Vibration Analysis Method of Cracked Beam Based on the Principle of Energy

2011 ◽  
Vol 94-96 ◽  
pp. 1633-1637
Author(s):  
De Liang Chen ◽  
Wen Ting Wang ◽  
Feng Liu
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Analysis Method ◽  
Structural Damping ◽  
Linear Vibration ◽  
Cracked Beam ◽  
Energy Principle ◽  
Crack Location ◽  
Nonlinear Elastic ◽  
Elastic Mechanics

Using the theory of nonlinear elastic mechanics and fracture mechanics, the equation of motion governing equation of cracked beam is derived by the energy method, and solved with separation method of variables. Vibration analysis method based on the energy principle in this paper is proved feasible.Through numerical analysis, the effects of structural damping, crack location and depth on natural frequencies of linear vibration is investigated.

scholarly journals Residual life estimation of structural beam using experimental and numerical modal analysis methods

2020 ◽  
Vol 4 (2) ◽  
pp. 135-146
Author(s):  
Ganda Anand Siva ◽  
Shinigam Ramakrishna
Keyword(s):  
Modal Analysis ◽  
Natural Frequencies ◽  
Residual Life ◽  
Crack Depth ◽  
Common Element ◽  
Cracked Beam ◽  
Element Analysis ◽  
Crack Location ◽  
Parametric Studies ◽  
Ship Propeller

A structural beam is a common element in many mechanical structures such as ship propeller shaft, crane boom, and air craft wings. In the present paper experimental and numerical modal analysis are carried out for estimating the damage detection, geometric location of the damage, severity of damage and residual life of structural beam to prevent unexpected failures of the mechanical structures. Experimental and numerical modal analysis results for healthy and cracked beam are compared for validation of numerical methodology used in the present paper. Experimental modal analysis is performed on both healthy and cracked beam with the help of impact hammer, acceleration sensor and FFT analyzer associated with EDM (Engineering Data Management) software. Modal tests are conducted using impact method on selected locations of the entire healthy and cracked beam to find the first three natural frequencies, which are used to detect the presence of damage and geometric location of the damage. Three parametric studies are carried out to know the effect of crack depth, crack location and crack orientation on the natural frequencies of the cracked beam. Finally,  residual life of a healthy and cracked beam was estimated using Basiquin’s equation and finite element analysis software called ANSYS 18.1.

Vibration Analysis of a Cracked Beam on an Elastic Foundation

2016 ◽  
Vol 16 (05) ◽  
pp. 1550006 ◽  
Author(s):  
Ali Çağri Batihan ◽  
Fevzi Suat Kadioğlu
Keyword(s):  
Elastic Foundation ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Crack Depth ◽  
Cracked Beam ◽  
Crack Location ◽  
Transverse Vibrations ◽  
Foundation Type ◽  
Foundation Parameters ◽  
Open Edge

The transverse vibrations of cracked beams with rectangular cross sections resting on Pasternak and generalized elastic foundations are considered. Both the Euler–Bernoulli (EB) and Timoshenko beam (TB) theories are used. The open edge crack is represented as a rotational spring whose compliance is obtained by the fracture mechanics. By applying the compatibility conditions between the beam segments at the crack location and the boundary conditions, the characteristic equations are derived, from which the nondimensional natural frequencies are solved as the roots. Sample numerical results showing the effects of crack depth, crack location, foundation type and foundation parameters on the natural frequencies of the beam are presented. It is observed that the existence of crack reduces the natural frequencies, whereas the elasticity of the foundation increases the stiffness of the system and thus the natural frequencies. It is also observed that the type of elastic foundation has a significant effect on the natural frequencies of the cracked beam.

Identification of Transverse Crack in Beam like Structure Using PSO

2014 ◽  
Vol 548-549 ◽  
pp. 1728-1734
Author(s):  
D.N. Thatoi ◽  
S. Choudhury ◽  
P.K. Jena ◽  
H.C. Das ◽  
A.K. Subudhi
Keyword(s):  
Natural Frequencies ◽  
Crack Depth ◽  
Population Based ◽  
Beam Structure ◽  
Cracked Beam ◽  
Swarm Optimization ◽  
Crack Location ◽  
Flexibility Matrix ◽  
Local Flexibility ◽  
Open Edge

The current proposed method has been developed using particle swarm optimization (PSO) technique. A single transverse open edge crack on a beam structure has been modeled using local flexibility matrix to determine natural frequencies. The PSO is a population based; bio-inspired evolutionary optimization algorithm that has been implemented for detection of crack. The frequencies obtained from analytical method have been used to train the PSO to get the desired output such as; relative crack depth and relative crack location. Mathematical modeling of the cracked beam structure is being done to ensure the integrity of the above algorithms. The results from the PSO show that both the size and location of the crack can be predicted efficiently through the proposed PSO.

Vibration Analysis and Simulation of Mast Section of Hoist

2012 ◽  
Vol 567 ◽  
pp. 3-9
Author(s):  
Ji Man Luo ◽  
Yang Jiang ◽  
Zhi Hui Xing
Keyword(s):  
Working Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Great Influence ◽  
System Stability ◽  
Analysis Method ◽  
External Excitation ◽  
Excitation Force ◽  
Stiffness Characteristics

In order to avoid the damage of structure caused by the vibration, the natural frequency and vibration mode figure of the stiffness characteristics of the hoist’s structure should be analyzed. Modal analysis method is presented for solving above problem, and the first 6 order natural frequencies in different working conditions have been calculated in this paper. Vibration mode figure of structure system have been simulated corresponding to the first 6 order natural frequencies based on ANSYS. It is shows that the external excitation force have a great influence on the top of the free end when the cage moves to a different location. So, in the actual construction, the stiffness of top free ends connected tie-in device should be strengthened, therefore the system stability will be improved.

Approximate analytical analysis of longitudinal natural frequencies of a cracked beam

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Hillal Ayas ◽  
Lyes Amara ◽  
Mohamed Chabaat
Keyword(s):  
Natural Frequencies ◽  
Crack Depth ◽  
Experimental Tests ◽  
Frequency Equation ◽  
Cracked Beam ◽  
Lagrange Inversion ◽  
Approximate Analytical Expression ◽  
Content Type ◽  
Inversion Theorem ◽  
Crack Location

PurposeIn this paper, an approximate analytical approach is developed for the determination of natural longitudinal frequencies of a cantilever-cracked beam based on the Lagrange inversion theorem.Design/methodology/approachThe crack is modeled by an equivalent axial spring with stiffness according to Castigliano's theorem. Thus, an implicit frequency equation corresponding to cantilever-cracked bar is obtained. The resulting equation is solved using the Lagrange inversion theorem.Findingseffect of different crack depths and crack positions on natural frequencies of the cracked beam is analyzed. It is shown that an increase in the crack depth ratio produces a decrease in the fundamental longitudinal natural frequency of a cracked bar. Furthermore, approximate analytical results are compared with those obtained numerically as well as from experimental tests.Originality/valueA new approximate analytical expression of a fundamental longitudinal frequency, as a function of crack depth and crack location, is obtained.

scholarly journals Natural frequency analysis of cracked beam

1997 ◽  
Vol 19 (2) ◽  
pp. 28-38 ◽  
Author(s):  
Nguyen Tien Khiem ◽  
Dao Nhu Mai
Keyword(s):  
Natural Frequencies ◽  
General Procedure ◽  
Frequency Equation ◽  
Dimensional Structure ◽  
Cracked Beam ◽  
Bending Vibration ◽  
Arbitrary Boundary ◽  
Crack Location ◽  
Natural Frequency Analysis ◽  
Crack Position

The model of cracked one-dimensional structure has been treated as two uniform beams connected by an equivalent rotation spring at the crack location. The frequency equation in bending vibration of the system is obtained in general form for arbitrary boundary conditions at both ends used for analysing the natural frequencies as function of crack position and magnitude. This investigation allows to carry out general procedure for identification of position as well as magnitude of the crack by natural frequencies measured experimentally.

Research on transformer vibration monitoring and diagnosis based on Internet of things

2021 ◽  
Vol 30 (1) ◽  
pp. 677-688
Author(s):  
Zhenzhuo Wang ◽  
Amit Sharma
Keyword(s):  
Internet Of Things ◽  
Power Distribution ◽  
Vibration Analysis ◽  
Vibration Monitoring ◽  
Power Transformers ◽  
Normal Operation ◽  
Analysis Method ◽  
Power Distribution Network ◽  
Monitoring And Diagnosis ◽  
Distribution Transformers

Abstract A recent advent has been seen in the usage of Internet of things (IoT) for autonomous devices for exchange of data. A large number of transformers are required to distribute the power over a wide area. To ensure the normal operation of transformer, live detection and fault diagnosis methods of power transformers are studied. This article presents an IoT-based approach for condition monitoring and controlling a large number of distribution transformers utilized in a power distribution network. In this article, the vibration analysis method is used to carry out the research. The results show that the accuracy of the improved diagnosis algorithm is 99.01, 100, and 100% for normal, aging, and fault transformers. The system designed in this article can effectively monitor the healthy operation of power transformers in remote and real-time. The safety, stability, and reliability of transformer operation are improved.

Effect of guy cable constraint on structural damping of open lattice antenna towers

1980 ◽  
Vol 7 (4) ◽  
pp. 614-620
Author(s):  
J. S. Kennedy ◽  
D. J. Wilson ◽  
P. F. Adams ◽  
M. Perlynn
Keyword(s):  
Natural Frequencies ◽  
Damping Ratio ◽  
Field Tests ◽  
Full Scale ◽  
Structural Damping ◽  
Scale Field ◽  
Modes Of Vibration

This paper presents the results of full-scale field tests on two steel guyed latticed towers. The towers were approximately 83 m in height, were guyed at three levels, and were of bolted angle construction. The observed results consist of the natural frequencies of the first two modes of vibration as well as the damping ratio for the first mode. The observed results are compared with analytical predictions and observations made concerning the contributions of structural and cable action to the damping ratio.

Nondestructive Detection of a Crack in a Triangular Cantilever Beam Based on Frequency Measurement

2007 ◽  
Vol 353-358 ◽  
pp. 2285-2288
Author(s):  
Fei Wang ◽  
Xue Zeng Zhao
Keyword(s):  
Cantilever Beam ◽  
Natural Frequencies ◽  
Frequency Measurement ◽  
Crack Size ◽  
Force Sensors ◽  
Rotational Spring ◽  
Cantilever Deflection ◽  
Crack Location ◽  
Small Force ◽  
Point Of Intersection

Triangular cantilevers are usually used as small force sensors in the transverse direction. Analyzing the effect of a crack on transverse vibration of a triangular cantilever will be of value to users and designers of cantilever deflection force sensors. We present a method for prediction of location and size of a crack in a triangular cantilever beam based on measurement of the natural frequencies in this paper. The crack is modeled as a rotational spring. The beam is treated as two triangular beams connected by a rotational spring at the crack location. Formulae for representing the relation between natural frequencies and the crack details are presented. To detect crack details from experiment results, the plots of the crack stiffness versus its location for any three natural modes can be obtained through the relation equation, and the point of intersection of the three curves gives the crack location. The crack size is then calculated using the relation between its stiffness and size. An example to demonstrate the validity and accuracy of the method is presented.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

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