Abstract
This paper shows that acoustoelasticity in one-dimensional (1D) multilayered isotropic hyperelastic materials can be understood through the analysis of elastic wave velocities as a function of applied stress. This theoretical framework is used for eigenvalue analyses in stressed elastic structures through a reformulation of the stiffness matrix method, obtaining modal solutions, as well as reflection and transmission coefficients for different multilayered configurations. Floquet wave analysis for the stressed 1D structures is supported using numerical results.
Highlights
Multilayered elastic structures are widely investigated in a broad range of fields including geophysics, bioengineering, manufacturing and communications
The propagation velocity of such acoustic waves will change in the presence of static or residual stresses within the layered media (Hughes and Kelly, 1953; Pao and Gamer, 1985)
Reformulation of the stiffness matrix method for analysis of the elastic wave velocities as a function of applied static stress in multilayered and 1D phononic structures has been presented in this work
Summary
Multilayered elastic structures are widely investigated in a broad range of fields including geophysics, bioengineering, manufacturing and communications. Given the importance of such submersed and air-coupled ultrasonic measurements in both engineering research and industrial applications, including their role as multilayered composite laminates (Demcenko et al, 2006; Lee and Soutis, 2007; Li et al, 2017), it is useful to analyse such periodic structures These composite laminates respond mechanically to ultrasound in a manner analogous to a one-dimensional (1D) phononic structure and can be considered as having band-gaps (Kushwaha et al, 1993), enabling the use of Floquet wave theory in their analysis (Braga and Herrmann, 1992; Wang and Rokhlin, 2002a). The main aim of this work is to investigate the application of the Floquet wave theory on statically stressed multilayered 1D periodic structures to enable the development of an efficient matrix method for analysis of the elastic wave velocities with associated reflection and transmission coefficients. We draw general conclusions from the study in the context of its application in the analysis of composite laminates in engineering research
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