Approximate method for controlling solid elastic waves by transformation media

Hu, Jin; Chang, Zheng; Hu, Gengkai

doi:10.1103/physrevb.84.201101

Cited by 58 publications

(70 citation statements)

References 23 publications

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“…According to the relations between the material properties and principal stretches [43,44], there exist many options for material property selection of the transformed medium. For ease of physical realization, the relationship between the transformed medium and the host plate is selected as [43] …”

Section: Flexural Waveguide With Active Emmsmentioning

confidence: 99%

Active elastic metamaterials for subwavelength wave propagation control

Chen

Huang

2015

Acta Mech Sin

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Recent research activities in elastic metamaterials demonstrate a significant potential for subwavelength wave propagation control owing to their interior locally resonant mechanism. The growing technological developments in electro/magnetomechanical couplings of smart materials have introduced a controlling degree of freedom for passive elastic metamaterials. Active elastic metamaterials could allow for a fine control of material physical behavior and thereby induce new functional properties that cannot be produced by passive approaches. In this paper, two types of active elastic metamaterials with shunted piezoelectric materials and electrorheological elastomers are proposed. Theoretical analyses and numerical validations of the active elastic metamaterials with detailed microstructures are presented for designing adaptive applications in band gap structures and extraordinary waveguides. The active elastic metamaterial could provide a new design methodology for adaptive wave filters, high signal-to-noise sensors, and structural health monitoring applications.

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Section: Flexural Waveguide With Active Emmsmentioning

confidence: 99%

Active elastic metamaterials for subwavelength wave propagation control

Chen

Huang

2015

Acta Mech Sin

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“…If the angular momentum balance is totally ignored and thus there are no zero-order approximations, then the asymmetric elasticity tensor can appear [32], which is in fact beyond the framework of classical elastodynamics, and asymmetric elasticity tensor is difficult if not impossible to realize in practice. Therefore, the transformed relations obtained by the proposed method in the context of classical Navier's equation [33,34] should be limited in high-frequency or slowly varying materials [35], i.e., the application scope of Navier's equation. Recently, Norris et al [36] also developed a comprehensive theory for elasto-mechanical transformation, and their results are still based on mathematical interpretation of form-invariance.…”

Section: Discussionmentioning

confidence: 99%

Constraint condition on transformation relation for generalized acoustics

Liu

2013

Wave Motion

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Contrary to transformation optics (TO), there exist many possibilities for transformed relations of material property and field variable in case of transformation acoustics (TA). To investigate the underlining mechanism and develop a general method that can obtain the full transformed relations, an alternative interpretation to the form-invariance is explored. We consider a spatial transformation, with which a physical phenomenon described in an initial space is transformed to a deformed space, and interpret the mapping by local affine transformation point-by-point. Further, we postulate that the transformed material property and field must rebuild the same physical process, and that the energy must be conserved at each point during the transformation. These conditions impose the constraint on the transformed relation for material property and field. By establishing two local Cartesian frames defined uniquely by the spatial transformation, any physical quantity is shown to first experience a rigid rotation and then a stretch operation during the transformation. We show that the constraint conditions are not enough to determine completely the transformed relation for TA, leaving a possibility to define them differently as found in the literature. New acoustic transformations with constant density or modulus are also proposed and verified by constructing a two-dimensional acoustic cloak.2 Finally, we show that the transformed relation is uniquely determined for transformation optics, and discuss how this method can be extended to other transformation physics.

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“…However, some special cases can still be examined: for example in quasistatic limit, an elastic cloak with a homogeneous metamaterial [26] or cylindrical cloak for bending wave in a thin plate [27]. Recently, we proposed a general method to derive the transformed relation for any governing differential equation without necessity to be form-invariant in any arbitrary curvilinear coordinate system [25], the transformed relation for elastic wave can also be obtained [28]. In this paper, we will summarize the progress of the works and present them in a unified way for different waves.…”

Section: Introductionmentioning

confidence: 99%

Transformation method and wave control

Chang

2010

Acta Mech Sin

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Transformation method provides an efficient way to control wave propagation by materials. The transformed relations for field and material during a transformation are essential to fulfill this method. We propose a systematic method to derive the transformed relations for a general physic process, the constraint conditions are obtained by considering geometrical and physical constraint during a mapping. The proposed method is applied to Navier's equation for elastodynamics, Helmholtz's equation for acoustic wave and Maxwell's equation for electromagnetic wave, the corresponding transformed relations are derived, which can be used in the framework of transformation method for wave control. We show that contrary to electromagnetic wave, the transformed relations are not uniquely determined for elastic wave and acoustic wave, so we have a freedom to choose them differently. Using the obtained transformed relations, we also provide some examples for device design, a concentrator for elastic wave, devices for illusion acoustic and illusion optics are conceived and validated by numerical simulations.

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Approximate method for controlling solid elastic waves by transformation media

Cited by 58 publications

References 23 publications

Active elastic metamaterials for subwavelength wave propagation control

Active elastic metamaterials for subwavelength wave propagation control

Constraint condition on transformation relation for generalized acoustics

Transformation method and wave control

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