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The purpose of this paper is to present a method for early crack detection in rotating shafts. A rotor-bearing system, consisting of an elastic rotor mounted on fluid film bearings, is used to detect the presence of the crack at a depth of around 5 percent of shaft radius. The fluid film bearings, the shaft and the crack introduce coupled bending vibrations both in the horizontal and vertical plane. Experimental time series of the rotor composite response under normal steady-state operation are uncoupled, to develop a signal processing procedure able to reveal the presence of the crack.

The variation of the coupling property that a crack (breathing or not) or a cut (always open) introduces into the system and the localization of the coupling in the time domain is a concept proposed as a means to detect transverse surface cracks in rotating shafts. This consideration is combined with the concept of external excitation for the development of an additional crack-sensitive response during system normal operation. Using an external excitation of an active magnetic bearing of specific duration, frequency and amplitude, the method uses this coupling variation during rotation.

The method is simple, quick and effective for early crack detection, being able to detect cracks as shallow as 5 percent of the shaft radius while the system is under normal operation, and can even be applied real-time. Experimental verification uses a simple elastic rotor with a cut mounted on fluid film bearings, with the cut producing similar coupling phenomena as an opened crack. Experimental results are encouraging.

The method used is simple, quick and effective for early crack detection, being able to detect cracks as shallow as 5 percent of the shaft radius while the system is under normal operation, and can even be applied real-time.

A nonlinear finite element (FE) beam-column model for the analysis of reinforced concrete (RC) frames with due account of shear is presented in this paper. The model is an expansion of the traditional flexural fibre beam formulations to cases where multiaxial behaviour exists, being an alternative to plane and solid FE models for the nonlinear analysis of entire frame structures. The paper aims to discuss these issues.

Shear is taken into account at different levels of the numerical model: at the material level RC is simulated through a smeared cracked approach with rotating cracks; at the fibre level, an iterative procedure guarantees equilibrium between concrete and transversal reinforcement, allowing to compute the biaxial stress-strain state of each fibre; at the section level, a uniform shear stress pattern is assumed in order to estimate the internal shear stress-strain distribution; and at the element level, the Timoshenko beam theory takes into account an average rotation due to shear.

The proposed model is validated through experimental tests available in the literature, as well as through an experimental campaign carried out by the authors. The results on the response of RC elements critical to shear include displacements, strains and crack patterns and show the capabilities of the model to efficiently deal with shear effects in beam elements.

A formulation for the nonlinear shear-bending interaction based on the fixed stress approach is implemented in a fibre beam model. Shear effects are accurately accounted during all the nonlinear path of the structure in a computationally efficient manner.

The paper is devoted to presenting a systematic investigation on the mechanical model and nonlinear dynamic characteristics of spur gear system with and without input shaft crack.

Considering the backlash, load-distribution, time-varying meshing stiffness and sliding friction, the modelling of a 5DOF gear system is proposed. Likewise, stiffness and damping models under elastohydrodynamic lubrication are developed, and sliding friction between gear pair is also outlined. In particular, a cracked input shaft which affects the support stiffness is presented, and breathing crack in keyway is adopted. On this basis, the dynamic responses of a gear system with and without input shaft crack are examined using numerical method, and some classical response diagrams are given, illustrating the effect of the important parameters on the gear system.

Dynamic simulation demonstrates that there exist periodic, quasi-periodic and chaotic motions in the gear system, and rational speed of the gear pair has noteworthy effects on vibration characteristic. Besides, comparison between healthy and cracked condition of input shaft indicates that occurring of crack convert periodic motion to quasi-periodic or chaotic motion.

The results give an understanding of the operating conditions under which undesirable dynamic behavior occurs, and provide some useful information to design and diagnose such gear system with crack fault.

Since the most of structures and structural components suffers from cyclic loadings, the study on the fatigue failure due to the crack growth has a great importance. The purpose of this paper is to present a three-dimensional fatigue crack growth simulation of embedded cracks using s-version finite element method (SFEM). Using the numerical results, the validity of the fitness-for-service (FFS) code evaluation method is verified.

In this paper, three-dimensional fatigue crack propagation analysis of embedded cracks is performed using the SFEM. SFEM is a numerical analysis method in which the shape of the structure is represented by a global mesh, and cracks are modeled by local meshes independently. The independent global and local meshes are superimposed to obtain the displacement solution of the problem simultaneously.

The fatigue crack growth of arbitrary shape of cracks is slow compared to that of the simplified circular crack and the crack approximated based on the FFS code of the Japan Society of Mechanical Engineers (JSME). The results tell us that the FFS code of JSME can provide a conservative evaluation of the fatigue crack growth and the residual life time.

This paper presents a three-dimensional fatigue crack growth simulation of embedded cracks using SFEM. Using this method, it is possible to apply mixed mode loads to complex shaped cracks that are closer to realistic conditions.

The purpose of this paper is to present integrated methodologies based on multilevel modelling concepts for finite element analysis (FEA) of reinforced concrete (RC) shell structures, with specific reference to account for the nonlinear behaviour of cracked concrete and the other associated features.

Geometric representation of the shell is enabled through multiple concrete layers. Composite characteristic of concrete is accounted by assigning different material properties to the layers. Steel reinforcement is smeared into selected concrete layers according to its position in the RC shell. The integrated model concurrently accounts for nonlinear effects due to tensile cracking, bond slip and nonlinear stress‐strain relation of concrete in compression. Smeared crack model having crack rotation capability is used to include the influence of tensile cracking of concrete. Propagation and change in direction of crack along thickness of shell with increase in load and deformation are traced using the layered geometry model. Relative movement between reinforcing steel and adjacent concrete is modelled using a compatible bond‐slip model validated earlier by the authors. Nonlinear iterative solution technique with imposed displacement in incremental form is adopted so that structures with local instabilities or strain softening can also be analysed.

Proposed methodologies are validated by evaluating ultimate strength of two RC shell structures. Nonlinear response of McNeice slab is found to compare well with that of experiment available in literature. Then, a RC cooling tower is analysed for factored wind loads to study its behaviour near ultimate load. Numerical validation demonstrates efficacy and usefullness of the proposed methodologies for nonlinear FEA of RC shell structures.

The present paper integrates critical methodologies used for behaviour modelling of concrete and reinforcement with the physical interaction among them. The study is unique by considering interaction of tensile cracking and bond‐slip which are the main contributors to nonlinearity in the nonlinear response of RC shell structures. Further, industrial application of the proposed modelling strategy is demonstrated by analysing a RC cooling tower shell for its nonlinear response. It is observed that the proposed methodologies in the integrated manner are unique and provide stability in nonlinear analysis of RC shell structures.

This paper presents a numerical study of inverse parameter identification problems in fracture mechanics. Inverse methodology is applied to the detection of subsurface cracks and to the study of propagating cracks. The procedure for detecting subsurface cracks combines the finite element method with a sequential quadratic programming algorithm to solve for the unknown geometric parameters associated with the internal flaw. The procedure utilizes finite element substructuring capabilities in order to minimize the processing and solution time for practical problems. The finite element method and non‐linear optimization are also used in determining the direction a crack will propagate in a heterogeneous planar domain. This procedure involves determining the direction that produces the maximum strain energy release for a given increment of crack growth. The procedure is applied to several numerical examples. The results of these numerical studies coincide with theoretical predictions and experimentally observed crack behavior.

In this manuscript, the authors aimed to demonstrate the influences of influential parameters in mixed-mode crack propagation phenomenon. The authors attempted to cover almost all surrounding issues of this subject as the authors know simulating of propagating cracks as internal strong discontinuity is a complicated issue.

In this manuscript, the authors demonstrated the influences of influential parameters in mixed-mode crack propagation phenomenon. The authors attempted to cover almost all surrounding issues of this subject as the authors know simulating of propagating cracks as internal strong discontinuity is a complicated issue. Furthermore, three different scenarios for crack growth are considered. In reality, edge-cracked plate, center-cracked plate and cracked plate in the presence of void and inclusion are studied. In fact, by designing suitable artificial neural network's (ANN) architectures all the three aforementioned conditions are trained and estimated through those architectures with very good agreement with input data. Also by conducting a series of sensitivity analysis, the most affecting factors in mixed-mode crack propagation in different situations are demonstrated. The obtained results are very interesting and useful for other researchers and also the authors hope the results would be cited by researchers.

The influential parameters on mixed-mode crack propagation were found in this paper.

The computer code using MATLAB was prepared to study the mixed-mode crack paths. Also using ANNs toolbox, the crack path estimation was investigated.

To investigate the feasibility of using single/multi variable optimisation techniques with vibration measurements in solving the inverse crack identification problem.

The finite element method is used to solve the forward crack problem with a special nodal crack force approach. The multi‐variable optimisation approach is reduced to a much more efficient single‐variable one by decoupling the physical variables in the problem.

It is shown that, for the crack identification problem, global optimisation algorithms perform much better than other algorithms relying heavily on objective function gradients. Simultaneous identification of crack size and location proved to be difficult. Decoupling of the physical variable is introduced and proved to provide efficient results with single‐variable optimisation algorithms.

Need for improving the reliability and accuracy of the procedure for smaller crack sizes. Need for developing and investigation more rigorous and robust multi‐variable optimisation algorithm.

Any information about approximate crack size and location provides significant aid in the maintenance and online monitoring of rotating equipment.

The paper offers practical approach and procedure for online monitoring and crack identification of slow rotating equipment.

Many incidents of rotor failures are reported due to the development and propagation of the crack. Condition monitoring is adopted for the identification of symptoms of the crack at very early stage in the rotating machinery. Identification requires a reliable and accurate vibration analysis technique for achieving the objective of the study. The purpose of this paper is to detect the crack in the rotating machinery by measuring vibration parameters at different measurement locations.

Two different types of cracks were simulated in these experiments. Experiments were conducted using healthy shaft, crack simulated shaft and glued shaft with and without added unbalance to observe the changes in vibration pattern, magnitude and phase. Deviation in vibration response allows the identification of crack and its location. Initial data were acquired in the form of time waveform. Run-up and coast-down measurements were taken to find the critical speed. The wavelet packet energy analysis technique was used to get better localization in time and frequency zone.

The presence of crack changes the dynamic behavior of the rotor. 1× and 2× harmonic components for steady-state test and critical speed for transient test are important parameters in condition monitoring to detect the crack. To separate the 1× and 2× harmonic component in the different wavelet packets, original signal is decomposed in nine levels. Wavelet packet energy analysis is carried out to find the intensity of the signal due to simulated crack.

Original signals obtained from the experiment test set up may contain noise component and dominant frequency components other than the crack. Wavelet packets contain the crack-related information that are identified and separated in this study. This technique develops the condition monitoring procedure more specific about the type of the fault and accurate due to the separation of specific fault features in different wavelet packets. From the experiment end results, it is found that there is significant rise in a 2× energy component due to crack in the shaft. The intensity of a 1× energy component depends upon the shaft crack and unbalance orientation angle.

The problem of damage and crack detection in structural components has acquired an important role in recent years. Since the presence of cracks in a structure may alter its vibrational characteristics, the estimation of such variations can be used to detect cracks and damage, and to monitor the integrity of structures. The use of fast, easy and inexpensive non‐destructive testing is thus a major task. In this paper, sensitivity analysis by measurement of the reduction of eigenfrequencies was utilized to localize a crack in a non‐rotating shaft coupled to an elastic foundation. The shaft was modeled by the finite element method and coupled to an experimentally identified foundation model. The detection of a crack with different depths and orientations was verified experimentally and a good agreement between actual and detected crack positions was achieved. Finally easiness, effectiveness, applicability of the method and its extensions are also shown.