Second-harmonic generation in an infinite layered structure with nonlinear spring-type interfaces

The second-harmonic generation characteristics in the elastic wave propagation across an infinite layered structure consisting of identical linear elastic layers and nonlinear spring-type interlayer interfaces are analyzed theoretically. The interlayer interfaces are assumed to have identical linear interfacial stiffness but can have different quadratic nonlinearity parameters. Using a perturbation approach and the transfer-matrix method, an explicit analytical expression is derived for the second-harmonic amplitude when the layered structure is impinged by a monochromatic fundamental wave. The analysis shows that the second-harmonic generation behavior depends significantly on the fundamental frequency reflecting the band structure of the layered structure. Two special cases are discussed in order to demonstrate such dependence, i.e., the second-harmonic generation by a single nonlinear interface as well as by multiple consecutive nonlinear interfaces. In particular, when the second-harmonic generation occurs at multiple consecutive nonlinear interfaces, the cumulative growth of the second-harmonic amplitude with distance is only expected in certain frequency ranges where the fundamental as well as the double frequencies belong to the pass bands of the layered structure. Furthermore, a remarkable increase of the second-harmonic amplitude is found near the terminating edge of pass bands. Approximate expressions for the low-frequency range are also obtained, which show the cumulative growth of the second-harmonic amplitude with quadratic frequency dependence.     

In-plane elastic wave propagation and band-gaps in layered functionally graded phononic crystals

In-plane wave propagation in layered phononic crystals composed of functionally graded interlayers arisen from the solid diffusion of homogeneous isotropic materials of the crystal is considered. Wave transmission and band-gaps due to the material gradation and incident wave-field are investigated. A classification of band-gaps in layered phononic crystals is proposed. The classification relies on the analysis of the eigenvalues of the transfer matrix for a unit-cell and the asymptotics derived for the transmission coefficient. Two kinds of band-gaps, where the transmission coefficient decays exponentially with the number of unit-cells are specified. The so-called low transmission pass-bands are introduced in order to identify frequency ranges, in which the transmission is sufficiently low for engineering applications, but it does not tend to zero exponentially as the number of unit-cells tends to infinity. A polyvalent analysis of the geometrical and physical parameters on band-gaps is presented.     

Fast spectral analysis of an axisymmetric layered structure

A spectral formulation is employed to analyze the response of an axisymmetric layered structure to an impulse load from a falling weight deflectometer (FWD), which constitutes a deflection basin test. This paper presents the derivation of the dynamic stiffness matrix, the numerical formulation using discrete frequencies and wave numbers, implementation of the layered structure, and fast calculation algorithms. It is found that computational costs can be saved, without sacrificing accuracy, through the validation of a developed spectral structural model.