Application of fractional order operators to the simulation of ducts with acoustic black hole terminations

Hollkamp, John P.; Semperlotti, Fabio

doi:10.1016/j.jsv.2019.115035

Cited by 73 publications

(25 citation statements)

References 32 publications

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“…There indeed exist some drawbacks in the design of FOGPSS, for example, the design parameterβ in ( 30) is chosen as a constant, so the given controller ( 29) is similar to the traditional fractional-order PD controller. However, β i in the original algorithm (11) for the integer-order PSS is time-varying, there is no doubt that the time-varying parameters are the main differences between PSS and normal error-feedback control. Therefore, to reduce the conservatism and avoid the occurrence of algebraic loop, how to implement more reasonable algorithms for β i is one of the main directions of our further research.…”

Section: Generalized Fractional-order Pssmentioning

confidence: 99%

“…In fact, compared with previous papers which are presented from the engineering standpoint, this article is intended to review and develop PSS from a theoretical point of view. The main contributions of this article are summarized as follows: (i) Combined the basic idea of PSS with fractional-order operators [10], [11] to introduce an extended PSS. (ii) Owing to the fact that eventtriggered mechanism can reduce the control updates while providing a satisfactory performance [12]- [14], an eventtriggered controller based on PSS is firstly proposed in this article.…”

Section: Introductionmentioning

confidence: 99%

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Principle of Self-Support (PSS) and Its Extensions With Fractional Calculus and Event-Triggered Scheme

Tian

Chen

2020

IEEE Open J. Circuits Syst.

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As an ingenious concept which broadens the traditional error-feedback mechanism, the principle of self-support (PSS) is reviewed in this article with two extensions. Instead of regarding a control signal as an input variable or a cause of the control processes, PSS emphasized the independence and significance of the control signal in the whole dynamics. Moreover, due to nonlocal and historydependent properties for fractional-order operators, many processes with memory and heredity can be well modeled by fractional-order systems, a pioneering work on the fractional-order generalized PSS (FOGPSS) is introduced. Meanwhile, motivated by the event-triggered schemes that enjoy benefits of reduced sampling efforts and better resource utilization, an event-triggered controller based on PSS is further presented. Finally, some future research directions are discussed in conclusion.INDEX TERMS Principle of self-support, fractional-order systems, event-triggered control, finite-time practical tracking.

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Section: Generalized Fractional-order Pssmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Principle of Self-Support (PSS) and Its Extensions With Fractional Calculus and Event-Triggered Scheme

Tian

Chen

2020

IEEE Open J. Circuits Syst.

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“…Unlike integer-order operators, the intrinsic multiscale nature of fractional operators enabled a very unique and effective approach to model historically challenging physical processes involving, as an example, nonlocality or memory effects. Indeed, many of the early applications of FC to physical modeling included viscoelastic effects [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 ], nonlocal behavior [ 8 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ], anomalous and hybrid transport [ 9 , 10 , 11 , 24 , 25 , 26 , 27 , 28 , 29 , 30 ], fractal media [ 12 , 31 , 32 , 33 , 34 , 35 ], and even control theory [ 36 , 37 , 38 , 39 ]. The interested reader is referred to the work in [ 40 ] for a detailed account of the birth and evolution of fractional calculus.…”

Section: Introductionmentioning

confidence: 99%

Applications of Distributed-Order Fractional Operators: A Review

Ding

Patnaik

Sidhardh

et al. 2021

Entropy

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Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader area of fractional calculus that has important and far-reaching applications for the modeling of complex systems. DOFC generalizes the intrinsic multiscale nature of constant and variable-order fractional operators opening significant opportunities to model systems whose behavior stems from the complex interplay and superposition of nonlocal and memory effects occurring over a multitude of scales. In recent years, a significant amount of studies focusing on mathematical aspects and real-world applications of DOFC have been produced. However, a systematic review of the available literature and of the state-of-the-art of DOFC as it pertains, specifically, to real-world applications is still lacking. This review article is intended to provide the reader a road map to understand the early development of DOFC and the progressive evolution and application to the modeling of complex real-world problems. The review starts by offering a brief introduction to the mathematics of DOFC, including analytical and numerical methods, and it continues providing an extensive overview of the applications of DOFC to fields like viscoelasticity, transport processes, and control theory that have seen most of the research activity to date.

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“…Acoustic black holes (ABHs) have revealed as an effective way to suppress structural vibrations and noise in mechanical systems. The ABH effect relies on removing material from beams and plates by tailoring indentations that follow a power-law thickness variation [1][2][3], or by altering the inner ring radii of thinwall separated cavities in duct terminations [4][5][6][7]. ABH profiles have the special feature of slowing down the propagation speed of input waves, which concentrate their energy at the center (plates) or termination (beams and ducts) of the ABH element.…”

Section: Introductionmentioning

confidence: 99%

Transmission loss of plates with multiple embedded acoustic black holes using statistical modal energy distribution analysis

Deng

Guasch

Maxit³

et al. 2021

Mechanical Systems and Signal Processing

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Acoustic black holes (ABHs) in beams and plates have been extensively studied as a passive method for vibration attenuation and noise reduction. However, most research to date has focused on analyzing the behavior of a single ABH structural element, using numerical or semi-analytical deterministic approaches. If ABHs are to be exploited for practical industrial applications, there is a need to characterize their performance in complex built-up structures and to describe them with statistical methods in the mid-high frequency range. This paper presents a first step towards this goal by employing statistical modal energy distribution analysis (SmEdA) to evaluate the transmission loss of ABH panels separating two air cavities. SmEdA splits vibroacoustic systems into subsystems and establishes power balance equations between the modes belonging to different subsystems. This avoids the energy equipartition assumption of traditional statistical energy analysis (SEA) and extends it to low modal overlap systems. In this work, the benefits of embedding ABHs on plates for noise reduction between cavities are predicted with SmEdA. The role played by the size, shape and number of ABH indentations on the plate are inspected, as well as the influence of other parameters like the truncation thickness, ABH order and damping. The effects of added mass and stiffness of the damping layer are investigated and it is observed that, with proper design, ABH plates can exhibit substantial transmission loss improvement in the vicinity of the critical frequency of uniform plates. Both resonant and non-resonant transmission are considered in the analysis.

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Application of fractional order operators to the simulation of ducts with acoustic black hole terminations

Cited by 73 publications

References 32 publications

Principle of Self-Support (PSS) and Its Extensions With Fractional Calculus and Event-Triggered Scheme

Principle of Self-Support (PSS) and Its Extensions With Fractional Calculus and Event-Triggered Scheme

Applications of Distributed-Order Fractional Operators: A Review

Transmission loss of plates with multiple embedded acoustic black holes using statistical modal energy distribution analysis

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