Identification of longitudinal incisions of the beam from its own frequencies

2012 ◽  
Vol 9 (1) ◽  
pp. 37-40
Author(s):  
A.M. Akhtyamov ◽  
A.R. Karimov
Keyword(s):  
Natural Frequency ◽  
Cross Section ◽  
Natural Frequencies ◽  
Bending Vibrations ◽  
Section Line ◽  
Prismatic Beam ◽  
Neutral Cross Section

The natural frequencies of bending vibrations of a prismatic beam with symmetrical bilateral longitudinal incisions are considered. A method is proposed that makes it possible to calculate the parameters of the incisions with by two frequencies taken from different spectra. These spectra belong to bending vibrations in two mutually perpendicular planes, which are chosen in such a way that in both cases the neutral cross-section line is parallel to the sides. The dependence of the natural frequency on the depth of the defect is also studied. It is proved that the values of the frequencies for the beam under consideration and the identical beam without cuts do not coincide for any value of the defects.

scholarly journals Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method

2021 ◽  
Vol 13 (11) ◽  
pp. 168781402110609
Author(s):  
Hossein Talebi Rostami ◽  
Maryam Fallah Najafabadi ◽  
Davood Domiri Ganji
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Variable Properties ◽  
The Third ◽  
Koch Snowflake

This study analyzed a Timoshenko beam with Koch snowflake cross-section in different boundary conditions and for variable properties. The equation of motion was solved by the finite element method and verified by Solidworks simulation in a way that the maximum error was about 2.9% for natural frequencies. Displacement and natural frequency for each case presented and compared to other cases. Significant research achievements illustrate that if we change the Koch snowflake cross-section of the beam from the first iteration to the second, the area and moment of inertia will increase, and we have a 5.2% rise in the first natural frequency. Similarly, by changing the cross-section from the second iteration to the third, a 10.2% growth is observed. Also, the hollow cross-section is considered, which can enlarge the natural frequency by about 26.37% compared to a solid one. Moreover, all the clamped-clamped, hinged-hinged, clamped-free, and free-free boundary conditions have the highest natural frequency for the Timoshenko beam with the third iteration of the Koch snowflake cross-section in solid mode. Finally, examining important physical parameters demonstrates that variable density from a minimum value to the standard value along the beam increases the natural frequencies, while variable elastic modulus decreases it.

Determination of the Natural Frequencies of the Bending Vibrations of Beams

1947 ◽  
Vol 14 (1) ◽  
pp. A1-A6
Author(s):  
A. I. Bellin
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Moment Equation ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Bending Vibrations ◽  
Elastic Beams ◽  
Lateral Vibrations

Abstract This paper presents a method for determining the natural frequencies of lateral vibrations for elastic beams. The beams may be of variable cross section and may have any number of spans. The five-moment equation is developed and is then applied to beams supported in various ways. The author reduces the necessary calculations to a simple tabular scheme. Several illustrative examples are included to demonstrate the method of computation.

Multi-crack detection in general cross-section swept wings based on natural frequency changes

2020 ◽  
pp. 107754632096401
Author(s):  
Fatemeh Barzegar ◽  
Saeedreza Mohebpour ◽  
Hekmat Alighanbari
Keyword(s):  
Mathematical Model ◽  
Natural Frequency ◽  
Cross Section ◽  
Crack Detection ◽  
Natural Frequencies ◽  
Detection Method ◽  
Mode Shapes ◽  
Modal Strain Energy ◽  
Torsional Mode ◽  
Frequency Changes

In this article, a multi-crack detection method, which is based on natural frequency changes and the concept of modal strain energy, is for the first time developed for the general cross-section swept tapered wings under coupled bending-torsional vibration and applied to the solid and thin-walled airfoil cross-section wings. The presented method is able to handle the problems with an unknown number of cracks and predicts the number of existent cracks, their locations and depths by optimization of an appropriate objective function. The stress intensity factors of airfoil-shaped crack surfaces are obtained using an approximation method. Inputs of the detection method are natural frequencies of uncracked and cracked wings which are calculated by using a mathematical model and finite element method software ANSYS, respectively, and validated by comparison with former research studies. In the mathematical model, the Rayleigh–Ritz method is used to calculate the coupled bending-torsional mode shapes of the uncracked wing and their corresponding natural frequencies. Results demonstrate that the proposed method has precisely predicted the number, locations and depths of cracks in all case studies.

Vibration Characteristics of Pre-twisted Blades of Asymmetrical Aerofoil Cross-Section

1971 ◽  
Vol 22 (3) ◽  
pp. 257-273 ◽  
Author(s):  
W. Carnegie ◽  
B. Dawson
Keyword(s):  
Natural Frequency ◽  
Cross Section ◽  
Natural Frequencies ◽  
Twist Angle ◽  
The Other ◽  
Mode Shapes ◽  
Inertia Effects ◽  
Theoretical Frequency ◽  
Frequency Ratios ◽  
Theoretical Results

SummaryThe natural frequencies and mode shapes of vibration of cantilever aerofoil cross-section blades of pre-twist angle in the range 0 to 90 degrees are obtained. The beams are 152·4 mm long and the width / thickness ratio is such that they may be regarded as slender. Theoretical frequency ratios and mode shapes of vibration, neglecting shear and rotary inertia effects, are obtained for two sets of beams, one with clockwise pre-twist relative to the root cross-section and the other with anti-clockwise pre-twist. The effect of variation in the value of the centre-of-flexure coordinates upon the natural frequency ratios and mode shapes of vibration is investigated. The theoretical results are compared to corresponding experimental results.

The Lowest Natural Frequency of an Axial Compressor Blade

1958 ◽  
Vol 62 (573) ◽  
pp. 677-680
Author(s):  
J. Dunham
Keyword(s):  
Natural Frequency ◽  
Cross Section ◽  
Natural Frequencies ◽  
Axial Compressor ◽  
Arbitrary Cross Section ◽  
Compressor Blade ◽  
Simple Method ◽  
Uniform Beam ◽  
Logical Extension ◽  
Made In

Published Works discuss the calculation of the natural frequencies of uniform beam systems, but not simple calculations on beams of arbitrary cross section. This note describes a simple method evolved for estimating the lowest natural frequency of an axial compressor blade, and compares its results with measurements and with other calculations. The logical extension of the method to calculating the frequency of any mode of any cantilever of arbitrary cross section is made in the Appendix.

Algorithm for diagnosing fastenings of pipe with liquid

2007 ◽  
Vol 5 ◽  
pp. 96-100
Author(s):  
A.M. Akhtyamov ◽  
F.F. Safina
Keyword(s):  
Frequency Spectrum ◽  
Natural Frequencies ◽  
Algebraic Equations ◽  
Bending Vibrations ◽  
Narrow Tube

An algorithm is considered for diagnosing fastening of a narrow tube filled with a fluid by a spectrum of natural frequencies of its bending vibrations. The constructed algorithm, based on the solution of systems of algebraic equations, allows one to determine any pipe fastenings by 9 values from the frequency spectrum of its vibrations when the liquid is flowing through the pipe.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

scholarly journals A Vibration-Based Structural Health Monitoring System for Transmission Line Towers

Electronics ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 515 ◽  
Author(s):  
Long Zhao ◽  
Xinbo Huang ◽  
Ye Zhang ◽  
Yi Tian ◽  
Yu Zhao
Keyword(s):  
Structural Health Monitoring ◽  
Transmission Line ◽  
Natural Frequency ◽  
Health Monitoring ◽  
Structural Changes ◽  
Natural Frequencies ◽  
Transmission Tower ◽  
Health Monitoring System ◽  
Wind Speeds ◽  
Before And After

In this paper, we present a vibration-based transmission tower structural health monitoring system consisting of two parts that identifies structural changes in towers. An accelerometer group realizes vibration response acquisition at different positions and reduces the risk of data loss by data compression technology. A solar cell provides the power supply. An analyser receives the data from the acceleration sensor group and calculates the transmission tower natural frequencies, and the change in the structure is determined based on natural frequencies. Then, the data are sent to the monitoring center. Furthermore, analysis of the vibration signal and the calculation method of natural frequencies are proposed. The response and natural frequencies of vibration at different wind speeds are analysed by time-domain signal, power spectral density (PSD), root mean square (RMS) and short-time Fouier transform (STFT). The natural frequency identification of the overall structure by the stochastic subspace identification (SSI) method reveals that the number of natural frequencies that can be calculated at different wind speeds is different, but the 2nd, 3rd and 4th natural frequencies can be excited. Finally, the system was tested on a 110 kV experimental transmission line. After 18 h of experimentation, the natural frequency of the overall structure of the transmission tower was determined before and after the tower leg was lifted. The results show that before and after the tower leg is lifted, the natural frequencies of each order exhibit obvious changes, and the differences in the average values can be used as the basis for judging the structural changes of the tower.

Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

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