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.

A Continuous Model for Forced Vibration Analysis of a Cracked Beam

2005 ◽  
Author(s):  
M. Behzad ◽  
A. Meghdari ◽  
A. Ebrahimi
Keyword(s):  
Natural Frequency ◽  
Vibration Analysis ◽  
Crack Depth ◽  
Continuous Model ◽  
Forced Response ◽  
Galerkin Projection ◽  
Cracked Beam ◽  
Bending Vibration ◽  
Crack Depth Ratio ◽  
Forced Vibration Analysis

In this paper the equation of motion and corresponding boundary conditions has been developed for forced bending vibration analysis of a beam with an open edge crack. A uniform Euler-Bernoulli beam and the Hamilton principle have been used in this research. The natural frequencies and the forced response of this beam have been obtained using the new developed model in conjunction with the Galerkin projection method. The crack has been modeled as a continuous disturbance function in displacement filed which could be obtained from fracture mechanics. The results show that the first natural frequency will reduce when the crack depth ratio increases. Also the rate of this reduction depends on the position of the crack. In addition it can be seen that the FRF amplitude for a cracked beam is more than a similar uncracked beam before the first natural frequency. But just after the first natural frequency the amplitude of vibration of a healthy beam is more than a cracked beam. There is an excellent agreement between the theoretical results and those obtained by the finite element method.

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 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.

Evaluation of Possible Stress Distributions in Abdominal Aorta on the Basis of Physiologically Loading Data

2004 ◽  
Author(s):  
Hiroshi Yamada ◽  
Shinya Momii
Keyword(s):  
Mechanical Properties ◽  
Wall Stress ◽  
Axial Direction ◽  
Vascular Wall ◽  
Cylindrical Shape ◽  
Stress Distributions ◽  
Reliability Of Results ◽  
Mean Pressure ◽  
Axisymmetric Shape ◽  
Force Equilibrium

It is highly desired to establish a method of estimating the stress state and mechanical properties in blood vessels numerically using diagnosis data. To obtain the mechanical state, it is necessary to evaluate the reliability of results from numerical simulation. In the current study, we investigate the possibility of stress distribution in a circular cylindrical shape of vascular wall based on the pressure-diameter relationship in the physiological pressure range with assumptions of a hyperelastic material and no residual stress. As another case, we simulate wall stress in an axisymmetric vessel at a mean pressure level. Results form the former case show that one has many solutions which reproduce the pressure-diameter (p-d) relationship and that more information is required to determine the mechanical properties. Results form the latter case show that a pair of Laplace equation and force equilibrium in the axial direction provides a wall stress for an axisymmetric shape of vessel.

Weight Functions for T-Stress for Edge Cracks in Thick-Walled Cylinders

2004 ◽  
Author(s):  
J. Li ◽  
C. L. Tan ◽  
X. Wang
Keyword(s):  
Boundary Element ◽  
Edge Crack ◽  
Complex Stress ◽  
Weight Functions ◽  
Stress Distributions ◽  
Internal Edge ◽  
Crack Face ◽  
Nonlinear Stress ◽  
Wide Range ◽  
T Stress

This paper presents T-stress solutions for an internal edge crack in thick-walled cylinders under complex stress distributions. First, the background of the weight function method for the calculation of T-stress is discussed. Then the T-stress results for edge-cracked cylinders obtained from extensive boundary element analyses are summarized. The crack geometries analyzed cover a wide range of radius ratios and relative crack lengths. The loading cases considered in the BEM analysis for the cracked cylinder are: i) crack face pressures with polynomial stress distributions acting on the crack face and ii) internal pressure or steady state thermal loading in the cylinder. Then, the T-stress results for uniform and linearly varying crack face pressure cases are used as the reference solutions to derive weight functions for T-stress. Boundary element results of T-stress for other nonlinear stress distributions are used to validate the derived T-stress weight functions. Excellent accuracy has been achieved. The weight functions derived are suitable for obtaining T-stress solutions for thick-walled cylinders with an internal edge crack under any complex stress fields.

Effect of a breathing crack on the damping changes in nonlinear vibrations of a cracked beam: Experimental and theoretical investigations

2020 ◽  
pp. 107754632096031
Author(s):  
Masoud Kharazan ◽  
Saied Irani ◽  
Mohammad Ali Noorian ◽  
Mohammad Reza Salimi
Keyword(s):  
Nonlinear Vibrations ◽  
Crack Depth ◽  
Beam Theory ◽  
Experimental Tests ◽  
Damping Coefficient ◽  
Crack Identification ◽  
Breathing Crack ◽  
Cracked Beam ◽  
Identification Method ◽  
Nonlinear Crack

The attempts to identify damping changes in a cracked beam can improve the accuracy of the nonlinear crack identification method. For the purpose of this aim, a parametric nonlinear equation of motion is obtained using the Euler–Bernoulli beam theory and parametric nonlinear breathing crack assumptions. Several experiments were conducted to identify the effect of breathing cracks on changing the damping value in nonlinear vibrations of a cracked beam. Experimental tests have revealed that increasing the crack depth and the level of excitation enlarges the damping coefficient in a vibrating beam. For this reason, the effects of the excitation force and crack depth on the structural damping coefficient are investigated. The obtained results indicated that considering the nonlinear response of a cracked beam and measuring the value of the damping changes can significantly improve the accuracy of the nonlinear crack identification method.

Finite Element Model for Cracked Beams with Bonded Piezoelectric Transducers

2011 ◽  
Vol 94-96 ◽  
pp. 73-76
Author(s):  
Wei Yan ◽  
Wan Chun Li ◽  
Wei Wang
Keyword(s):  
Finite Element ◽  
Mass Density ◽  
Crack Depth ◽  
Element Model ◽  
Numerical Results ◽  
Parameter Study ◽  
Bonding Layer ◽  
Cracked Beam ◽  
Electromechanical Impedance ◽  
Finite Element Software

Based on the finite element software ANSYS, an electromechanical impedance (EMI) model for a cracked beam with imperfectly bonded piezoelectric patches is established in the paper. The property of bonding layer between the PZT sensor/actuators and the host beam is taken into account and thus the three-dimensional (3D) model of piezoelectric patch-adhesive-cracked beam coupled system is developed. Comparison with existing numerical results validates the effectiveness and accuracy of the present analysis. Then, parameter study is conducted by considering effects of the vibration mode of the host beam, the mass density of the adhesive and crack depth etc. on EMI signatures. The numerical results indicate that the present EMI model can be used to detect the cracks in the structures.

Effect of Adhesive Behavior on Normal Stress Distributions in the Single-Lap Adhesive Joints

2015 ◽  
Vol 1088 ◽  
pp. 769-773
Author(s):  
Xiao Cong He
Keyword(s):  
Finite Element ◽  
Normal Stress ◽  
Three Dimensional ◽  
Adhesive Layer ◽  
Elastic Stiffness ◽  
Adhesive Joints ◽  
Stress Distributions ◽  
Element Analysis ◽  
Element Technique ◽  
Three Dimensional Finite Element

The effect of adhesives behavior on the normal stress distributions of single-lap adhesive joints is investigated using the three-dimensional finite element technique. Numerical examples are provided to show the influence on the normal stresses of the joints using adhesives of different characteristics which encompass the entire spectrum of elastic stiffness behaviour. finite element analysis solutions of the normal stress distributions in the adhesive layer have been obtained for four typical characteristics of adhesives. The results indicate that Young’s modulus and Poisson’s ratios of adhesives strongly affect the normal stress distributions of the joints.

Three-Dimensional Electromechanical Impedance Model for Damaged Beams with Imperfectly Bonded Piezoelectric Patches

2011 ◽  
Vol 52-54 ◽  
pp. 1285-1290
Author(s):  
Wan Chun Li ◽  
Wei Yan ◽  
Wei Wang
Keyword(s):  
Crack Depth ◽  
Damage Index ◽  
Three Dimensional ◽  
Adhesive Layer ◽  
Coupled System ◽  
Physical Parameters ◽  
Cracked Beam ◽  
Electromechanical Impedance ◽  
Lag Model ◽  
Peel Stress

Dynamic analysis is conducted for a cracked beam with imperfectly bonded piezoelectric patches using the finite element method in the paper. The property of adhesive between the PZT patches and the host beam is taken into account based on the peel stress model as well as the shear lag model and thus the three-dimensional (3D) model of piezoelectric patch-adhesive-host beam coupled system is developed. Based on the established three-dimensional EMI model, the effect of some physical parameters such as vibration mode of main structure, the mass of adhesive layer and crack depth etc. on electromechanical impedance signatures is investigated. Finally, the root-mean-square deviation (RMSD), a kind of non-parametric damage index, is also employed to identify the damage severity of the cracked beam.

Vibration Analysis of Multi-Cracked Beam Traversed by Moving Masses Using Discrete Element Technique

2013 ◽  
Vol 376 ◽  
pp. 220-223
Author(s):  
Reza Alebrahim ◽  
Nik Abdullah Nik Mohamed ◽  
Sallehuddin Mohamed Haris ◽  
Salvinder Singh Karam Singh
Keyword(s):  
Vibration Analysis ◽  
Beam Theory ◽  
Discrete Element ◽  
Maximum Deflection ◽  
Bernoulli Beam ◽  
Cracked Beam ◽  
Time To Build ◽  
Element Technique ◽  
Euler Bernoulli Beam ◽  
Good Agreement

The vibration analysis of a multi-cracked beam using discrete element technique (DET) was investigated in this study. Undamped simply supported beam was traversed by moving mass with constant speed and Euler Bernoulli beam theory was considered. Cracks are located in different positions and maximum deflection of mid-span was derived and compared. The results showed that increasing numbers of cracks in the beam causes more deflection while maximum deflection of beam takes longer time to build up. The results were validated by solving the equations generated using finite element method (FEM) and their comparison with already established results from previous similar studies (literatures) showed good agreement.

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