The two-dimensional and three-dimensional acoustic cloaks composed of homogeneous and nonsingular materials are designed by choosing appropriate spatial transformation. The mass density tensor and bulk modulus of the acoustic cloaks with diamond shape are derived, and extended to an acoustic carpet cloak. Performance of the acoustic cloaks is confirmed by full-wave simulation. The work represents an important progress towards the practical realization of the metamaterial-assisted acoustic cloak and expands the application of the coordinate transformation method.

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