Abstract
Soft phononic crystals have the advantages over their stiff counterparts of being flexible and reconfigurable. Normally, the band gaps of soft phononic crystals will be modified after deformation due to both geometric and constitutive nonlinearity. Indeed these are important properties that can be exploited to tune the dynamic properties of the material. However, in some instances, it may be that one wishes to deform the medium while retaining the band gap structure. A special class of soft phononic crystals is described here with band gaps that are independent or almost-independent of the imposed mechanical deformation, which enables the design of phononic crystals with robust performance. This remarkable behaviour originates from transformation elasticity theory, which leaves the wave equation and the eigenfrequencies invariant after deformation. The necessary condition to achieve such a property is that the Lagrangian elasticity tensor of the hyperelastic material should be constant, i.e. independent of deformation. It is demonstrated that incompressible neo-Hookean materials exhibit such a unique property. Semilinear materials also possess this property under special loading conditions. Phononic crystals composed of these two materials are studied theoretically and the predictions of invariance, or the manner in which the response deviates from invariance, are confirmed via numerical simulation.
Highlights
Phononic crystals (PCs) are periodic structures that can control the propagation of acoustic or elastic waves via wave filtering in specific frequency ranges [1,2,3,4,5,6,7,8,9,10].2017 The Authors
It was indicated that the invariance of the band gaps is associated with the invariance of the Lagrangian wave speeds in the medium, which are derived from transformation elasticity
Numerical simulations illustrate that a specified soft phononic crystals (SPCs) with semilinear hyperelastic matrix and aluminium stiff cylindrical inclusions does have band gaps that are almost-deformation-independent for wave modes in the frequency ranges considered
Summary
Phononic crystals (PCs) are periodic structures that can control the propagation of acoustic or elastic waves via wave filtering in specific frequency ranges [1,2,3,4,5,6,7,8,9,10]. Attention has switched to the study of compliant or soft phononic crystals (SPCs) due to their potential for flexibility, tunability and multifunctionality. Almost all work on SPCs is related to their tunability, i.e. band gaps are tuned via mechanical deformation or some other mechanism such as an imposed electrical or magnetic field. Mousanezhad et al [17] designed flexible honeycomb structures with tunable band gaps under compression and buckling Most of these aforementioned works are related to body waves. In addition to exploiting instability, a number of other methods have been proposed to tune the dynamic behaviour of PCs. Tang et al [19] designed super-stretchable structures with cut hinges to achieve both tunable band gaps and enhanced strength simultaneously.
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