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 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.

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).

scholarly journals Out-of-Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Hamdi Alper Özyiğit ◽  
Mehmet Yetmez ◽  
Utku Uzun
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Variable Cross ◽  
Additional Mass ◽  
Inertia Effects ◽  
Tapered Beam ◽  
Out Of Plane ◽  
Good Agreement

As there is a gap in literature about out-of-plane vibrations of curved and variable cross-sectioned beams, the aim of this study is to analyze the free out-of-plane vibrations of curved beams which are symmetrically and nonsymmetrically tapered. Out-of-plane free vibration of curved uniform and tapered beams with additional mass is also investigated. Finite element method is used for all analyses. Curvature type is assumed to be circular. For the different boundary conditions, natural frequencies of both symmetrical and unsymmetrical tapered beams are given together with that of uniform tapered beam. Bending, torsional, and rotary inertia effects are considered with respect to no-shear effect. Variations of natural frequencies with additional mass and the mass location are examined. Results are given in tabular form. It is concluded that (i) for the uniform tapered beam there is a good agreement between the results of this study and that of literature and (ii) for the symmetrical curved tapered beam there is also a good agreement between the results of this study and that of a finite element model by using MSC.Marc. Results of out-of-plane free vibration of symmetrically tapered beams for specified boundary conditions are addressed.

Evaluation of Motorized Rotating Pancake Coil Probe Signals Simulated by Numerical Analysis in Steam Generator Tubes

2006 ◽  
Vol 321-323 ◽  
pp. 451-454
Author(s):  
Joo Young Yoo ◽  
Sung Jin Song ◽  
Chang Hwan Kim ◽  
Hee Jun Jung ◽  
Young Hwan Choi ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Numerical Analysis ◽  
Steam Generator ◽  
Integral Method ◽  
Volume Integral ◽  
Analysis Software ◽  
Steam Generator Tubes ◽  
Calibration Tool ◽  
High Possibility ◽  
Good Agreement

In the present study, the synthetic signals from the combo tube are simulated by using commercial electromagnetic numerical analysis software which has been developed based on a volume integral method. A comparison of the simulated signals to the experiments is made for the verification of accuracy, and then evaluation of five deliberated single circumferential indication signals is performed to explore a possibility of using a numerical simulation as a practical calibration tool. The good agreement between the evaluation results for two cases (calibration done by experiments and calibration made by simulation) demonstrates such a high possibility.

Solitons propagation dynamics in a saturable PT-symmetric fractional medium

2021 ◽  
Author(s):  
Davood Hajitaghi Tehrani ◽  
Mehdi Solaimani ◽  
Mahboubeh Ghalandari ◽  
Bahman Babayar Razlighi
Keyword(s):  
Monte Carlo ◽  
Numerical Methods ◽  
Physical Properties ◽  
Maximum Intensity ◽  
Step Method ◽  
Saturation Parameter ◽  
Potential Depth ◽  
Fractional System ◽  
Nonlinear Fractional Schrödinger Equation ◽  
Good Agreement

Abstract In the current research, the propagation of solitons in a saturable PT-symmetric fractional system is studied by solving nonlinear fractional Schrödinger equation. Three numerical methods are employed for this purpose, namely Monte Carlo based Euler-Lagrange variational schema, split-step method, and extrapolation approach. The results show good agreement and accuracy. The effect of different parameters such as potential depth, Levy indices, and saturation parameter, on the physical properties of the systems such as maximum intensity and soliton width oscillations are considered.

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