Temporal behavior of laser induced elastic plate resonances

This paper investigates the dependence on Poisson’s ratio of local plate resonances in low attenuating materials. In our experiments, these resonances are generated by a pulse laser source and detected with a heterodyne interferometer measuring surface displacement normal to the plate. The laser impact induces a set of resonances that are dominated by Zero Group Velocity (ZGV) Lamb modes. For some Poisson’s ratio, thickness-shear resonances are also detected. These experiments confirm that the temporal decay of ZGV modes follows a t^−0.5$t^{-0.5}$ law and show that the temporal decay of the thickness resonances is much faster. Similar decays are obtained by numerical simulations achieved with a finite difference code. A simple model is proposed to describe the thickness resonances. It predicts that a thickness mode decays as t^−1.5$t^{-1.5}$ for large times and that the resonance amplitude is proportional to D^−1.5$D^{-1.5}$ where D$D$ is the curvature of the dispersion curve ω(k)$\omega \left(k\right)$ at k=0$k=0$. This curvature depends on the order of the mode and on the Poisson’s ratio, and it explains why some thickness resonances are well detected while others are not.     

A Riemannian approach to strain measures in nonlinear elasticity

The isotropic Hencky strain energy appears naturally as a distance measure of the deformation gradient to the set SO(n)$\mathrm{SO}(n)$ of rigid rotations in the canonical left-invariant Riemannian metric on the general linear group GL(n)$\mathrm{GL}(n)$. Objectivity requires the Riemannian metric to be left-GL(n)$\mathrm{GL}(n)$-invariant, isotropy requires the Riemannian metric to be right-O(n)$\mathrm{O}(n)$-invariant. The latter two conditions are only satisfied for a three-parameter family of Riemannian metrics on the tangent space of GL(n)$\mathrm{GL}(n)$. Surprisingly, the final result is basically independent of the chosen parameters.     

Lamb wave mode decomposition for structural health monitoring

Lamb waves propagate over large distances in plate-like thin structures and they have received great attention in the structural health monitoring (SHM) field as an efficient means to inspect a large area of a structure by using only a small number of sensors. The times-of-flight of the Lamb wave modes are useful for detecting damage generated in a structure. However, due to the dispersive and multi-mode nature of Lamb waves, it is very challenging to decompose Lamb wave modes into symmetric and anti-symmetric modes for potential applications to structural health monitoring. Thus, we propose an efficient Lamb wave mode decomposition method based on two fundamental rules: the group velocity ratio rule and the mode amplitude ratio rule. The group velocity ratio rule means that the ratio of the group velocities of _A0$A_0$ and _S0$S_0$ modes must be constant. The mode amplitude ratio rule means that the ratio of the magnitudes of _A0$A_0$ and _S0$S_0$ modes in a measured response signal must be always greater than one once the center frequency of the input signal is determined, such that the magnitude of the _A0$A_0$ mode in the excited signal is larger than that of the _S0$S_0$ mode, and vice versa. The proposed method is verified through experiments conducted for a plate specimen.     

Grain orientation fragmentation in hot-deformed aluminium: Experiment and simulation

Grain orientation fragmentation is studied in a set of 176 individual grains of an aluminium polycrystal deformed in plane strain compression at 400 °C to a strain of $\epsilon =1.2$. Experimental observations were made by EBSD at successive strains of 0, 0.42, 0.77 and 1.2 on the internal surface of a split sample. Statistics of the in-grain orientation spreads were computed based on approximately 3000 orientation measurements per grain. A high-resolution finite element simulation (about 1000 elements per grain) was carried out on a polycrystal whose grains were assigned the initial experimental crystal orientations. The experimental and simulation results were compared in terms of the fractions of grains that exhibit fragmentation and the lattice orientations of the fragmenting grains. The numbers of fragmented grains increase with strain, reaching values of 10% in the experiment (2-D characterization) and 20% in the simulation (3-D characterization) at $\epsilon =1.2$. For both experiment and simulation, fragmentation is more likely in grains whose lattice is symmetrically oriented with respect to the loading axes. Under plane strain compression, the orientations of the fragmented grains coincide with regions of orientation space in which the reorientation velocity field in the plane perpendicular to the reorientation velocity direction is unstable.     

Effect of cylinder proximity to the wall on channel flow heat transfer enhancement

Heat-transfer enhancement in a uniformly heated slot mini-channel due to vortices shed from an adiabatic circular cylinder is numerically investigated. The effects of gap spacing between the cylinder and bottom wall on wall heat transfer and pressure drop are systemically studied. Numerical simulations are performed at Re=100$\mathit{Re}=100$, 0.1?Pr?10$0.1?\mathrm{Pr}?10$ and a blockage ratio of D/H=1/3$D/H=1/3$. Results within the thermally developing flow region show heat transfer augmentation compared to the plane channel. It was found that when the obstacle is placed in the middle of the duct, maximum heat transfer enhancement from channel walls is achieved. Displacement of circular cylinder towards the bottom wall leads to the suppression of the vortex shedding, the establishment of a steady flow and a reduction of both wall heat transfer and pressure drop. Performance analysis indicates that the proposed heat transfer enhancement mechanism is beneficial for low-Prandtl-number fluids.     

Mode-stirred reverberation chambers: A paradigm for spatio-temporal complexity in dynamic electromagnetic environments

We investigate probability distributions in dynamic multi-mode electromagnetic cavities, commonly referred to as mode-stirred reverberation chambers. We show that Bessel K$K$ and Bessel I$I$ distributions play a prominent role when a large but finite number of excited modes, loss of energy (through aperture leakage or dissipation), or nonstationary transient fields are involved. With the aim at reducing the number of simultaneously excited cavity modes as much as possible while maintaining a well-characterizable quasi-random field, measurement results indicate that single-mode stirring is feasible at certain frequencies well below the usual ‘lowest usable frequency’ of the cavity. Distributions for nonstationary fields are shown to allow for improved estimation of the maximum-to-mean ratio of the received power during stepwise rotation of the mode stirrer.     

Lateral migration of a capsule in a plane Poiseuille flow in a channel

Three-dimensional numerical simulation is presented on the motion of a deformable capsule undergoing large deformation in a plane Poiseuille flow in a channel at small inertia. The capsule is modeled as a liquid drop surrounded by an elastic membrane which follows neo-Hookean law. The numerical methodology is based on a mixed finite-difference/Fourier transform method for the flow solver and a front-tracking method for the deformable interface. The methodology can address large deformation of a capsule over a wide range of capsule-to-medium viscosity ratio. An extensive validation of the methodology is presented on capsule deformation in linear shear flow and compared with the boundary-element/integral simulations. Motion of a capsule in wall-bounded parabolic flow is simulated over an extended period of time to consider both transient and steady-state motion. Lateral migration of the capsule towards the centerline of the channel is observed. Results are presented over a range of capillary number, viscosity ratio, capsule-to-channel size ratio, and lateral location. After an initial transient phase during which the capsule deforms very quickly, the flow of the capsule is observed to be a quasi-steady process irrespective of capillary number (Ca)$(\mathit{Ca})$, capsule-to-channel size ratio (a/H)$(a/H)$, and viscosity ratio (λ)$(\lambda )$. Migration velocity and capsule deformation are observed to increase with increasing Ca$\mathit{Ca}$ and a/H$a/H$, but decrease with increasing λ$\lambda$, and increasing distance from the wall. Numerical results on the capsule migration are compared with the analytical results for liquid drops, and capsules with Hookean membrane which are valid in the limit of small deformation. Unlike the prediction for liquid drops, capsules are observed to migrate toward the centerline for 0.2?λ?5$0.2?\lambda ?5$ range considered here. The migration velocity is observed to depend linearly on (a/H)³$(a/H{)}^3$, in agreement with the small-deformation theory, but non-linearly on Ca$\mathit{Ca}$ and the distance from the wall, in violation of the theory. Using the present numerical results and the analytical results, we present a correlation that can reasonably predict migration velocity of a capsule for moderate values of a/H$a/H$ and Ca$\mathit{Ca}$.     

Acoustic wave propagation in inhomogeneous,layered waveguides based on modal expansions and hp-FEM

A new model is presented for harmonic wave propagation and scattering problems in non-uniform, stratified waveguides, governed by the Helmholtz equation. The method is based on a modal expansion, obtained by utilizing cross-section basis defined through the solution of vertical eigenvalue problems along the waveguide. The latter local basis is enhanced by including additional modes accounting for the effects of inhomogeneous boundaries and/or interfaces. The additional modes provide implicit summation of the slowly convergent part of the local-mode series, rendering the remaining part to be fast convergent, increasing the efficiency of the method, especially in long-range propagation applications. Using the enhanced representation, in conjunction with an energy-type variational principle, a coupled-mode system of equations is derived for the determination of the unknown modal-amplitude functions. In the case of multilayered environments, h$h$- and p$p$-FEM have been applied for the solution of both the local vertical eigenvalue problems and the resulting coupled mode system, exhibiting robustness and good rates of convergence. Numerical examples are presented in simple acoustic propagation problems, illustrating the role and significance of the additional mode(s) and the efficiency of the present model, that can be naturally extended to treat propagation and scattering problems in more complex 3D waveguides.     

Inversion for weak triclinic anisotropy from acoustic axes

Acoustic axes are directions in anisotropic elastic media, in which phase velocities of two or three plane waves (P$P$, S1$S1$ or S2$S2$ waves) coincide. Acoustic axes are important, because they can cause singularities in the field of polarization vectors and anomalies in the shape of the slowness surface. The maximum number of acoustic axes in triclinic anisotropy is 16, and their directions depend on anisotropy parameters in a complicate way. Under weak anisotropy approximation this dependence simplifies and the directions of acoustic axes can be used for the inversion for anisotropy parameters. The maximum acoustic axes under weak anisotropy is 16, the minimum number of acoustic axes is zero. In the inversion, we can retrieve 13 combinations of anisotropy parameters provided we use directions of 7 acoustic axes at least. Under weak anisotropy approximation, the directions of acoustic axes are insensitive to strength of anisotropy; hence we cannot invert for absolute values of weak anisotropy parameters, but only for their relative values. Numerical tests have shown that the inversion is applicable only to very weak anisotropy with strength of less than 5%, provided that the acoustic axes used in the inversion are determined with an accuracy of 0.1^°$0.1^{°}$ or better. In this case the inversion yields an average error for elastic parameters of less than 10%. In order to invert for the total set of 21 anisotropy parameters it is necessary to combine the measurements of the directions of the acoustic axes with measurements of other attributes of elastic waves in anisotropic media.     

Adhesive contact on power-law graded elastic solids: The JKR–DMT transition using a double-Hertz model

A cohesive zone model of axisymmetric adhesive contact between a rigid sphere and a power-law graded elastic half-space is established by extending the double-Hertz model of Greenwood and Johnson (1998). Closed-form solutions are obtained analytically for the surface stress, deformation fields and equilibrium relations among applied load, indentation depth, inner and outer radii of the cohesive zone, which include the corresponding solutions for homogeneous isotropic materials and the Gibson solid as special cases. These solutions provide a continuous transition between JKR and DMT type contact models through a generalized Tabor parameter μ$\mu$. Our analysis reveals that the magnitude of the pull-off force ranges from (3+k)πRΔγ/2$(3+k)\pi R\mathrm{\Delta }\gamma /2$ to 2πRΔγ$2\pi R\mathrm{\Delta }\gamma$, where k$k$, R$R$ and Δγ$\mathrm{\Delta }\gamma$ denote the gradient exponent of the elastic modulus for the half-space, the radius of the sphere and the work of adhesion, respectively. Interestingly, the pull-off force for the Gibson solid is found to be identically equal to 2πRΔγ,$2\pi R\mathrm{\Delta }\gamma ,$ independent of the corresponding Tabor parameter. The obtained analytical solutions are validated with finite element simulations.