Nonlinear pseudo-force in a breathing crack to generate harmonics

2021 ◽  
Vol 492 ◽  
pp. 115734
Author(s):  
Wei Xu ◽  
Zhongqing Su ◽  
Maciej Radzieński ◽  
Maosen Cao ◽  
Wiesław Ostachowicz
Keyword(s):  
Breathing Crack

Employing Surface Roughness for Bridge-Vehicle Interaction Based Damage Detection

2011 ◽  
Author(s):  
Vesna Jaksic ◽  
Vikram Pakrashi ◽  
Alan O’Connor
Keyword(s):  
Surface Roughness ◽  
Damage Detection ◽  
Flexural Rigidity ◽  
Single Point ◽  
Point Load ◽  
Ride Quality ◽  
Breathing Crack ◽  
Bernoulli Beam ◽  
Statistical Parameters ◽  
Euler Bernoulli Beam

Damage detection and Structural Health Monitoring (SHM) for bridges employing bridge-vehicle interaction has created considerable interest in recent times. In this regard, a significant amount of work is present on the bridge-vehicle interaction models and on damage models. Surface roughness on bridges is typically used for detailing models and analyses are present relating surface roughness to the dynamic amplification of response of the bridge, the vehicle or to the ride quality. This paper presents the potential of using surface roughness for damage detection of bridge structures through bridge-vehicle interaction. The concept is introduced by considering a single point observation of the interaction of an Euler-Bernoulli beam with a breathing crack traversed by a point load. The breathing crack is treated as a nonlinear system with bilinear stiffness characteristics related to the opening and closing of crack. A uniform degradation of flexural rigidity of an Euler-Bernoulli beam traversed by a point load is also considered in this regard. The surface roughness of the beam is essentially a spatial representation of some spectral definition and is treated as a broadband white noise in this paper. The mean removed residuals of beam response are analyzed to estimate damage extent. Uniform velocity and acceleration conditions of the traversing load are investigated for the appropriateness of use. The detection and calibration of damage is investigated through cumulant based statistical parameters computed on stochastic, normalized responses of the damaged beam due to passages of the load. Possibilities of damage detection and calibration under benchmarked and non-benchmarked cases are discussed. Practicalities behind implementing this concept are also considered.

Vibration Analysis of the Flexible Connecting Rod With the Breathing Crack in a Slider-Crank Mechanism

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Yan-Shin Shih ◽  
Chen-Yuan Chung
Keyword(s):  
Governing Equation ◽  
Moving Boundary ◽  
Beam Theory ◽  
Crack Model ◽  
Breathing Crack ◽  
Connecting Rod ◽  
Bernoulli Beam ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam ◽  
Crank Mechanism

This paper investigates the dynamic response of the cracked and flexible connecting rod in a slider-crank mechanism. Using Euler–Bernoulli beam theory to model the connecting rod without a crack, the governing equation and boundary conditions of the rod's transverse vibration are derived through Hamilton's principle. The moving boundary constraint of the joint between the connecting rod and the slider is considered. After transforming variables and applying the Galerkin method, the governing equation without a crack is reduced to a time-dependent differential equation. After this, the stiffness without a crack is replaced by the stiffness with a crack in the equation. Then, the Runge–Kutta numerical method is applied to solve the transient amplitude of the cracked connecting rod. In addition, the breathing crack model is applied to discuss the behavior of vibration. The influence of cracks with different crack depths on natural frequencies and amplitudes is also discussed. The results of the proposed method agree with the experimental and numerical results available in the literature.

scholarly journals Crack Parameters Identification Based on a Kriging Surrogate Model for Operating Rotors

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Danyang Wang ◽  
Chunrong Hua ◽  
Dawei Dong ◽  
Biao He ◽  
Zhiwen Lu
Keyword(s):  
Surrogate Model ◽  
Parameters Identification ◽  
The Finite Element Method ◽  
Breathing Crack ◽  
Kriging Surrogate Model ◽  
Crack Location ◽  
Rotor Bearing ◽  
Location Depth ◽  
Nondominated Sorting ◽  
Bearing System

Parameters identification of cracked rotors has been gaining importance in recent years, but it is still a great challenge to determine the crack parameters including crack location, depth, and angle for operating rotors. This work proposes a new method to identify crack parameters in a rotor-bearing system based on a Kriging surrogate model and an improved nondominated sorting genetic algorithm-III (NSGA-III). A rotor-bearing system with a breathing crack is established by the finite element method and the superharmonic components are used as index to detect the cracks, the Kriging surrogate model between crack parameters and the superharmonic component amplitudes of the vibration response for rotors are constructed, and an improved NSGA-III is proposed to obtain the optimal crack parameters. Numerical experiments show that the proposed method can identify the crack location, depth, and angle accurately and efficiently for operating rotors.

Vibrations of beams with a breathing crack and large amplitude displacements

2015 ◽  
Vol 230 (1) ◽  
pp. 34-54 ◽  
Author(s):  
Gonçalo Neves Carneiro ◽  
Pedro Ribeiro
Keyword(s):  
Time Domain ◽  
Equations Of Motion ◽  
Shape Functions ◽  
Breathing Crack ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Time Histories ◽  
Linear Effects ◽  
Fourier Spectra ◽  
The Time Domain

The vibrations of beams with a breathing crack are investigated taking into account geometrical non-linear effects. The crack is modeled via a function that reduces the stiffness, as proposed by Christides and Barr (One-dimensional theory of cracked Bernoulli–Euler beams. Int J Mech Sci 1984). The bilinear behavior due to the crack closing and opening is considered. The equations of motion are obtained via a p-version finite element method, with shape functions recently proposed, which are adequate for problems with abrupt localised variations. To analyse the dynamics of cracked beams, the equations of motion are solved in the time domain, via Newmark's method, and the ensuing displacements, velocities and accelerations are examined. For that purpose, time histories, projections of trajectories on phase planes, and Fourier spectra are obtained. It is verified that the breathing crack introduce asymmetries in the response, and that velocities and accelerations can be more affected than displacements by the breathing crack.

Reference-Free Breathing Crack Identification of Beam-Like Structures Using an Enhanced Spatial Fourier Power Spectrum with Exponential Weighting Functions

2019 ◽  
Vol 19 (02) ◽  
pp. 1950017 ◽  
Author(s):  
J. Prawin ◽  
A. Rama Mohan Rao
Keyword(s):  
Fatigue Crack ◽  
Power Spectrum ◽  
Crack Detection ◽  
Crack Problem ◽  
Experimental Studies ◽  
Crack Identification ◽  
Successful Implementation ◽  
Breathing Crack ◽  
Fourier Power Spectrum ◽  
Exponential Weighting

Detection of incipient damage of structures at the earliest possible stage is desirable for successful implementation of any health monitoring system. In this paper, we focus on breathing crack problem and present a new reference-free algorithm for fatigue crack detection, localization, and characterization for beam-like structures. We use the spatial curvature of the Fourier power spectrum as a damage sensitive feature for fatigue crack identification. An exponential weighting function that takes into account nonlinear dynamic signatures, such as sub- and superharmonics, is proposed in the Fourier power spectrum in order to enrich the damage-sensitive features of the structure. Both numerical and experimental studies have been carried out to test and verify the proposed algorithm.

Free and Forced Longitudinal Vibrations of a Cantilevered Bar With a Crack

1992 ◽  
Vol 114 (2) ◽  
pp. 171-177 ◽  
Author(s):  
K. R. Collins ◽  
R. H. Plaut ◽  
J. Wauer
Keyword(s):  
Steady State ◽  
Natural Frequency ◽  
Transverse Crack ◽  
Breathing Crack ◽  
Longitudinal Vibrations ◽  
Harmonic Force ◽  
Frequency Spectra ◽  
Crack Location ◽  
Fundamental Natural Frequency ◽  
Steady State Amplitude

Longitudinal vibrations of a cantilevered bar with a transverse crack are investigated. For undamped, unforced vibrations, frequency spectra are computed and the effects of the crack location and compliance on the fundamental natural frequency are determined. For vibrations caused by a distributed, longitudinal, harmonic force, the steady-state amplitude of motion of the free end is plotted as a function of the forcing frequency, crack location, and crack compliance, and frequency spectra are also obtained. Results for a breathing crack are compared to those for a crack which remains open and those for an uncracked bar.

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