The Influence of Axial-Torsional Coupling on the Natural Frequencies of an Aerial Cable

1993 ◽  
Vol 115 (3) ◽  
pp. 271-276
Author(s):  
S. H. Venkatasubramanian ◽  
W. N. White
Keyword(s):  
Close Agreement ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Element Analysis ◽  
Small Oscillations ◽  
Overhead Transmission Line ◽  
Coupling Case ◽  
Aerial Cable ◽  
Torsional Coupling ◽  
Zero Coupling

The equations of motion for the small oscillations of a stranded, overhead transmission line are derived and linearized about the static equilibrium position. The influence of axial-torsional coupling on the natural frequencies is studied analytically and an expression is presented for the coupled natural frequency in torsion. In order to verify the analytical results, a finite element analysis of the linearized coupled differential equations is carried out. The results of each analysis are compared and show close agreement. The results of the zero coupling case also closely agree with previous work.

The Natural Frequencies and Mode Shapes of Cables With Attached Masses

1981 ◽  
Vol 103 (3) ◽  
pp. 237-242 ◽  
Author(s):  
S. S. Sergev ◽  
W. D. Iwan
Keyword(s):  
Experimental Data ◽  
Close Agreement ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Fortran Program ◽  
Mode Shapes ◽  
Iterative Technique ◽  
Accurate Calculation ◽  
Simple Experiment ◽  
Transcendental Equations

An algorithm has been developed to calculate mode shapes and natural frequencies of taut cables with attached masses. The transcendental equations of motion are solved by an iterative technique allowing accurate calculation of extremely high mode numbers. The algorithm has been implemented as a FORTRAN program primarily as a tool in determining drag coefficients of strumming cables. To assess the accuracy of the program a simple experiment was conducted to determine the natural frequencies and mode shapes of a wire with attached masses driven sinusoidally by a shaker. The algorithm shows close agreement with the experimental data.

Modal and harmonic analysis of three-dimensional wind turbine models

2016 ◽  
Vol 40 (6) ◽  
pp. 518-527 ◽  
Author(s):  
Takwa Sellami ◽  
Hanen Berriri ◽  
A Moumen Darcherif ◽  
Sana Jelassi ◽  
M Faouizi Mimouni
Keyword(s):  
Finite Element ◽  
Wind Turbine ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Operating Conditions ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Element Analysis ◽  
Micro Turbine

In this article, the dynamic responses of wind turbine systems are analytically and numerically investigated. For this purpose, analytic differential equations of motion of wind turbine components subjected to vibration (the blades, the nacelle, and the tower) are solved. This allows determining their dynamic characteristics, mode shapes, and natural frequencies. Two models of two three-dimensional (3D) micro-turbine that are created by the finite element method are set up using the new version of the academic finite element analysis software ANSYS. The first wind turbine is a standard micro three-bladed turbine and the second one is a micro six-bladed Rutland 504. Their natural frequencies and mode shapes are identified based on the modal analysis principle to check the validity of designed models. Dynamic behaviors at several operating conditions of wind turbines are established. Then, spectrum graphs of the structures along x-, y- and z-axis are analyzed.

Bionic design of the tower for wind turbine

2021 ◽  
pp. 095440622110046
Author(s):  
Yuqiao Zheng ◽  
Fugang Dong ◽  
Huquan Guo ◽  
Bingxi Lu ◽  
Zhengwen He
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Maximum Stress ◽  
Natural Frequencies ◽  
Bionic Design ◽  
Analytic Hierarchy ◽  
Element Analysis ◽  
Maximum Deformation ◽  
Overall Stability ◽  
Biological Selection

The study obtains a methodology for the bionic design of the tower for wind turbines. To verify the rationality of the biological selection, the Analytic Hierarchy Procedure (AHP) is applied to calculate the similarity between the bamboo and the tower. Creatively, a bionic bamboo tower (BBT) is presented, which is equipped with four reinforcement ribs and five flanges. Further, finite element analysis is employed to comparatively investigate the performance of the BBT and the original tower (OT) in the static and dynamic. Through the investigation, it is suggested that the maximum deformation and maximum stress can be reduced by 5.93 and 13.75% of the BBT. Moreover, this approach results in 3% and 1.1% increase respectively in the First two natural frequencies and overall stability.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

Vibration-Based Crack Detection in L-Frames

2014 ◽  
Vol 658 ◽  
pp. 261-268
Author(s):  
Jean Louis Ntakpe ◽  
Gilbert Rainer Gillich ◽  
Florian Muntean ◽  
Zeno Iosif Praisach ◽  
Peter Lorenz
Keyword(s):  
Strain Energy ◽  
Crack Detection ◽  
Natural Frequencies ◽  
Vibration Modes ◽  
Structural Elements ◽  
Element Analysis ◽  
Accurate Localization ◽  
Mathematical Expressions ◽  
Measurement Results ◽  
Non Destructive

This paper presents a novel non-destructive method to locate and size damages in frame structures, performed by examining and interpreting changes in measured vibration response. The method bases on a relation, prior contrived by the authors, between the strain energy distribution in the structure for the transversal vibration modes and the modal changes (in terms of natural frequencies) due to damage. Using this relation a damage location indicator DLI was derived, which permits to locate cracks in spatial structures. In this paper an L-frame is considered for proving the applicability of this method. First the mathematical expressions for the modes shapes and their derivatives were determined and simulation result compared with that obtained by finite element analysis. Afterwards patterns characterizing damage locations were derived and compared with measurement results on the real structure; the DLI permitted accurate localization of any crack placed in the two structural elements.

scholarly journals The formation of vortices from a surface of discontinuity

1931 ◽  
Vol 134 (823) ◽  
pp. 170-192 ◽  
Keyword(s):  
Steady State ◽  
Plane Surface ◽  
Equations Of Motion ◽  
Steady Motion ◽  
Small Oscillations ◽  
Approximate Form ◽  
History Of ◽  
State Increase ◽  
Liquid Surfaces

Helmholtz was the first to remark on the instability of those “liquid surfaces” which separate portions of fluid moving with different velocities, and Kelvin, in investigating the influence of wind on waves in water, supposed frictionless, has discussed the conditions under which a plane surface of water becomes unstable. Adopting Kelvin’s method, Rayleigh investigated the instability of a surface of discontinuity. A clear and easily accessible rendering of the discussion is given by Lamb. The above investigations are conducted upon the well-known principle of “small oscillations”—there is a basic steady motion, upon which is superposed a flow, the squares of whose components of velocity can be neglected. This method has the advantage of making the equations of motion linear. If by this method the flow is found to be stable, the equations of motion give the subsequent history of the system, for the small oscillations about the steady state always remain “small.” If, however, the method indicates that the system is unstable, that is, if the deviations from the steady state increase exponentially with the time, the assumption of small motions cannot, after an appropriate interval of time, be applied to the case under consideration, and the equations of motion, in their approximate form, no longer give a picture of the flow. For this reason, which is well known, the investigations of Rayleigh only prove the existence of instability during the initial stages of the motion. It is the object of this note to investigate the form assumed by the surface of discontinuity when the displacements and velocities are no longer small.

Axial Wave Propagation in Infinitely Long Periodic Curved Panels

2003 ◽  
Vol 125 (1) ◽  
pp. 24-30 ◽  
Author(s):  
C. Pany ◽  
S. Parthan
Keyword(s):  
Wave Propagation ◽  
Natural Frequencies ◽  
Propagation Constant ◽  
Infinite Length ◽  
Approximate Methods ◽  
Bending Vibration ◽  
Element Analysis ◽  
Curved Panel ◽  
Propagation Of Waves ◽  
Curved Panels

Propagation of waves along the axis of the cylindrically curved panels of infinite length, supported at regular intervals is considered in this paper to determine their natural frequencies in bending vibration. Two approximate methods of analysis are presented. In the first, bending deflections in the form of beam functions and sinusoidal modes are used to obtain the propagation constant curves. In the second method high precision triangular finite elements is used combined with a wave approach to determine the natural frequencies. It is shown that by this approach the order of the resulting matrices in the FEM is considerably reduced leading to a significant decrease in computational effect. Curves of propagation constant versus natural frequencies have been obtained for axial wave propagation of a multi supported curved panel of infinite length. From these curves, frequencies of a finite multi supported curved panel of k segments may be obtained by simply reading off the frequencies corresponding to jπ/kj=1,2…k. Bounding frequencies and bounding modes of the multi supported curved panels have been identified. It reveals that the bounding modes are similar to periodic flat panel case. Wherever possible the numerical results have been compared with those obtained independently from finite element analysis and/or results available in the literature.

Free Vibration Analysis of a Carbon Nanotube Reinforced Composite Beam

2014 ◽  
Vol 592-594 ◽  
pp. 2041-2045 ◽  
Author(s):  
B. Naresh ◽  
A. Ananda Babu ◽  
P. Edwin Sudhagar ◽  
A. Anisa Thaslim ◽  
R. Vasudevan
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Composite Beam ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Element Formulation ◽  
Reinforced Composite ◽  
Vibration Responses

In this study, free vibration responses of a carbon nanotube reinforced composite beam are investigated. The governing differential equations of motion of a carbon nanotube (CNT) reinforced composite beam are presented in finite element formulation. The validity of the developed formulation is demonstrated by comparing the natural frequencies evaluated using present FEM with those of available literature. Various parametric studies are also performed to investigate the effect of aspect ratio and percentage of CNT content and boundary conditions on natural frequencies and mode shapes of a carbon nanotube reinforced composite beam. It is shown that the addition of carbon nanotube in fiber reinforced composite beam increases the stiffness of the structure and consequently increases the natural frequencies and alter the mode shapes.

scholarly journals Vibration Characteristics of Piezoelectric Microbeams Based on the Modified Couple Stress Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
R. Ansari ◽  
M. A. Ashrafi ◽  
S. Hosseinzadeh
Keyword(s):  
Boundary Conditions ◽  
Couple Stress ◽  
Natural Frequencies ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Modified Couple Stress Theory ◽  
Beam Model ◽  
Governing Equations ◽  
Stress Theory ◽  
Modified Couple Stress

The vibration behavior of piezoelectric microbeams is studied on the basis of the modified couple stress theory. The governing equations of motion and boundary conditions for the Euler-Bernoulli and Timoshenko beam models are derived using Hamilton’s principle. By the exact solution of the governing equations, an expression for natural frequencies of microbeams with simply supported boundary conditions is obtained. Numerical results for both beam models are presented and the effects of piezoelectricity and length scale parameter are illustrated. It is found that the influences of piezoelectricity and size effects are more prominent when the length of microbeams decreases. A comparison between two beam models also reveals that the Euler-Bernoulli beam model tends to overestimate the natural frequencies of microbeams as compared to its Timoshenko counterpart.

Design and Analysis of a Miniaturization Nanoindentation and Scratch Device

2011 ◽  
Vol 314-316 ◽  
pp. 1792-1795
Author(s):  
Hu Huang ◽  
Hong Wei Zhao ◽  
Jie Yang ◽  
Shun Guang Wan ◽  
Jie Mi ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Amorphous Alloy ◽  
Natural Frequencies ◽  
Geometric Parameters ◽  
Flexure Hinge ◽  
Element Analysis ◽  
Modal Characteristics

In this paper, a miniaturization nanoindentation and scratch device was developed. Finite element analysis was carried out to study static and modal characteristics of x/y flexure hinge and z axis driving hinge as well as effect of geometric parameters on output performances of z axis driving hinge. Results indicated that x/y flexure hinge and z axis driving hinge had enough strength and high natural frequencies. Geometric parameters of z axis driving hinge affected output performances significantly. The model of developed device was established. Indentation experiments of Si and amorphous alloy showed that the developed miniaturization nanoindentation and scratch device worked well and can carry out indentation experiments with certain accuracy.

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