scholarly journals Exact receptance function and receptance curvature of a clamped-clamped continuous cracked beam

2019 ◽  
Vol 41 (4) ◽  
pp. 349-361
Author(s):  
Nguyen Viet Khoa ◽  
Cao Van Mai ◽  
Dao Thi Bich Thao
Keyword(s):  
Numerical Simulations ◽  
Frequency Domain ◽  
Crack Detection ◽  
Harmonic Excitation ◽  
Second Derivative ◽  
Cracked Beam ◽  
Cracked Beams

The receptance function has been studied and applied widely since it interrelates the harmonic excitation and the response of a structure in the frequency domain. This paper presents the derivation of the exact receptance function of continuous cracked beams and its application for crack detection. The receptance curvature is defined as the second derivative of the receptance. The influence of the crack on the receptance and receptance curvature is investigated. It is concluded that when there are cracks the receptance curvature has sharp changes at the crack positions. This can be applied for the crack detection purpose. In this paper, the numerical simulations are provided.

scholarly journals Exact Receptance Function of Cracked Beams and Its Application for Crack Detection

2019 ◽  
Vol 2019 ◽  
pp. 1-19
Author(s):  
Khoa Viet Nguyen ◽  
Mai Van Cao
Keyword(s):  
Boundary Conditions ◽  
Numerical Simulations ◽  
Frequency Domain ◽  
Crack Detection ◽  
Harmonic Excitation ◽  
General Boundary ◽  
Second Derivative ◽  
General Boundary Conditions ◽  
Cracked Beams

The receptance function is very important which interrelates the harmonic excitation and the response of a structure in the frequency domain. This paper presents the exact receptance function of cracked beams. In this work, the “receptance curvature” is defined as the second derivative of the receptance. The influence of the crack on the receptance curvature is investigated. The results show that when there are cracks, the receptance curvature is influenced significantly at crack positions. This might be useful for the detection of cracks. In this paper, the derivation of exact receptance of the beam with general boundary conditions is presented, and the numerical simulations are provided.

Modelling of a Beam with a Breathing Edge Crack and Some Observations for Crack Detection

2002 ◽  
Vol 8 (5) ◽  
pp. 673-693 ◽  
Author(s):  
A. Nandi ◽  
S. Neogy
Keyword(s):  
Edge Crack ◽  
Crack Detection ◽  
Spectral Characteristics ◽  
Crack Size ◽  
Small Displacement ◽  
Harmonic Load ◽  
Cracked Beam ◽  
Frequency Spectra ◽  
Proposed Model ◽  
Cracked Beams

The breathing behaviour of closing cracks has been adequately simulated as a small-displacement, frictionless contact problem. The problem of a beam with an edge crack subjected to harmonic loading has been considered as a plane problem and an attempt is made to solve it by using finite elements employing eight-node plane isoparametric elements. The proposed model allows the crack size and position to be varied. Another physically important problem of a cantilever beam held between two heavy jaws at the top and bottom, which are not equally flushed, is considered. This beam is also excited by a harmonic load at the tip. The contact model and a simple single degree of freedom model are used to solve the problem. Both the above problems (cracked beam and beam in offset jaws) show presence of integral multiples of the forcing frequency in their frequency spectra. An important observation regarding cracked beams and beams with imperfect support is made. If the forcing frequency is such that it coincides or is close to any one of the integral sub-multiples (1/ n) of the first natural frequency of the system, then the nth harmonic of the forcing frequency will considerably shoot up. This effect is highly pronounced for the case n = 2 and this observation may be used to detect cracks in beams as small as 2.5% of the depth. For cracked beams, the even harmonics are considerably stronger than the odd ones. As the crack size decreases, the odd harmonics become weaker. For a 2.5% crack only the second and fourth harmonics are visible in an 80 dB scale, with the former being the stronger. However, it is important to note that cracked beams and beams with imperfect support have closely similar spectral characteristics and so due caution must be exercised during crack detection.

Crack detection and vibration behavior of cracked beams

2001 ◽  
Vol 79 (16) ◽  
pp. 1451-1459 ◽  
Author(s):  
P.N. Saavedra ◽  
L.A. Cuitiño
Keyword(s):  
Crack Detection ◽  
Vibration Behavior ◽  
Cracked Beams

scholarly journals Monitoring a sudden crack of beam-like bridge during earthquake excitation

2013 ◽  
Vol 35 (3) ◽  
Author(s):  
Nguyen Viet Khoa
Keyword(s):  
Fourier Transform ◽  
Crack Detection ◽  
Crack Depth ◽  
Sudden Change ◽  
Wavelet Spectrum ◽  
Cracked Beam ◽  
Earthquake Excitation ◽  
Time Frequency ◽  
Short Time ◽  
Time Information

This paper presents a wavelet spectrum technique for monitoring a sudden crack of a beam-like bridge structure during earthquake excitation. When there is a sudden crack caused by earthquake excitation the stiffness of the structure is changed leading to a sudden change in natural frequencies during vibration. It is difficult to monitor this sudden change in the frequency using conventional approaches such as Fourier transform because in Fourier transform the time information is lost so that it is impossible to analyse short time events. To overcome this disadvantage, wavelet spectrum, a time-frequency analysis, is used for monitoring a sudden change in frequency duringearthquake excitation for crack detection. In this study, a model of 3D crack is applied. The derivation of the stiffness matrix of a 3D cracked beam element with rectangular section adopted from fracture mechanics is presented. Numerical results showed that the sudden occurrence of the crack during earthquake excitation can be detected by the sudden change in frequency using wavelet power spectrum. When the crack depth increases, the instantaneous frequency (IF) of the structure is decreased.

scholarly journals Stiffness Estimation of Cracked Beams Based on Nonlinear Stress Distributions Near the Crack

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Chunyu Fu ◽  
Yuyang Wang ◽  
Dawei Tong
Keyword(s):  
Crack Depth ◽  
Internal Force ◽  
Stress Distributions ◽  
Cracked Beam ◽  
Section Shape ◽  
Nonlinear Stress ◽  
Crack Depth Ratio ◽  
Element Technique ◽  
Force Equilibrium ◽  
Cracked Beams

The crack presence causes nonlinear stress distributions along the sections of a beam, which change the neutral axis of the sections and further affect the beam stiffness. Thus, this paper presents a method for the stiffness estimation of cracked beams based on the stress distributions. First, regions whose stresses are affected by the crack are analyzed, and according to the distance to the crack, different nonlinear stress distributions are modeled for the effect regions. The inertia moments of section are evaluated by substituting these stress distributions into the internal force equilibrium of section. Then the finite-element technique is adopted to estimate the stiffness of the cracked beam. The estimated stiffness is used to predict the displacements of simply supported beams with a crack, and the results show that both static and vibrational displacements are accurately predicted, which indicates that the estimated stiffness is precise enough. Besides, as the section shape of beam is not limited in the process of modeling the stress distributions, the method could be applicable not only to the stiffness estimation of cracked beams with a rectangular section, but also to that of the beams with a T-shaped section if the crack depth ratio is not larger than 0.7.

scholarly journals Multi-physics phenomena influencing the performance of the car horn

2019 ◽  
Vol 38 (2) ◽  
pp. 544-557 ◽  
Author(s):  
Cristian Medè ◽  
Alberto Doria ◽  
Paolo Munaretto ◽  
Jorge SG Valdecasas
Keyword(s):  
Numerical Simulations ◽  
Mechanical Energy ◽  
Input Voltage ◽  
Harmonic Excitation ◽  
Electromagnetic Energy ◽  
Electrical Parameters ◽  
Detailed Model ◽  
Non Linear ◽  
Linear Effects ◽  
Car Horn

Usually cars are equipped with disk horns. In these devices electromagnetic energy is converted into mechanical energy of two nuclei that vibrate and impact each other – the impacts excite the disk that radiates sound. This paper aims at understanding the results of acoustic tests carried out on horns with different excitation voltages and different mounting brackets. Since many non-linear phenomena are inherent in the vibrations of the nuclei, a detailed model of the electromechanical system is developed. Results show the dependence of operating frequency on the input voltage and the role played by the various mechanical and electrical parameters on the dynamics of the horn. Particular non-linear effects, like sub-harmonic excitation, are presented and discussed. A general agreement between experimental results and numerical simulations is found.

scholarly journals Vibration Induced by Subway Trains: Open-Trench Mitigation Analysis in the Time and Frequency Domains

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Wenbo Yang ◽  
Ran Yuan ◽  
Juan Wang
Keyword(s):  
Numerical Simulations ◽  
Frequency Domain ◽  
Frequency Domain Analysis ◽  
Soil Response ◽  
Physical Model Tests ◽  
Frequency Domains ◽  
Trench Isolation ◽  
Open Trench ◽  
Isolation Performance ◽  
Time And Frequency Domains

In this paper, we analyse the mitigation effects of open trenches on the vibrations induced by subway trains. The study is performed by using both physical model tests and numerical simulations. The effectiveness is evaluated by calculating the frequency response function (FRF) and the vibration acceleration peak (VAP) in both time and frequency domains. The experimental and numerical results demonstrate that the open trench has clear effects on the dynamic soil response. Both time and frequency domain results suggest that the dynamic response of the soils beyond the open trenches could be significantly affected, due to the existence of the open trench. According to the frequency domain analysis, the inclusion of open trenches could effectively reduce the soil response in a higher frequency range. Due to reflection effects at the boundaries of the trench, an amplification of the soil response in front of the open trench is observed. Parametric study by means of numerical simulations is also performed. The width of the open trench demonstrates negligible effects on the dynamic soil response, whilst the trench depth exhibits a large influence on the trench isolation performance. With an increase in the trench depth, the isolation performance is significantly improved. It is concluded that the open trenches perform well as an isolation barrier, in mitigating the vibration induced by subway trains.

scholarly journals Mode shape curvature of multiple cracked beam and its use for crack identification in beam-like structures

2020 ◽  
Author(s):  
Nguyen Tien Khiem
Keyword(s):  
Finite Difference ◽  
Mode Shape ◽  
Crack Detection ◽  
Exact Expression ◽  
Finite Difference Approximation ◽  
Theoretical Development ◽  
Difference Approximation ◽  
Crack Identification ◽  
Cracked Beam ◽  
Modal Curvature

The problem of using the modal curvature for crack detection is discussed in this paper based on an exact expression of mode shape and its curvature. Using the obtained herein exact expression for the mode shape and its curvature, it is demonstrated that the mode shape curvature is really more sensitive to crack than mode shape itself. Nevertheless, crack-induced change in the approximate curvature calculated from the exact mode shape by the central finite difference technique (Laplacian) is much greater in comparison with both the mode shape and curvature. It is produced by the fact, shown in this study, that miscalculation of the approximate curvature is straightforwardly dependent upon crack magnitude and resolution step of the finite difference approximation. Therefore, it can be confidently recommended to use the approximate curvature for multiple crack detection in beam by properly choosing the approximation mesh. The theoretical development has been illustrated by numerical results.

scholarly journals An Analytical Method for Crack Detection of Beams with Uncertain Boundary Conditions by a Concentrated Test Mass

2018 ◽  
Vol 4 (7) ◽  
pp. 1629
Author(s):  
Seyed Milad Mohtasebi ◽  
Naser Khaji
Keyword(s):  
Boundary Conditions ◽  
Crack Detection ◽  
Beam Theory ◽  
Element Model ◽  
Test Mass ◽  
Cracked Beam ◽  
Stationary Mass ◽  
Numerical Finite Element ◽  
Torsion Springs ◽  
Uncertain Boundary

The aim of this study is to introduce a method for crack detection and simultaneously assessing boundary conditions in beams. This study suggests a method based on the effect of a concentrated test mass on the natural frequency that is defined as a stationary mass, which can be located in different positions of the beam and cannot be separated from the beam. Timoshenko beam theory is used to calculate the frequencies. In this method, a beam with the desired number of cracks is modeled. The beam is divided into separated parts at crack section which are joined together by elastic weightless torsion springs, to avoid non-linearity effects, it is assumed that the crack is always open. At the first step, equations for a cracked beam are extracted by considering the spring boundary conditions. Then, to verify the equations, numerical finite element model is used. In this way, a new method is also applied to model the torsion springs in supports and it is shown that suggested model is acceptable. Eventually, the obtained responses are evaluated and the sources of errors are identified. To correct the existing errors, a modifying function is suggested. Finally, the inverse problem is solved.

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