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A new type of the acoustic black hole beam—a helix-acoustic black hole—is proposed to overcome the spatial restriction on modular acoustic black hole structures. The modular acoustic black hole structure, consisted of a base and several number of acoustic black hole beams, has potential to apply into real engineering world. There are two main secti...
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... exponent m is a positive number and must be greater equal than 2.0, coefficient ϵ is a constant value, and y is the distance from the tip of the power-law profile with truncated thickness, h 1 , as shown in Figure 2(a). Because it is impossible in reality to build a structure of zero thickness, a truncated thickness is required at the end of the ABH region. ...
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... it is impossible in reality to build a structure of zero thickness, a truncated thickness is required at the end of the ABH region. Vibration of the incident wave, shown in Figure 2(b), usually occurs in the transverse direction in conventional ABH beams, as shown in Figure 3(a). Under the Euler-Bernoulli assumptions, one-dimensional wave propagation, in which a flexural wave propagates through the ABH region with power-law profile, can be described using complex amplitude W(y) as follows ...
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... compare bending wave propagation in the conventional ABH and h-ABH beams, transient analyses Kim and Lee (2018) were conducted. A five-period Hanning-windowed pure-tone burst-force signal, as shown in Figure 2(b), was used to excite the beams at the edge of the uniform thickness parts. Table 1 presents the mechanical material properties and parameters for both conventional and h-ABH beams. ...
Citations
... respectively. Hence, after considering (51) into (50), the wavenumber function takes the form ...
... Moreover, expressions (53) and (54) show us that both velocities ( ( ) and ( )) decrease as ℎ( ) decreases. Thus, as the thickness of the ABH termination goes to zero, the wavenumber approaches infinity and the wave speed approaches zero, which induces the ABH effect [50]. ...
... As a consequence, the wave never reaches the tip of the wedge and hence it is never reflected back. In other words, for an ideal design of the tapered wedge, no wave can escape from the ABH termination [11,35,50]. Such a feature makes the ABHs very attractive for structural design in controlling vibration and noise. ...
This paper investigates the performance of an integrated control system based on the acoustic
black hole effect and piezoelectric actuators for structural vibration suppression in beams. The
acoustic black hole is a technique for passive vibration control consisting of a power-law tapered
profile built on structures. Its effect takes place in the acoustic black hole termination, where
the velocity of the incoming wave is reduced to zero so that the wave never reaches the tip
of the wedge, and therefore the vibration energy is concentrated within the acoustic black
hole. Here, we consider embedded and equally spaced elliptical-shaped acoustic black holes.
The active control, in turn, consists of piezoelectric actuators which are operated by a linear
quadratic regulator scheme in order to improve the control performance. We use the finite
element method to discretize the structural domain, the modal analysis to obtain the vibration
modes, and the fast Fourier transformation for calculating the maximum amplitudes of vibration
in the frequency domain. All numerical tests are performed in a two-dimensional cantilever
beam under free vibration conditions in order to evaluate the efficiency of the passive and
active control techniques proposed in this work.
... Despite the illustration of its efficacy, 1D beam-type ABHs show strong orientation-dependent properties to cope with multi-directional rotational excitations, in addition to their bulky dimension. For better space occupation efficiency [24,25], which is also of great concern for other mechanical sub-systems [26,27], existing spiral/helix design partly addresses the compactness issue, but does not resolve the orientation-dependent problem when used as an absorber. The problem becomes crucial when dealing with two-dimensional vibration field such as in a plate, where waves propagate along various directions simultaneously. ...
... Such a swirl coil form is more applicable for thin structures with larger spans. The control efficiency can be further improved by optimizing the ABH design, such as extending the thin tip by a platform [29], adopting a variable width [21] or using other 3D geometric features [24,25,49]. ...
A planar swirl-shaped Acoustic Black Hole (ABH) absorber is proposed and investigated in this paper. In addition to the well-known bending wave retarding phenomena, the speed of torsional waves in the curved ABH with a rectangular cross section is also shown to decrease with the thickness thinning. Alongside the enhanced bending-twisting coupling brought about by the planar and curvilinear configuration, the curved ABH absorber exhibits reduced orientation-dependent properties to cope with multi-directional rotational moment excitations, and meanwhile generates enriched dynamics and enhanced energy trapping and dissipation. As a result, the absorber enables broadband multi-directional vibration suppression when added on a primary thin structure. Experimental studies demonstrate that deploying multiple distributed ABH absorbers can entail effective, robust and broadband vibration reduction for an arbitrarily selected polygon plate. Analyses also confirm the dual vibration reduction mechanisms in terms of structural interaction and damping enhancement, both being fully played out through the proposed curvilinear ABH design.
The acoustic black hole (ABH) effect is investigated within the framework of thin shell theory. Asymptotic solutions to the dispersion equation for the thin cylindrical shell are obtained, and the ABH effect is examined using analytical formulas for group velocities and anti-derivatives of the asymptotic expansions of wave numbers. It is shown that the ABH effect is achievable in thin cylindrical shells with variable thickness, in a similar manner as for beams and plates. However, it should not be expected to exist in the low-frequency range where the flexural wave motion in the wall of a shell is strongly coupled with uniform longitudinal wave motion.
Beam structures are widely used in industrial applications such as automobiles, aircraft, naval architecture, trains, and buildings. The vibration characteristics of beams are inherent phenomenon and directly affect usage comfort and service life, but more dangerously may damage the structure due to excessive vibrations that are transmitted through the surrounding structure of the system. Vibration reduction of beam structures is a continuous challenge for industrial applications. It is important to reduce vibrations of the beam structures for stability. In this study, experimental research on vibration reduction characteristics of adhesively bonded beam structures with Acoustic Black Hole technique is presented. The Acoustic Black Hole, which is a geometry, tapered with a power-law profile enables vibration reduction by decreasing the velocity and the wavelength of vibration. The inherent natural vibration properties called modal parameters such as the natural frequencies, damping, and mode shapes of the beam structure with and without damping layer using power-law profile having various the Acoustic Black Hole length and exponent values were investigated and evaluated with experimental modal analysis. For validation, natural frequencies are determined numerically by the finite element method, and then compared with results obtained by the experimental modal analysis. The overall results indicated that the Acoustic Black Hole has ability to significantly suppress the vibration level and showed the capability of enhancing the damping efficiency when using the damping layer attached to the Acoustic Black Hole length of the beam structure.
Based on the symplectic and higher-order WKB theory, a semi-analytical method is developed for the forced vibration of a built-up system comprising rectangular thin plate terminated by multiple acoustic black hole beams. The analytical waves are used to describe the vibration of the plate and ABH beam components. The dynamic flexibility matrix and dynamic stiffness matrix are derived based on the analytical wave expressions for the plate and ABH beam component, respectively. By enforcing the displacement continuity and equilibrium of force at the connection interface, the dynamic coupling between the plate component and the ABH beam component is established. The proposed method can obtain the system balance equation by assembling the component matrix just like the traditional finite element method and has a much less degree of freedom. Numerical examples compare results from the proposed method with those from the finite element method. The comparison illustrates that the proposed method gives good predictions for the forced response of the built-up system considered here. The present approach is of high accuracy and can be used to provide benchmark solutions for other prediction methods.
In this paper, we present a study of vibration characteristics of the double-beam structures combined with the concept of the acoustic black hole (ABH), which is an effective technique for vibration and noise control. In the proposed double-beam structure, the ABH beam as the vibration damper is attached to the primary uniform beam by a range of translational and rotational springs. We formulate the closed-form spectral element matrix of the double-beam structure and calculate the natural frequencies and mode shapes of the system. The results demonstrate the ABH effect of increasing the modal damping ratios. We also study the power flow and mechanical intensity of the system to offer physical insight into the vibration suppression mechanism of the ABH. A detailed parametric analysis of both translational and rotational springs is carried out. The investigation contributes to the exact dynamic modelling and analysis of the double-beam system containing ABH elements. Furthermore, the proposed ABH double-beam structure shows great potential for vibration control and energy harvesting.
An acoustic black hole (ABH) resonator is regarded as an efficient approach for controlling vibration caused by flexural wave energy. In this paper, the beam models with periodic ABH beam resonators are designed. Both the vibration absorption and isolation performances are investigated. Theoretical models based on the Transfer Matrix Method are presented to evaluate the reflection coefficient, which is validated both by the semi-analytic method combined with the Finite Element Method (FEM) and the Impedance Matrix Method. Meanwhile, FEM models of periodic ABH beam resonators acting as the beam terminator and isolator are established and analyzed. The results show that the periodic ABH beam resonators are of a better vibration reduction performance in lower frequency and have wider bandgaps for lower reflection coefficient and higher transmission loss than the single wedge. Moreover, with the increasing number of periods, the advantages of the periodic ABH beam resonators in reducing vibration become more obvious. Through the complex plane and dynamic analyses, it shows that multimode coupling and meta-damping effect lead to superior performance since the enriched modal content is introduced by the periodic ABH beam structure. This effect is also verified by the experimental result. Besides, the study also reveals the paradoxical relationship between vibration absorption and isolation performances. Additionally, parametric studies are conducted to disclose the effects of structural parameters. Based on the analyses, two approaches are proposed to enhance the vibration reduction performances, including the composite beam resonators and compound beam resonators. This paper illustrates a promising vision for applying the periodic ABH beam resonators to various vibration control fields.
