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Design of Arbitrarily Shaped Inertial and Three Dimensional Pentamode Acoustic Cloaks

Li, Qi (2018) Design of Arbitrarily Shaped Inertial and Three Dimensional Pentamode Acoustic Cloaks. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Acoustic cloaks are devices that can make a space acoustically invisible. Acoustic cloaks can be designed using transformation acoustics. The properties of these cloaks are, by necessity, anisotropic. Inertial acoustic cloaks have anisotropic density and isotropic bulk modulus, while pentamode cloaks have isotropic density and anisotropic stiffness.
The ultimate goal of this work is to build cloaks of arbitrary 2D and 3D shape that are composed of homogenous materials. Five different design methods are presented which contribute toward this goal. The first contribution of the work is a method of designing 2D inertial acoustic cloaks having arbitrary shapes, based on transformation acoustics to map along radial directions. The derived properties are complicated. By dividing the cloak into small sections, the transverse anisotropy is removed, but the radial anisotropy remains. The properties within each section are inhomogeneous, but could theoretically be realized using layered media.
The second and third contributions of the work are two methods of designing 2D arbitrarily shaped cloaks such that homogeneous material properties occur. One method accomplishes homogeneity by simply dividing the cloaks into triangular patterns. Each triangle in physical space is mapped to a corresponding triangle in virtual space, resulting in homogeneous properties. The second method is through the use of multiple transforms. Arc sections are divided into two triangles. The first triangle undergoes a single transform, while the second undergoes two. The fourth contribution of the work is extending these methods to three dimensions. Here, 3D arbitrarily shaped cloaks can be composed of homogeneous tetrahedral parts.
The fifth contribution of the work is the introduction of a new pentamode material that is amenable to designing 3D cloaks. Pentamode materials have special structures such that only compressional waves are supported. Hexagonal cells with double-cone structures (DCS) are designed and analyzed, which can approximate the shape of a layered spherical pentamode structure. From the dispersion relations, it is observed that there are bandgaps where all shear modes disappear. The effect of the unit cell geometry on the acoustic properties is studied. Unit cells for a 3D pentamode acoustic cloak are explored.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Li, Qiqil36@pitt.eduqil360000-0003-1439-8059
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairVipperman, Jeffreyjsv@pitt.edu0000-0001-5585-954X
Committee MemberClark,
Committee MemberTo,
Committee MemberKim, Hong
Date: 25 September 2018
Date Type: Publication
Defense Date: 11 July 2018
Approval Date: 25 September 2018
Submission Date: 23 July 2018
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 156
Institution: University of Pittsburgh
Schools and Programs: Swanson School of Engineering > Mechanical Engineering
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Acoustic metamaterials; Transformation acoustics; Anisotropic materials; Pentamode materials; Band structures
Date Deposited: 25 Sep 2018 16:37
Last Modified: 25 Sep 2018 16:37


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