Spectral element-based method for a
one-dimensional damaged structure with distributed random properties

Machado, Marcela; Adhikari, Sondipon; Santos, José Maria Campos dos

doi:10.1007/s40430-018-1330-2

Cited by 22 publications

(10 citation statements)

References 45 publications

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“…Propagating waves are the dispersion diagram's real part printed in solid lines (positive axis), and imaginary part is the evanescent waves shown in dashed lines (negative axis). The spectral element of the unimorph beam without control was presented and validated in the papers [1,34]. Band gap creation presented on the controlled beam's vibration response follow the behaviour published in [12,16,26,56] considered for validation of presented results.…”

Section: Critical Deterministic Insights On Vibration and Flexural Wa...mentioning

confidence: 84%

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Bandgap manipulation of single and multi-frequency smart metastructures with random impedance disorder

Machado¹,

Moura²,

Dey³

et al. 2022

Smart Mater. Struct.

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Randomness in the media breaks its periodicity aﬀecting the vibration and wave propagation performance. Such disorder caused by the variability may lead to interesting physical phenomena such as trapping and scattering waves, wave reﬂection, and energy localisation. While the randomness may be attributed to manufacturing irregularities and quantifying its eﬀect is crucial for ensuring adequate performance of a range of smart systems, these eﬀects can also be exploited for manipulating the wave properties. Here we investigate a smart metastructure in the form of a beam integrated with piezoelectric transducers coupled to a resonant shunt circuit. The piezoelectric shunt in a periodical arrangement can induce locally resonant bandgaps that can be employed in wave and vibration manipulation (and control). This paper quantiﬁes the uncertainty associated with electrical circuit components that aﬀect the circuit impedance. Such uncertainty essentially propagates to the beam smart metamaterial, inﬂuencing its wave and vibration control feature. Numerical results of the unimorph meta-beam with single and multi-frequency shunt conﬁguration show that the bandgap behaviour is sensitive to the random disorder associated with circuit impedance parameters, which can, in turn, be exploited for enhanced functionalities based on optimal RL shunt circuits for controlling structural vibration response along with wave propagation and attenuation.

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Section: Critical Deterministic Insights On Vibration and Flexural Wa...mentioning

confidence: 84%

“…Variabilities in the media break its periodicity, causing disorder that affects the wave propagation and dynamic performances [34,35]. The problem of vibration control using resonant shunts with random electrical components was analysed in [36,37].…”

Section: Introductionmentioning

confidence: 99%

Bandgap manipulation of single and multi-frequency smart metastructures with random impedance disorder

Machado¹,

Moura²,

Dey³

et al. 2022

Smart Mater. Struct.

View full text Add to dashboard Cite

show abstract

“…The theory is also expected to be extended to other analytical vibrational models such as membranes [72] , plates [73][74][75][76][77][78] , shells [79][80][81] , solids [82] for the vibration and buckling analysis [83,84] by using associated techniques, e.g., [85][86][87] . Besides, the analytical nature of this proposed method facilitates the consideration of uncertainties that may occur during the manufacturing and assembly procedure, such as the uncertainties in rigid bodies (mass, rotatory inertia), the beam sections [88][89][90] (Young's modulus, density, cross section and etc), their connections (relative positions) and more complex engineering problems [91] . Also, in the context of inverse problems [63][64][65]92] for which accuracy and efficiency predictions in higher frequencies ranges are essential, the proposed method will be most useful when compared with other methods.…”

Section: Discussionmentioning

confidence: 99%

An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies

Xiang

Sun

Banerjee

et al. 2021

Mechanical Systems and Signal Processing

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An exact dynamic stiffness method is proposed for the free vibration analysis of multi-body systems consisting of flexible beams and rigid bodies. The theory is sufficiently general in that the rigid bodies can be of any shape or size, but importantly, the theory permits connections of the rigid bodies to any number beams at any arbitrary points and oriented at any arbitrary angles. For beam members, a range of theories including the Bernoulli-Euler and Timoshenko theories are applied. The assembly procedure for the beam and rigid body properties is simplified without resorting to matrix inversion. The difficulty generally encountered in computing the problematic J0 count when applying the Wittrick-Williams algorithm for modal analysis has been overcome. Applications of different beam theories for both axial and bending vibrations have enabled the examination of the role played by rigid-body parameters on the multibody system's dynamic behaviour. Some exact benchmark results are provided and compared with published results and with finite element solutions. This research provides an exact and highly efficient analysis tool for multibody system dynamics which is for the free vibration analysis, ideally suited for optimization and inverse problems such as modal parameter identification.

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“…Palacz (2018) published an overview of spectral methods to model and use wave propagation in damage detection problems. Ng et al (2011), Flynn et al (2012, Machado and Santos (2015), Machado et al (2017), and Machado et al (2018) proposed a structural damage detection including random parameters and stochastic models.…”

Section: Introductionmentioning

confidence: 99%

Damage indices evaluation for one-dimensional guided wave-based structural health monitoring

Barreto

Machado

Santos

et al. 2021

Lat. Am. j. solids struct.

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Damage detection in structures and systems is essential for monitoring parameters that can affect their integrity. This paper evaluates the efficiency of four damage indices (DIs) commonly used with temporal wave signals. The root mean square deviation, mean absolute percentage deviation, covariance, and correlation coefficient deviation DIs are presented, and a normalization is then proposed. An Euler-Bernoulli beam is used as a guided wave modelled with the spectral element method and excited by a toneburst signal. It includes the theoretical background of the throw-off beam, undamaged and cracked beam spectral elements. The DIs for a single crack position and a map varying crack depth and positions are calculated with deterministic and random temporal signal responses derived from noise addition. Results showed that DIs could identify and quantify the damage conditioned to the pulse location point and the influence of noise in the estimation, which leads in an analysis comparable to practical applications.

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Spectral element-based method for a one-dimensional damaged structure with distributed random properties

Cited by 22 publications

References 45 publications

Bandgap manipulation of single and multi-frequency smart metastructures with random impedance disorder

Bandgap manipulation of single and multi-frequency smart metastructures with random impedance disorder

An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies

Damage indices evaluation for one-dimensional guided wave-based structural health monitoring

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