Vibration based damage detection in composite beams under temperature variations using Poincaré maps

Manoach, Emil; Samborski, Sylwester; Mitura, Andrzej; Warmiński, Jerzy

doi:10.1016/j.ijmecsci.2012.06.006

Cited by 62 publications

(35 citation statements)

References 29 publications

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“…In this way, if we know from the experimental measurements the natural frequencies and modes of vibrations ω n and w n , following a simple numerical procedure we obtain time series describing the forced response of the beam subjected to artificially applied harmonic loading p(x,t)=p 0 sin(ω e t), where p 0 is the amplitude of the artificial excitation and ω e is the excitation frequency (see, for example [3]). In order to check these formulas for DD and to check the applicability of a few of the popular and easy modal methods for damage detections, numerical and experimental testing were performed.…”

Section: Obtaining the Time Series From The Modal Datamentioning

confidence: 99%

“…It was shown by many authors that significant damage may cause very small changes in natural frequencies, particularly for larger structures, and these changes may go undetected due to measurement or processing errors. [1][2][3]. The natural frequencies are global parameters of the systems and often they are weakly affected by local faults Developing of the experimental techniquescontactless method with sensors or specially Scanning Laser Doppler Vibrometers (SLDV) makes possible to measure the modal displacements in large numbers of nodes.…”

Section: Introductionmentioning

confidence: 99%

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Vibration Based Methods For Damage Detection In Structures

et al. 2016

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Abstract. Vibration based damage detection methods are among the most popular and promising approaches for health monitoring of structures. In this work a critical review of different methods for damage detection methods of structures is presented. The theoretical bases of the most popular methods based on the changes in the modal properties of the structures are deduced. The review includes the modal displacements, the mode shape slopes, the modal curvatures and the strain energy methods. The efficiency of all these methods is compared by using a finite element analysis of intact and damaged beams. The methods are tested experimentally by using a scanning laser vibrometer to measure the modal properties of specially prepared composite beams with defects. All this methods are compared with the damage detection method based on the analysis of the Poincaré maps of the motion of the structures). Conclusions concerning the advantages and the applicability of the considered methods are deduced.

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Section: Obtaining the Time Series From The Modal Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vibration Based Methods For Damage Detection In Structures

et al. 2016

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“…The mathematical model of the Timoshenko beam presented in Fig. 1 has been derived in papers [13,16]. The dimensionless equations of motion have the form:…”

Section: A Model Of a Timoshenko Beam Under Thermo-mechanical Loadingsmentioning

confidence: 99%

“…This approach is widely used to model the thermoelastic behaviour of structures. The geometrically nonlinear vibrations of structures at the elevated temperature are studied by many authors as [14][15][16], etc. In [17] and [18] thermomechanical, geometrically nonlinear vibrations of plates and beams, correspondingly, are studied.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of a reduced multimodal Timoshenko beam subjected to thermal and mechanical loadings

2014

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Large amplitude vibrations of a Timoshenko beam under an influence of temperature are analysed in this paper. In the considered model the temperature increases instantly and the heat is uniformly distributed along the beams length and crosssection. The mathematical model, represented by partial differential equations takes into account thermal and mechanical loadings. Next, the problem is reduced by means of the Galerkin method, considering the first three natural vibration modes of a simply supported beam in the both ends. The influence of the temperature on amplitudes and localisation of the resonance zones and stability of the solutions is studied numerically and analytically by the multiple time scale method. The bifurcation points, existence of unstable lobes and transition from regular to chaotic oscillations are shown.

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“…In some cases in order to simplify the model, it is assumed that the structure gets the elevated temperature. This approach has been used to model geometrically nonlinear vibrations of structures [24][25][26].…”

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confidence: 99%

Regular and chaotic oscillations of a Timoshenko beam subjected to mechanical and thermal loadings

Warmińska

Manoach

Warmiński

et al. 2014

Continuum Mech. Thermodyn.

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Dynamics of a Timoshenko beam under an influence of mechanical and thermal loadings is analysed in this paper. Nonlinear geometrical terms and a nonuniform heat distribution are taken into account in the considered model. The mathematical model is represented by a set of partial differential equations (PDEs) which takes into account thermal and mechanical loadings. The problem is simplified to two PDEs and then reduced to ordinary differential equations (ODEs) by means of the Galerkin method taking into account three modes of a linear Timoshenko beam. Correctness of the analytical model is verified by a finite element method. Then, the nonlinear model is studied numerically by a continuation method or by a direct numerical integration of ODEs. An effect of the temperature distribution on the resonance near the first natural frequency and on stability of the solutions is presented. The increase of mechanical loading results in hardening of the resonance curve. Thermal loading may stabilise the beam dynamics when the temperature is decreased. The elevated temperature may transit dynamics from regular to chaotic oscillations.

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Vibration based damage detection in composite beams under temperature variations using Poincaré maps

Cited by 62 publications

References 29 publications

Vibration Based Methods For Damage Detection In Structures

Vibration Based Methods For Damage Detection In Structures

Nonlinear dynamics of a reduced multimodal Timoshenko beam subjected to thermal and mechanical loadings

Regular and chaotic oscillations of a Timoshenko beam subjected to mechanical and thermal loadings

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