Exploring Localization in Nonperiodic Systems

Kolan, Amy J.; Cipra, Barry; Titus, Bill

doi:10.1063/1.168542

Cited by 3 publications

(3 citation statements)

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“…The vibrating response at the centre of the beam is shown in Figure 2, which corresponds to a typical transient of a simply supported beam (Kolan et al, 1995). The frequency spectrum shown in Figure 3 has several peaks but the strongest ones were located at 12.9 Hz, 41.3 Hz and 100.6 Hz, related to the first three vibrating modes of the beam.…”

Section: Resultsmentioning

confidence: 99%

“…The effective evaluation of the performance of the constitutive materials of bridges and civil engineering structures, especially to predict fatigue, crack propagation and to evaluate damage conditions, requires not only a detailed knowledge of the values of the mechanical loads applied, but also of the specific frequencies at which they occur. It is also known that any structural damage affects the dynamical behaviour, to the extent that modal localization can take place (Kolan et al, 1995;Fertis, 1995). If a localization phenomenon occurs at a specific frequency and location where it either affects locally the structure or increases previous damage, the integrity of the structure itself might be at risk.…”

Section: Introductionmentioning

confidence: 99%

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Condition monitoring of vibrating steel‐reinforced concrete beams through wavelet transforms

2006

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Purpose -The purpose of this research is to show that wavelets are mathematical tools capable of separating vibration data into different frequency components, allowing the study of each component with a resolution matched to its specific time scale. Wavelets have advantages over traditional Fourier methods, particularly when a signal contains sharp spikes, discontinuities, and transients. Design/methodology/approach -This paper presents a brief description of wavelets and shows their application to the analysis of typical transient signals due to vibrations in a steel-reinforced concrete beam. Findings -The research clearly shows that it is possible to evaluate modes and components separately by using the wavelet analysis. Originality/value -The beam analysed can be used as a simple model of other more complicated structures, such as bridges and other high scale civil engineering constructions, where vibration analysis is a key issue for maintenance and failure assessments, thus representing an alternative mathematical tool for condition monitoring.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Condition monitoring of vibrating steel‐reinforced concrete beams through wavelet transforms

2006

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“…Localization of vibration in disordered chains is investigated explicitly, for instance, by Kolan et al [12], Allen and Kelner [13], and de Moura et al [14]. More recent investigations regarding dispersion properties and wave scattering are reported by Taraskin and Elliott [15] and Hehlen and Rufflé [16].…”

Section: Introductionmentioning

confidence: 99%

Vibrational analysis of harmonic oscillator chains with random topological constraints

Mühlich

2022

Mathematics and Mechanics of Solids

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The effect of topological disorder on the dynamic behaviour of topologically constrained oscillator chains is investigated through a normal mode analysis. A measure for mode localization based on the skewness of the density of energy states of normal modes is proposed, which correlates well with main configuration characteristics. Appropriate configuration sampling is achieved by employing the Ising model together with the Metropolis algorithm.

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Normal modes of a defected linear system of beaded springs

Aghamohammadi

Foulaadvand

Yaghoubi

et al. 2017

American Journal of Physics

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A model of a one-dimensional mass-spring chain with mass or spring defects is investigated. With a mass defect, all oscillators except the central one have the same mass, and with a spring defect, all the springs except those connected to the central oscillator have the same stiffness constant. The motion is assumed to be one-dimensional and frictionless, and both ends of the chain are assumed to be fixed. The system vibrational modes are obtained analytically, and it is shown that if the defective mass is lighter than the others, then a high frequency mode appears in which the amplitudes decrease exponentially with the distance from the defect. In this sense, the mode is localized in space. If the defect mass is greater than the others, then there will be no localized mode and all modes are extended throughout the system. Analogously, for some values of the defective spring constant, there may be one or two localized modes. If the two defected spring constants are less than that of the others, there is no localized mode.

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Exploring Localization in Nonperiodic Systems

Cited by 3 publications

References 0 publications

Condition monitoring of vibrating steel‐reinforced concrete beams through wavelet transforms

Condition monitoring of vibrating steel‐reinforced concrete beams through wavelet transforms

Vibrational analysis of harmonic oscillator chains with random topological constraints

Normal modes of a defected linear system of beaded springs

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