scholarly journals Damage Detection on a Beam with Multiple Cracks: A Simplified Method Based on Relative Frequency Shifts

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5215
Author(s):  
Gilbert-Rainer Gillich ◽  
Nuno M. M. Maia ◽  
Magd Abdel Wahab ◽  
Cristian Tufisi ◽  
Zoltan-Iosif Korka ◽  
...  
Keyword(s):  
Relative Frequency ◽  
Superposition Principle ◽  
Detection Methods ◽  
Multiple Cracks ◽  
Superposition Method ◽  
Vibration Modes ◽  
Engineering Structures ◽  
Frequency Shifts ◽  
Frequency Drop ◽  
The Individual

Identifying cracks in the incipient state is essential to prevent the failure of engineering structures. Detection methods relying on the analysis of the changes in modal parameters are widely used because of the advantages they present. In our previous research, we found that eigenfrequencies were capable of indicating the position and depth of damage when sufficient vibration modes were considered. The damage indicator we developed was based on the relative frequency shifts (RFS). To calculate the RFSs for various positions and depths of a crack, we established a mathematical relation that involved the squared modal curvatures in the healthy state and the deflection of the healthy and damaged beam under dead mass, respectively. In this study, we propose to calculate the RFS for beams with several cracks by applying the superposition principle. We demonstrate that this is possible if the cracks are far enough from each other. In fact, if the cracks are close to each other, the superposition method does not work and we distinguish two cases: (i) when the cracks affect the same beam face, the frequency drop is less than the sum of the individual frequency drops, and (ii) on the contrary, cracks on opposite sides cause a decrease in frequency, which is greater than the sum of the frequency drop due to individual damage. When the RFS curves are known, crack assessment becomes an optimization problem, the cost function being the distance between the measured RFSs and all possible RFSs for several vibration modes. Thus, the RFS constitutes a benchmark that characterizes damage using only the eigenfrequencies. We can accurately locate multiple cracks and estimate their severity through experiments and thus prove the reliability of the proposed method.

scholarly journals Damage Detection on a Beam with Multiple Cracks: A Simplified Method Based on Relative Frequency Shifts

2021 ◽  
Author(s):  
Gilbert-Rainer Gillich ◽  
Nuno M. M. Maia ◽  
Magd Abdel Wahab ◽  
Cristian Tufisi ◽  
Zoltan-Iosif Korka ◽  
...  
Keyword(s):  
Relative Frequency ◽  
Superposition Principle ◽  
Detection Methods ◽  
Multiple Cracks ◽  
Superposition Method ◽  
Vibration Modes ◽  
Engineering Structures ◽  
Frequency Shifts ◽  
Frequency Drop ◽  
The Individual

Identifying cracks in the incipient state is essential to prevent the failure of engineering structures. Detection methods relying on the analysis of the changes in modal parameters are widely used because of the advantages they present. In our previous research, we have found that eigenfrequencies were capable of indicating the position and depth of damage when sufficient vibration modes were considered. The damage indicator we developed was based on the relative frequency shifts (RFS). To calculate the RFSs for various positions and depths of a crack, we established a mathematical relation that involved the squared modal curvatures in the healthy state and the deflection of the healthy and damaged beam under dead mass, respectively. In this study, we propose to calculate the RFS for beams with several cracks by applying the superposition principle. We demonstrate that this is possible if the cracks are far enough from each other. In fact, if the cracks are close to each other, the superposition method does not work and we distinguish two cases: (i) when the cracks affect the same beam face, the frequency drop is less than the sum of the individual frequency drops, and (ii) on the contrary, cracks on opposite sides cause a decrease in frequency, which is greater than the sum of the frequency drop due to individual damage. When the RFS curves are known, crack assessment becomes an optimization problem, the cost function being the distance between the measured RFSs and all possible RFSs for several vibration modes. Thus, the RFS constitutes a benchmark that characterizes damage using only the eigenfrequencies. We can accurately locate multiple cracks and estimate their severity trough experiments and thus prove the reliability of the proposed method.

The Infrared Absorption Spectra of Some Samarium Chelates

1970 ◽  
Vol 25 (5) ◽  
pp. 472-475 ◽  
Author(s):  
S. P. Tandon ◽  
P. C. Mehta ◽  
R. N. Kapoor ◽  
S. N. Misra
Keyword(s):  
Absorption Spectra ◽  
Infrared Absorption ◽  
Relative Frequency ◽  
Vibration Modes ◽  
Frequency Shifts ◽  
Infrared Absorption Spectra

The infrared absorption of samarium (di-isopropoxy) mono dibenzoylmethide [Sm (ΟΡri) 2DBM] and samarium tris dibenzoylmethide [Sm(DBM)3] in the region 4000 - 250 cm-1 have been studied. About 25 bands in each chelate have been observed and assigned to different modes of vibrations. The number of metal-oxygen vibration modes of the chelates suggest Vh and D3 sym. metries for Sm (OPri) 2DBM and Sm (DBM) 3 respectively. The relative frequency shifts of CO and CC stretching modes indicate that the metal-oxygen bonding in Sm(DBM)3 is relatively stronger than in Sm (OPri) 2DBM.

scholarly journals About the calculus of the relative frequency shifts for a beam with multiple cracks

2020 ◽  
Vol 1426 ◽  
pp. 012024
Author(s):  
G R Gillich ◽  
D Nedelcu ◽  
C O Hamat ◽  
M Abdel Wahab ◽  
C I Barbinta
Keyword(s):  
Relative Frequency ◽  
Multiple Cracks ◽  
Frequency Shifts

scholarly journals Structural and Acoustic Responses of a Submerged Stiffened Conical Shell

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Meixia Chen ◽  
Cong Zhang ◽  
Xiangfan Tao ◽  
Naiqi Deng
Keyword(s):  
Conical Shell ◽  
Element Model ◽  
Analytical Models ◽  
Superposition Method ◽  
Far Field ◽  
Fluid Loading ◽  
Low Frequencies ◽  
Structural Responses ◽  
The Individual ◽  
Field Sound

This paper studies the vibrational behavior and far-field sound radiation of a submerged stiffened conical shell at low frequencies. The solution for the dynamic response of the conical shell is presented in the form of a power series. A smeared approach is used to model the ring stiffeners. Fluid loading is taken into account by dividing the conical shell into narrow strips which are considered to be local cylindrical shells. The far-field sound pressure is solved by the Element Radiation Superposition Method. Excitations in two directions are considered to simulate the loading on the surface of the conical shell. These excitations are applied along the generator and normal to the surface of the conical shell. The contributions from the individual circumferential modes on the structural responses of the conical shell are studied. The effects of the external fluid loading and stiffeners are discussed. The results from the analytical models are validated by numerical results from a fully coupled finite element/boundary element model.

Using complementary remote detection methods for retrofitted eco-passages: a case study for monitoring individual koalas in south-east Queensland

2016 ◽  
Vol 43 (5) ◽  
pp. 369 ◽  
Author(s):  
C. E. Dexter ◽  
R. G. Appleby ◽  
J. P. Edgar ◽  
J. Scott ◽  
D. N. Jones
Keyword(s):  
Road Construction ◽  
Primary Objective ◽  
Correlated Data ◽  
Camera Traps ◽  
Detection Methods ◽  
Urban Landscapes ◽  
Monitoring Methods ◽  
Monitoring Method ◽  
Phascolarctos Cinereus ◽  
The Individual

Context Vehicle-strike has been identified as a key threatening process for koala (Phascolarctos cinereus) survival and persistence in Australia. Roads and traffic act as barriers to koala movement and can impact dispersal and metapopulation dynamics. Given the high cost of wildlife mitigation structures such as purpose-built fauna-specific underpasses or overpasses (eco-passages), road construction and management agencies are constantly seeking cost-effective strategies that facilitate safe passage for fauna across roads. Here we report on an array of detection methods trialled to verify use of retrofitted road infrastructure (existing water culverts or bridge underpasses) by individual koalas in fragmented urban landscapes in south-east Queensland. Aims The study examined whether the retrofitting of existing road structures at six sites facilitated safe passage for koalas across roads. Our primary objective was to record utilisation of retrofitted infrastructure at the level of the individual. Methods We used a combination of existing monitoring methods such as GPS/VHF collars, camera traps, sand plots, and RFID tags, along with a newly developed animal-borne wireless identification (WID) tag and datalogging system, specifically designed for this project, to realise the study aims. Key results We were able to verify 130 crossings by koalas involving a retrofitted structure or a road surface over a 30-month period by using correlated data from complementary methods. We noted that crossings were generally uncommon and mostly undertaken by only a subset of our tagged individuals at each site (21% overall). Conclusions An important element of this study was that crossing events could be accurately determined at the level of the individual. This allowed for detailed assessment of eco-passage usage, rather than the more usual approach of simply recording species’ presence. Implications This study underscores the value of identifying the constraints of each individual monitoring method in relation to site conditions. It also highlights the benefits of contingency planning to limit data loss (i.e. using more than one method to collect data). We suggest an approach that uses complementary monitoring methods has significant advantages for researchers, particularly with reference to improving understanding of whether eco-passages are meeting their prescribed conservation goals.

scholarly journals Identification of Acoustic-Vibratory System by Acoustic Measurement

1996 ◽  
Vol 3 (1) ◽  
pp. 27-37
Author(s):  
Takuzo Iwatsubo ◽  
Shozo Kawamura ◽  
Masahito Kamada
Keyword(s):  
Inverse Analysis ◽  
Coefficient Matrix ◽  
Superposition Method ◽  
Vibration Modes ◽  
Identification Problems ◽  
Mathematical Property ◽  
Vibratory System ◽  
Stochastic Error ◽  
Mode Superposition Method ◽  
Ill Conditioning

A new method for reducing ill-conditioning in a class of identification problems is proposed. The key point of the method is that the identified vibration of the sound source is expressed as a superposition of vibration modes. The mathematical property of the coefficient matrix, the practical error expanding ratio, and the stochastic error expanding ratio are investigated in a numerical example. The mode-superposition method is shown to be an effective tool for acoustic-vibratory inverse analysis.

scholarly journals Estimation of the Effects of Distortion on the Longitudinal Stability of Swept Wing Aircraft at High Speeds (Sub-Critical Mach Numbers)

1954 ◽  
Vol 5 (5) ◽  
pp. 280-322
Author(s):  
B. S. Campion
Keyword(s):  
Control Circuit ◽  
Superposition Method ◽  
Swept Wing ◽  
Longitudinal Stability ◽  
Fighter Aircraft ◽  
High Speeds ◽  
Mach Numbers ◽  
The Individual ◽  
And Control

SummaryThe effects of distortion on the longitudinal stability of swept wing aircraft at high speeds (sub-critical Mach numbers) are considered on a quasi-static basis. The method is based on the theory of Gates and Lyon but involves some extension of this theory.The treatment of wing distortion is considered in some detail and the effects of built-in twist and camber and wing weight are included, using the so-called superposition method. The application of the analysis of Lyon and Ripley for investigating fuselage, tail and control circuit distortion is suggested, but means of modifying and simplifying this procedure where desirable are put forward.The analysis is illustrated by means of a simple example of a swept wing fighter aircraft for which wing, fuselage and tail distortion effects are considered, and the results are discussed with reference to the individual and combined distortion effects, as well as the effect of compressibility.

The Infrared Absorption Spectra of Some Samarium Diketo-ester Complexes

1970 ◽  
Vol 25 (2) ◽  
pp. 139-141 ◽  
Author(s):  
S. P. Tandon ◽  
P. C. Mehta
Keyword(s):  
Coordination Number ◽  
Absorption Spectra ◽  
Infrared Absorption ◽  
Relative Frequency ◽  
Methyl Acetoacetate ◽  
Frequency Shifts ◽  
Modes Of Vibration ◽  
Infrared Absorption Spectra ◽  
Stretching Vibrations ◽  
First Time

Infrared absorption spectra of some four- and five-coordinated (ethyl 1-methyl acetoacetate) complexes of trivalent samarium have been studied in the region 4000 - 250 cm-1 for the first time. About twenty bands in each chelate have been observed and assigned to different modes of vibration. A study of relative frequency shifts of CO stretching vibrations reveals that the metal-oxygen bonds in all the complexes are nearly of the same strength. The vibrational frequencies, with few exceptions, are found to be nearly independent of the coordination number of the metal.

Local scour at piled bridge piers including an examination of the superposition method

2014 ◽  
Vol 41 (5) ◽  
pp. 461-471 ◽  
Author(s):  
Ata Amini ◽  
Bruce W. Melville ◽  
Thamer M. Ali
Keyword(s):  
Bridge Piers ◽  
Prediction Methods ◽  
Scour Depth ◽  
Superposition Method ◽  
Clear Water ◽  
Laboratory Flume ◽  
Pile Cap ◽  
The Individual ◽  
Comparison Of The Results ◽  
Bed Material

An experimental investigation of clear water scour at complex piers is presented. Five complex piers, comprising different configurations of piles, pile cap, and column, were tested in a laboratory flume using uniform bed material. The piers were tested for a range of possible elevations relative to the streambed elevation. Experiments were undertaken using the complex piers and also using the individual components of each complex pier. A comparison of the results for the intact piers and for their components enabled an evaluation of the prediction methods involving superposition of scour depths at piles, pile cap, and pier column. The superposition method is found to give inadequate estimates of total scour depth in many cases.

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