Journal ArticleDOI
Analysis of forced bilinear oscillators and the application to cracked beam dynamics
Y. C. Chu,M.-H. H. Shen +1 more
TLDR
In this paper, a closed-form solution based on the use of two square wave functions to model stiffness change is proposed for bilinear oscillators under low-frequency excitation.Abstract:
A new closed-form solution based on the use of two square wave functions to model stiffness change is proposed for bilinear oscillators under low-frequency excitation. The solution procedure is extended to cases with bilinear forcing function, which usually occur in the dynamics of damaged structures. The proposed solution provides the spectral pattern and the magnitude of each harmonic component for a damaged rectangular beam according to the size and location of the crack. The predicted spectral pattern and the magnitude of each harmonic component for a simply supported beam containing a fatigue crack are validated by numerical simulation; experimental work has not been done. The results show that the proposed solution may be used to predict efficiently spectral patterns of damaged structures, while avoiding lengthy computation. Such a procedure may be developed into an attractive on-line diagnostic tool.read more
Citations
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ReportDOI
Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review
TL;DR: A review of the technical literature concerning the detection, location, and characterization of structural damage via techniques that examine changes in measured structural vibration response is presented in this article, where the authors categorize the methods according to required measured data and analysis technique.
Journal ArticleDOI
Vibration of cracked structures: A state of the art review
TL;DR: In this paper, a crack in a structural member introduces a local flexibility that affects its vibration response, and the crack will open and close in time depending on the rotation and vibration amplitude.
Journal ArticleDOI
Vibration of a beam with a breathing crack
TL;DR: In this paper, a continuous cracked beam vibration theory is used for the prediction of changes in transverse vibration of a simply supported beam with a breathing crack, where the equation of motion and the boundary conditions of the cracked beam considered as a one-dimensional continuum were used.
Journal ArticleDOI
Non-linear dynamics of a cracked cantilever beam under harmonic excitation
TL;DR: In this article, a cantilever beam with an asymmetric edge crack subjected to a harmonic forcing at the tip is considered as a plane problem and is solved by using two-dimensional finite elements; the behaviour of the breathing crack is simulated as a frictionless contact problem.
Journal ArticleDOI
Harmonic analysis of the vibrations of a cantilevered beam with a closing crack
TL;DR: In this article, the vibrational response of a cracked cantilevered beam to harmonic forcing is analyzed using a finite element model of the beam, in which a so-called closing crack model, fully open or fully closed, is used to represent the damaged element.
References
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Journal ArticleDOI
A periodically forced piecewise linear oscillator
Steven W. Shaw,Philip Holmes +1 more
TL;DR: In this article, a single-degree of freedom non-linear oscillator is considered and the nonlinearity is in the restoring force and is piecewise linear with a single change in slope.
Journal ArticleDOI
The dynamic behaviour and crack detection of a beam with a crack
TL;DR: In this paper, an element stiffness matrix of a cantilever beam with a crack is derived from an integration of stress intensity factors, and then a finite element model of a cracked beam is established.
Journal ArticleDOI
Chaotic vibrations of a beam with non-linear boundary conditions
Francis C. Moon,Steven W. Shaw +1 more
TL;DR: Forced vibrations of an elastic beam with non-linear boundary conditions are shown to exhibit chaotic behavior of the strange attractor type for a sinusoidal input force as mentioned in this paper, where the beam is clamped at one end, and the other end is pinned for the tip displacement less than some fixed value and is free for displacements greater than this value.
Journal ArticleDOI
High Order Subharmonic Response of High Speed Rotors in Bearing Clearance
TL;DR: In this article, a simple but exact computer model of the subharmonic vibration was developed based on the numerical integration of a finite difference formulation. But the model is not suitable for systems with low damping and extreme nonlinearity.
Journal ArticleDOI
Vibrations of beams with a fatigue crack
M.-H. H. Shen,Y.C. Chu +1 more
TL;DR: In this paper, a bilinear equation of motion for each vibration mode of a simply supported beam is formulated by a Galerkin procedure, and the dynamic response of this equation under a concentrated forcing excitation is calculated through a numerical analysis.