Abstract
Abstract In this study, band gaps of SH-waves (horizontally polarized shear waves) propagating in a thermal-sensitive viscoelastic matrix are investigated. Metallic films acting as heat sources are periodically embedded into the matrix, which establishes a periodically inhomogeneous thermal field. The homogenous matrix is therefore transformed into functionally gradient phononic crystals (PCs). A three-parameter solid model is employed to describe the viscoelasticity of the present matrix. By virtue of a transfer matrix method incorporated within a laminated model, the dispersion equation of SH-waves is finally obtained, from which the band gaps are determined. The transmission spectra of a finite-periodic PC are also solved to validate the band gaps. In numerical examples, the influences of incident angles of SH-waves and viscoelasticity of matrix on band gaps are discussed first. Then the research focuses on the means to tune the band gaps by manipulating the inputted powers of heat sources. Numerical examples demonstrate that such a strategy is effective and convenient in tuning the positions and widths of band gaps. A viscous parameter, i.e., the ratio of initial-state to final-state storage moduli, significantly affects the band locations and bandwidths, while the locations of low-order band gaps hardly move with the incident angle of SH-waves. Band gaps of several orders are expected to locate in lower-frequency domain, and the total bandwidth becomes larger as the inputted heat flux increases. This paper lays theoretical foundation to manufacture viscoelastic functionally graded PCs which can be used in frequency-selective devices.
Highlights
Phononic crystals (PCs), exhibiting forbidden band gaps, are artificial periodic structures made up of at least two types of materials with different mechanical and physical properties
For functionally graded phononic crystals (FGPCs) discussed here, each unit cell is evenly discretized into 40 fictitious layers in the laminated model, to assure the numerical results have a high precision
Band gaps of a normal incident SH-wave characterized by dispersion curves in an infinite-periodic PC and transmission spectra in a finite-periodic PC with five unit cells are first calculated and displayed in Figure 3, where the ratio of initial-state modulus to final-state modulus, ζ = E0/E∞, is taken as 10
Summary
Phononic crystals (PCs), exhibiting forbidden band gaps, are artificial periodic structures made up of at least two types of materials with different mechanical and physical properties. The forbidden band gaps of PCs mean that elastic wave with specific frequency is not allowed to propagate through the periodic structures. This unique ability endows PCs with a bright prospect to be applied in the area of noise suppression [1], filter [2,3], shock insulation [4,5], acoustic transducers [6], and so on. Wu et al [18] investigated one-dimensional PCs made of isotropic FGMs by applying spectral finite elements and transfer matrix method. Their results showed that the desired forbidden band gaps can be designed by appropriate selection of structure parameters.
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