Detection of Cracks in Stationary Rotors via the Modal Frequency Changes Induced by a Roving Disc

2014 ◽  
Author(s):  
Z. N. Haji ◽  
S. O. Oyadiji
Keyword(s):  
Natural Frequencies ◽  
Crack Depth ◽  
Mode Shapes ◽  
Crack Identification ◽  
Open Crack ◽  
Suggested Approach ◽  
Rotor Systems ◽  
Crack Location ◽  
High Crack ◽  
Frequency Changes

In this study, a crack identification approach based on a finite element cracked model is presented to identify the location and depth ratios of a crack in rotor systems. A Bernoulli-Euler rotor carrying an auxiliary roving disc has been used to model the cracked rotor, in which the effect of a transverse open crack is modelled as a time-varying stiffness matrix. In order to predict the crack location in the rotor-disc-bearing system, the suggested approach utilises the variation of the normalized natural frequency curves versus the non-dimensional location of a roving disc which traverses along the rotor span. The merit of the suggested approach is to identify the location and sizes of a crack in a rotor by determining only the natural frequencies of the stationary rotor system. The first four natural frequencies are employed for the identification and localisation of a crack in the stationary rotor. Furthermore, this approach is not only efficient and practicable for high crack depth ratios but also for small crack depth ratios and for a crack close to or at the node of mode shapes, where natural frequencies are unaffected.

Coupled Transverse and Axial Vibrations of Cracked Cantilever Beams With Roving Mass and Rotary Inertia

2010 ◽  
Author(s):  
Hurang Hu ◽  
Akindeji Ojetola ◽  
Hamid Hamidzadeh
Keyword(s):  
Cantilever Beam ◽  
Natural Frequencies ◽  
Coupling Effect ◽  
Rectangular Cross Section ◽  
Crack Depth ◽  
Rotary Inertia ◽  
Mode Shapes ◽  
Axial Deformation ◽  
Crack Location ◽  
Axial Vibrations

The vibration behavior of a cracked cantilever beam with a stationary roving mass and rotary inertia is investigated. The beam is modeled as an Euler-Bernoulli beam with rectangular cross section. The transverse deformation and axial deformation of the cracked beam are coupled through a stiffness matrix which is determined based on fracture mechanics principles. The analytical solutions are obtained for the natural frequencies and mode shapes of a cracked cantilever beam with a roving mass and rotary inertia. The effects of the location and depth of the crack, the location and the weight of the roving mass and rotary inertia on the natural frequencies and mode shapes of the beam are investigated. The numerical results show that the coupling between the transverse and axial vibrations for moderate values of crack depth and/or roving mass and rotary inertia is weak. Increasing the crack depth and the mass and rotary inertia will increase the coupling effect. Detection of the crack location using natural frequencies and mode shapes as parameters is also discussed.

scholarly journals Modified and Simplified Sectional Flexibility of a Cracked Beam

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Chih-Shiung Wang ◽  
Lin-Tsang Lee
Keyword(s):  
Structural Model ◽  
Natural Frequencies ◽  
Numerical Solutions ◽  
Crack Depth ◽  
Research Literature ◽  
Mode Shapes ◽  
Open Crack ◽  
Beam Model ◽  
Single Edge ◽  
Cracked Beam

This paper presents a new sectional flexibility factor to simulate the reduction of the stiffness of a single-edge open cracked beam. The structural model for crack of the beam is considered as a rotational spring which is related to the ratio of crack depth to the beam height,a/h. The mathematical model of this single-edge open crack beam is considered as an Euler-Bernoulli beam. The modified factor,f(a/h), derived in this paper is in good agreement with previous researchers' results for crack depth ratioa/hless than 0.5. The natural frequencies and corresponding mode shapes for lateral vibration with different types of single-edge open crack beams can then be evaluated by applying this modified factorf(a/h). Using the compatibility conditions on the crack and the analytical transfer matrix method, the numerical solutions for natural frequencies of the cracked beam are obtained. The natural frequencies and the mode shapes with crack at different locations are obtained and compared with the latest research literature. The numerical results of the proposed cracked beam model obtained by this method can be extended to construct frequency contour. The natural frequencies measured from field can be used in solving the inverse problem to identify cracks in structures.

Analytical Solution for Free Vibration of Annular Mindlin Plate with a Circumferential Open Crack

2019 ◽  
Vol 24 (3) ◽  
pp. 494-503
Author(s):  
Eshagh Derakhshan ◽  
Mahboobeh Fakhrzarei ◽  
Shahram Derakhshan
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Crack Depth ◽  
Current Method ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Open Crack ◽  
Element Analysis ◽  
Radial Location

Mindlin plate theory is employed to obtain the free vibration response of an annular moderately thick plate with a circumferential open crack with fixed-free boundary conditions. To model the crack, a set of continuously distributed rotational springs are employed at the crack location. The corresponding spring stiffness value is a function of the crack depth and is given as a closed-form function. To obtain the vibration behaviour, the eigenvalue problem is solved to obtain the natural frequencies and mode shapes. The current method is verified by comparing the results with those obtained from finite element analysis. Through a parametric study, the effects of the crack depth and its radial location on the natural frequencies and mode shapes are investigated. The results show that for a constant crack depth, the reduction in natural frequency is a strong function of the radial location of the crack.

scholarly journals Crack Identification and Localization In Structural Beams Using Numerical and Experimental Modal Analysis- A Review

2020 ◽  
pp. 62-68
Keyword(s):  
Modal Analysis ◽  
Natural Frequency ◽  
Structural Damage ◽  
Experimental Modal Analysis ◽  
Mode Shapes ◽  
Crack Identification ◽  
Engineering Structures ◽  
Aircraft Wings ◽  
Crack Location ◽  
Damaged Beams

This article presents a critical review of recent research done on crack identification and localization in structural beams using numerical and experimental modal analysis. Crack identification and localization in beams are very crucial in various engineering applications such as ship propeller shafts, aircraft wings, gantry cranes, and Turbo machinery blades. It is necessary to identify the damage in time; otherwise, there may be serious consequences like a catastrophic failure of the engineering structures. Experimental modal analysis is used to study the vibration characteristics of structures like natural frequency, damping and mode shapes. The modal parameters like natural frequency and mode shapes of undamaged and damaged beams are different. Based on this reason, structural damage can be detected, especially in beams. From the review of various research papers, it is identified that a lot of the research done on beams with open transverse crack. Crack location is identified by tracking variation in natural frequencies of a healthy and cracked beam

Observed Natural Frequencies, Damping Ratios, and Mode Shapes of Vibration of a 30-Story Building Excited by a Major Earthquake and Typhoon

2010 ◽  
Vol 26 (2) ◽  
pp. 371-397 ◽  
Author(s):  
Kun-Sung Liu ◽  
Yi-Ben Tsai
Keyword(s):  
Natural Frequencies ◽  
Transfer Functions ◽  
Measurement Data ◽  
Spectral Ratio ◽  
Transverse Mode ◽  
Structural Vibration ◽  
Mode Shapes ◽  
Building Structures ◽  
Ambient Vibrations ◽  
Frequency Changes

The safety of building structures and contents, as well as the comfort of occupants, under such strong forces as earthquakes and typhoons remain major engineering concerns. In order to improve our understanding of building structural responses, records of a structural array in the 30-story PS Building in Taipei from the M7.6 Chi-Chi earthquake and Typhoon Aere are analyzed. In addition, wind data measured at the Taipei Meteorological Station are also used. First, the field measurement data clearly demonstrate that serviceability of the PS Building met the criteria for occupant comfort during Typhoon Aere. Secondly, several structural vibration parameters of this highrise building, including the transfer functions, natural frequencies, damping ratios and mode shapes, excited by the Chi-Chi earthquake, Typhoon Aere, and ambient vibrations are also determined and compared. The results show the frequency of the first mode for the longitudinal components is approximately 8.6% lower for the earthquake than the ambient vibrations. The transverse mode frequencies behave similarly. In contrast, frequency changes from the typhoon to ambient vibrations are in the third decimal (1.3% and 0.9% lower in the longitudinal and transverse directions, respectively), indicating little nonlinearity. The damping ratios of the PS Building apparently increase with vibration amplitudes. Finally, results of a spectral ratio analysis of the Chi-Chi earthquake data do not indicate significant SSI effects in the longitudinal and transverse directions.

Torsional Vibration Analysis of Shafts With Sections of Tapered Diameter

1993 ◽  
Author(s):  
John R. Baker ◽  
Keith E. Rouch
Keyword(s):  
Torsional Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Displacement Function ◽  
The Other ◽  
Mode Shapes ◽  
Axial Distance ◽  
Rotational Degree ◽  
Rotor Systems ◽  
Constant Diameter

Abstract This paper presents the development of two tapered finite elements for use in torsional vibration analysis of rotor systems. These elements are particularly useful in analysis of systems that have shaft sections with linearly varying diameters. Both elements are defined by two end nodes, and inertia matrices are derived based on a consistent mass formulation. One element assumes a cubic displacement function and has two degrees of freedom at each node: rotation about the shaft’s axis and change in angle of rotation with respect to the axial distance along the shaft. The other element assumes a linear displacement function and has one rotational degree of freedom at each node. The elements are implemented in a computer program. Calculated natural frequencies and mode shapes are compared for both tapered shaft sections and constant diameter sections. These results are compared with results from an available constant diameter element. It is shown that the element derived assuming a cubic displacement function offers much better convergence characteristics in terms of calculated natural frequencies, both for tapered sections and constant diameter sections, than either of the other two elements. The finite element code that was developed for implementation of these elements is specifically designed for torsional vibration analysis of rotor systems. Lumped inertia, lumped stiffness, and gear connection elements necessary for rotor system analysis are also discussed, as well as calculation of natural frequencies, mode shapes, and amplitudes of response due to a harmonic torque input.

QUANTITATIVE IDENTIFICATION OF ROTOR CRACKS BASED ON FINITE ELEMENT OF B-SPLINE WAVELET ON THE INTERVAL

2009 ◽  
Vol 07 (04) ◽  
pp. 443-457 ◽  
Author(s):  
XUEFENG CHEN ◽  
BING LI ◽  
JIAWEI XIANG ◽  
ZHENGJIA HE
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Beam Element ◽  
Rotational Inertia ◽  
Spline Wavelet ◽  
B Spline ◽  
Rotor Systems ◽  
Crack Location ◽  
Contour Lines ◽  
Quantitative Identification

Based on finite element of B-spline wavelet on the interval (BSWI), the quantitative identification method of transverse crack for rotor systems was studied. The new model of BSWI Rayleigh–Euler rotary beam element considering gyroscopic effect and rotational inertia was constructed to solve the first three natural frequencies of the cracked rotor with high precision, and the first three frequencies solution surfaces of normalized crack location and size were obtained by using surface-fitting technique. Then the first three metrical natural frequencies were employed as inputs of the solution curve surfaces. The intersection of the three frequencies contour lines predicted the normalized crack location and size. The numerical and experimental examples were given to verify the validity of the beam element for crack quantitative identification in rotor systems. The new method can be applied to prognosis and quantitative diagnosis of cracks in the rotor system.

Effect of a Circumferential Arc Crack on the Vibration Characteristics of a Flexible Spinning Disk

2007 ◽  
Author(s):  
Nikhit N. Nair ◽  
Hamid N. Hashemi ◽  
Grant M. Warner
Keyword(s):  
Crack Opening ◽  
Equations Of Motion ◽  
Crack Depth ◽  
Bending Moment ◽  
Rotating Disk ◽  
Vibration Characteristics ◽  
Coupled Systems ◽  
Mode Shapes ◽  
Critical Speeds ◽  
Crack Location

The vibration characteristics of a circumferentially cracked rotating disk are investigated. The disk is assumed to be axisymmetric, flexible and clamped at the center. The crack increases the local flexibility of the disk at the crack location and is modeled as linear and torsional springs, connecting the two segments of the disk. The spring constants are evaluated by considering crack opening displacements due to bending moment and shear force at the crack location. The equations of motion of two segments of the disk, for disk operating in vacuum as well as subjected to shear fluid flow are developed. Using the Finite Difference Technique, the coupled systems of equations are solved and the natural frequencies and mode shapes are obtained. The mode shapes are seen to be comparatively flattened in the inner region of the disk separated by the crack and heightened towards the periphery of the disk. Shear fluid loading reduces the critical speeds and results in a quicker onset of instability. The degree of instability caused by the crack is a function of crack depth and location. Critical speeds increase with increasing crack distance from the central clamp and decrease with increasing crack depth.

Free Vibration of Damaged Frame Structures Considering the Effects of Axial Extension, Shear Deformation and Rotatory Inertia: Exact Solution

2017 ◽  
Vol 17 (10) ◽  
pp. 1750111
Author(s):  
Ugurcan Eroglu ◽  
Ekrem Tufekci
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Shear Deformation ◽  
Natural Frequencies ◽  
Plane Motion ◽  
Mode Shapes ◽  
Frame Structures ◽  
Crack Identification ◽  
Rotatory Inertia ◽  
Axial Extension

In this paper, a procedure based on the transfer matrix method for obtaining the exact solution to the equations of free vibration of damaged frame structures, considering the effects of axial extension, shear deformation, rotatory inertia, and all compliance components arising due to the presence of a crack, is presented. The crack is modeled by a rotational and/or translational spring based on the concept of linear elastic fracture mechanics. Only the in-plane motion of planar structures is considered. The formulation is validated through some examples existing in the literature. Additionally, the mode shapes and natural frequencies of a frame with pitched roof are provided. The variation of natural frequencies with respect to the crack location is presented. It is concluded that considering the axial compliance, and axial-bending coupling due to the presence of a crack results in different dynamic characteristics, which should be considered for problems where high precision is required, such as for the crack identification problems.

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