Towards a combined perfectly matching layer and infinite element formulation for unbounded elastic wave problems

This paper presents a framework for implementing a novel perfectly matching layer and infinite element (PML+IE) combination boundary condition for unbounded elastic wave problems in the time domain. To achieve this, traditional hexahedral finite elements are used to model wave propagation in the inner domain and IE test functions are implemented in the exterior domain. Two alternative implementations of the PML formulation are studied: the case with constant stretching in all three dimensions and the case with spatially dependent stretching along a single direction. The absorbing ability of the PML+IE formulation is demonstrated by the favourable comparison with the reflection coefficient for a plane wave incident on the boundary achieved using a finite-element-only approach where stress free boundary conditions are implemented at the domain edge. Values for the PML stretching function parameters are selected based on the minimisation of the reflected wave amplitude and it is shown that the same reduction in reflection amplitude can be achieved using the PML+IE approach with approximately half of the number of elements required in the finite-element-only approach.

In-plane free vibrations of functionally graded sandwich arches using shear and quasi-3D deformation theories

The in-plane vibration problem of functionally graded (FG) sandwich circular arch made up of two layers of power law FGM face sheet and one layer of homogeneous core is investigated. A framework for the vibration analysis of FG sandwich circular arches is presented, and the quasi-3D theories for the arch structures compatible with this framework are established for the first time. The quasi-3D theories take into account the changes of displacement through the thickness of the arch, and satisfy the stress-free boundary conditions naturally. The Lagrange equation is employed to derive the equation of motion, and various boundary conditions are implemented by applying simple algebraic polynomials as admissible functions to discrete the displacement fields of the FG sandwich arches. The comparison study of various high-order shear deformation theories and quasi-3D deformation theories for the FG sandwich circular arches is carried out via different numerical examples. The influences of material distributions and geometric parameters on the vibration characteristics of the FG sandwich circular arches are also presented and discussed for the first time.

Transmission Phase Control of Annular Array Transducers for Efficient Second Harmonic Generation in the Presence of a Stress-Free Boundary

The through-transmission (TT) method is mainly used to measure the amplitude of the second harmonic from which the acoustic nonlinear parameter is determined for early damage detection of materials. The pulse echo (PE) method, however, has been excluded from nonlinear studies of solid materials because the stress-free boundary suppresses the generation of second harmonics. It is more demanding to develop the PE method for practical applications and this paper considers a novel phase shift technique of annular array transducers to improve second harmonic generation (SHG) at the stress-free boundary. The fundamental and second harmonic fields after phase-shifted radiation are calculated, and their received amplitudes are investigated. The phase difference between the two second harmonic components after reflection from the stress-free boundary is analyzed to explain the enhanced SHG. The PE method with optimal phase shift can generate an improved second harmonic amplitude as high as about 45% of the TT method. Four element array transducers are also found to be more efficient in improved SHG than two element transducers.

Reflection of Thermoelastic Waves From the Insulated Surface of a Solid Half-Space With Time-Delay

This paper is devoted to study the reflection of thermoelastic plane waves from the thermally insulated stress-free boundary of a homogeneous, isotropic and thermally conducting elastic half-space. A new linear theory of generalized thermoelasticity under heat transfer with memory-dependent derivative (MDD) is employed to address this study. It has been found that three basic waves consisting of two sets of coupled longitudinal waves and one independent vertically shear-type wave may travel with distinct phase speeds. The formulae for various reflection coefficients and their respective energy ratios are determined in case of an incident coupled longitudinal elastic wave at the thermally insulated stress-free boundary of the medium. The results for the reflection coefficients and their respective energy ratios for various values of the angle of incidence are computed numerically and presented graphically for copper-like material and discussed.

Dispersion equation of Rayleigh waves in transversely isotropic nonlocal piezoelastic solids half-space

This study is devoted to investigate the propagation of Rayleigh-type waves in transversely isotropic nonlocal piezoelastic half-space. When the stress-free boundary is maintained at charge-free condition, the dispersion equation for the propagation of Rayleigh waves at the free surface of transversely isotropic piezoelastic solids has been obtained. Based on the obtained dispersion equation, the effect of the nonlocality on the speed of Rayleigh wave is numerically considered. The dependence of velocities of plane waves in transversely isotropic nonlocal piezoelastic medium on the direction of propagation as well as non-dimensional frequency parameter has been also illustrated.

Inclined convection in a porous Brinkman layer: linear instability and nonlinear stability

In this article, we deal with thermal convection in an inclined porous layer modelled by the Brinkman Law . Inertial effects are taken into account, and the physically significant rigid boundary conditions are imposed. This model is an extension of the work by Rees & Bassom (Rees & Bassom 2000 Acta Mech. 144 , 103–118 ( doi:10.1007/BF01181831 )), where Darcy's Law is adopted, and only linear instability is investigated. It also completes the work of Falsaperla & Mulone (Falsaperla & Mulone 2018 Ric. Mat. 144 , 1–17 ( doi:10.1007/s11587-018-0371-2 )), where the case of stress-free boundary conditions is studied and the inertial terms are absent. In this model, the basic laminar solution for the velocity is a combination of hyperbolic and polynomial functions, which makes the linear and nonlinear analysis much more complex. The original features of the paper are the following: we study three-dimensional perturbations , providing critical surfaces for the linear and nonlinear analyses; we study nonlinear stability with the Lyapunov method and, for the first time in the case of inclined layers, we compute the critical nonlinear Rayleigh regions by solving the associated variational maximum problem ; we give some estimates of global nonlinear asymptotical stability; we study linear instability and nonlinear stability also with the presence of the inertial term , i.e. for a finite Va.