An approximate method for controlling solid elastic waves by transformation media

Abstract

By idealizing a general mapping as a series of local affine ones, we derive approximately transformed material parameters necessary to control solid elastic waves within classical elasticity theory. The transformed elastic moduli are symmetric, and can be used with Navier's equation to manipulate elastic waves. It is shown numerically that the method can provide a powerful tool to control elastic waves in solids in case of high frequency or small material gradient. Potential applications can be anticipated in nondestructive testing, structure impact protection, petroleum exploration and seismology.

11 pages, 1 figures

References in corpus (6)

• Broadband Acoustic Cloak for Ultrasound Waves
• Acoustic cloaking theory
• Cloaking of Matter Waves
• Achieving control of in-plane elastic waves
• Controlling elastic wave with isotropic transformation materials
• Constraint condition on transformed relation for generalized acoustics

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• Constraint condition on transformed relation for generalized acoustics
• Realizing the Willis equations with pre-stresses
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• The form-invariance of wave equations without requiring a priori relations between field variables
• Hyperelastic antiplane ground cloaking
• Manipulate elastic waves with conventional isotropic materials
• Modified 1D elastic wave equations that retain time synchronization under spatial coordinate transformations
• Determining the full transformation relations in the transformation method
• Orthotropic metamaterials with freely tailorable elastic constants
• Design Omnidirectional Wave Absorbers by Transformation Method