  
J Horácek ◽  
K Dedouch
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Acoustic Medium ◽  
Element Analysis ◽  
Acoustic Coupling ◽  
The Galerkin Method ◽  
Cylindrical Duct ◽  
Good Agreement

This paper describes the free vibration analysis of a thin disc vibrating and interacting with an acoustic medium contained in a cylindrical duct. The effects of structural-acoustic coupling are studied by means of an analytical-numerical method that is based upon classical theory and the Galerkin method. The coupling effects are discussed, and results obtained from the analysis are compared with corresponding values obtained both experimentally and from a finite element analysis. There is good agreement between the three sets of results.

Vibration Analysis of Bidirectional Functionally Graded Timoshenko Beams Using Chebyshev Collocation Method

2020 ◽  
pp. 2150009 ◽  
Author(s):  
Wei-Ren Chen ◽  
Heng Chang
Keyword(s):  
Collocation Method ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Timoshenko Beams ◽  
Algebraic Equations ◽  
Chebyshev Collocation Method ◽  
Chebyshev Collocation ◽  
Proposed Model ◽  
Good Agreement

This paper studies the vibration behaviors of bidirectional functionally graded (BDFG) Timoshenko beams based on the Chebyshev collocation method. The material properties of the beam are assumed to vary simultaneously in the beam length and thickness directions. The Chebyshev differentiation matrices are used to reduce the ordinary differential equations into a set of algebraic equations to form the eigenvalue problem for free vibration analysis. To validate the accuracy of the proposed model, some calculated results are compared with those obtained by other investigators. Good agreement has been achieved. Then the effects of slenderness ratios, material distribution types, gradient indexes, and restraint types on the natural frequency of BDFG beams are examined. Through the parametric study, the influences of the various geometric and material parameters on the vibration characteristics of BDFG beams are evaluated.

scholarly journals Bending Vibration Analysis of Nanobeams using the Nonlocal Motion Equations Solved by an Integral Approach

2021 ◽  
Vol 13 (1) ◽  
pp. 11-18
Author(s):  
Viorel ANGHEL ◽  
Stefan SOROHAN
Keyword(s):  
Vibration Analysis ◽  
Integral Method ◽  
Scale Effects ◽  
Integral Approach ◽  
Bending Vibrations ◽  
Bending Vibration ◽  
Motion Equations ◽  
Numerical Examples ◽  
Method Effects ◽  
Good Agreement

This paper deals with the dynamic characteristics for bending vibrations of Euler-Bernoulli type nanobeams taking into account the scale effects via the nonlocal motion equations. An integral method, based on the use of Green’s functions, has been used in order to obtain the corresponding eigenvalue problem. The proposed integral approach is an approximate matrix method. Effects of different boundary conditions and of an elastic foundation have been also included. The presented numerical examples show good agreement when compared to results from literature. The proposed method can be used in the case of nanodevices analysis modeled as beams (MEMS, NEMS).

Smoothing Technique Based Beta FEM (βFEM) for Static and Free Vibration Analyses of Reissner–Mindlin Plates

2019 ◽  
Vol 17 (02) ◽  
pp. 1845006 ◽  
Author(s):  
F. Wu ◽  
W. Zeng ◽  
L. Y. Yao ◽  
M. Hu ◽  
Y. J. Chen ◽  
...  
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Steel Plate ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Shear Locking ◽  
Smoothing Technique ◽  
Smoothed Finite Element Method ◽  
Edge Based ◽  
Good Agreement

Recently, the edge-based and node-based smoothed finite element method (ES-FEM and NS-FEM) has been proposed for Reissner–Mindlin plate problems. In this work, in order to utilize the numerical advantages of both ES-FEM and NS-FEM for static and vibration analysis, a hybrid smoothing technique based beta FEM ([Formula: see text]FEM) is presented for Reissner–Mindlin plate problems. A tunable parameter [Formula: see text] is introduced to tune the proportion of smoothing domains calculated by ES-FEM or NS-FEM, which controlled the accuracy of the results. Numerical illustrations in both static and free vibration analysis are conducted. The shear locking free property, converge property and dynamic stability are carefully examined via several well-known benchmark examples. Moreover, an experimental test is carefully designed and conducted for validations, in which the mode values and shape of a rectangular steel plate is tested. Numerical examples demonstrate the advantages of [Formula: see text]FEM, in comparison with the standard FEM, ES-FEM and NS-FEM using the same meshes. The numerical and experimental results are in good agreement with each other and the [Formula: see text]FEM achieves the best accuracy among all the methods for the static or free vibration analysis of plates.

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