Ultrasonic high frequency lamb waves for evaluation of plate structures

The potentials of high frequency Lamb wave modes are investigated in the inspection of plate-like structures. The wave propagation characteristics of higher order wave modes and the corresponding sensitivity and detectability are studied. Finite element simulations are carried out using infinite elements to model the ultrasonic wedge transducer and the inspection system. Experimental pulse–echo measurements are conducted to verify the influence of different modes characteristics predicted from the finite element simulations. The experimental measurements show a good agreement with the obtained numerical results for the fundamental modes, S₀ and A₀, and the higher order modes, S₁ and A₁, at 4 MHz mm of frequency–thickness.     

Asymmetric propagation of the first order antisymmetric lamb wave in a tapered plate based on time domain analysis

The asymmetric propagation of the first order antisymmetric (A₁) Lamb wave in a tapered plate respectively carved with sharp bottom corner and round bottom corner is theoretically investigated. Through numerical simulation of A₁ Lamb wave in time domain, we find that when the thickness of the waveguide abruptly decreases to below the cut-off thickness, about half of the A₁ mode is converted into the fundamental symmetrical S₀ and antisymmetrical A₀ modes to pass through the defected region. Furthermore, the transmitted modes A₀ and S₀ are completely apart from each other and can be quantitatively evaluated. Conversely, when the thickness change is very smooth, most of the energy of A₁ Lamb wave is reflected back. It is the unique mode conversion behavior that leads to great transmission difference value of A₁ Lamb wave along the opposite directions. Finally, the influence of geometrical parameters on the transmission coefficient is also studied. The higher efficiency and proper working frequency range can be realized by adjusting the slope angle θ, height h ₁ and h ₂. The simple asymmetric systems will be potentially significant in applications of ultrasound diagnosis and therapy.     

Laser-induced circumferential waves on hollow cylinder and their interaction with defects by finite element method

A three dimensional (3-D) finite element model for simulating laser induced circumferential wave on a hollow cylinder is developed based on the thermoelastical mechanism, which can take any laser source into account and simulate the interactions between circumferential wave and defects in the hollow cylinder. The model is verified by a control calculation. The results show that the waveforms of circumferential wave are in very good agreement with those available in literature, not only on the arrival time and shape but also on the amplitudes of A ₀, S ₀ and A₁ modes. Using the model, circumferential waves on the surfaces of two series hollow cylinders are simulated, one with same thickness but different outer radius, and the other with the same outer radius but different thickness. The results show that a new mode appears in circumferential wave, compared with Lamb wave in plate. With increase of thickness or radius, the amplitude of the new mode reduces. Another conclusion is that with increase of the thickness of the hollow cylinder, the circumferential wave evolves gradually to the cylindrical Rayleigh waveform, which results from the attenuation of the coupling effect between the outer and inner surface. Moreover, the circumferential waves generated on a hollow cylinder with a surface defect are also simulated, and the results indicate that in the circumferential waves obtained at the point beyond the defect, the amplitude of A ₀ mode decreases and its dispersion enhances. More importantly, a new bipolar waveform corresponding to the interaction of S ₀ mode with the defect appears, its amplitude is larger than three times of that of S ₀ mode. As a result, we consider that the new bipolar waveform will be the optimal feature to nondestructively detect the surface defect on the hollow cylinder.     

Nonlinear guided waves in plates: A numerical perspective

Harmonic generation from non-cumulative fundamental symmetric (_S0$S_0$) and antisymmetric (_A0$A_0$) modes in plate is studied from a numerical standpoint. The contribution to harmonic generation from material nonlinearity is shown to be larger than that from geometric nonlinearity. Also, increasing the magnitude of the higher order elastic constants increases the amplitude of second harmonics. Second harmonic generation from non-phase-matched modes illustrates that group velocity matching is not a necessary condition for harmonic generation. Additionally, harmonic generation from primary mode is continuous and once generated, higher harmonics propagate independently. Lastly, the phenomenon of mode-interaction to generate sum and difference frequencies is demonstrated.     

Subsonic flapping flutter

A mathematical model of two-dimensional flow through a flexible channel is analyzed for its stability characteristics. Linear theory shows that fluid viscosity, modelled by a Darcy friction factor, induces flutter instability when the dimensionsless fluid speed, S, attains a critical flutter speed, S₀. This is in qualitative agreement with experimental results, and it is at variance with previous analytical studies where fluid viscosity was neglected and divergence instability was predicted. The critical flutter speed and the associated critical flutter frequency depend on three other dimensionless parameters: the ratio of fluid to wall damping; the ratio of wall to fluid mass; and the ratio of wall bending resistance to elastance. Non-linear theory predicts stable, finite amplitude flutter for S>S₀, which increases in frequency and amplitude as S increases. Both symmetric and antisymmetric modes of deformation are discussed.     

Polar optical phonon states and dispersive spectra of wurtzite ZnO nanocrystals embedded in zinc-blende MgO matrix

Based on the macroscopic dielectric continuum model and Loudon’s uniaxial crystal model, the polar optical phonon modes of a quasi-0-dimensional (Q0D) wurtzite spherical nanocrystal embedded in zinc-blende dielectric matrix are derived and studied. It is found that there are two types of polar phonon modes, i.e. interface optical (IO) phonon modes and the quasi-confined (QC) phonon modes coexisting in Q0D wurtzite ZnO nanocrystal embedded in zinc-blende MgO matrix. Via solving Laplace equations under spheroidal and spherical coordinates, the unified and analytical phonon states and dispersive equations of IO and QC modes are derived. Numerical calculations on a wurtzite/zinc-blende ZnO/MgO nanocrystal are performed. The frequency ranges of the IO and QC phonon modes of the ZnO/MgO nanocrystals are analyzed and discussed. It is found that the IO modes only exist in one frequency range, while QC modes may appear in three frequency ranges. The dispersive frequencies of IO and QC modes are the discrete functions of orbital quantum numbers l and azimuthal quantum numbers m. Moreover, a pair of given l and m corresponds to one IO mode, but to more than one branches of QC. The analytical phonon states and dispersive equations obtained here are quite useful for further investigating Raman spectra of phonons and other relative properties of wurtzite/zinc-blende Q0D nanocrystal structures.     

Magnetoelastic waves in an in-plane magnetized ferromagnetic plate

The spectrum of magnetoelastic waves propagating along the magnetic field in an in-plane magnetized ferromagnetic plate is numerically investigated in the exchangeless approximation. No restrictions are imposed either on the field pattern of backward volume magnetostatic waves (BVMSWs) or elastic waves supported by a plate of a given geometry across the plate or on the relationship between the sound velocity v _S and the phase velocity of the magnetoelastic waves v=ω/q (ω is the frequency, q is the wave number). The resonance interaction of the BVMSWs and elastic waves is accompanied, as a rule, by the formation of “stop” bands δω that are proportional to the magnetoelastic coupling constant b. When the BVMSWs are in resonance with Lamb and shear elastic modes the values of the magnetoelastic gaps δω at v≈v _S turn out to be of the same order. For v≫v _S , the efficiency of the interaction between the BVMSWs and transverse Lamb modes is almost one order of magnitude higher. If the frequency spacing Δω between the elastic modes is smaller than the mag-netoelastic gap in the spectrum (Δω≤δω), which takes place, particularly, in the region of crowding the elastic mode spectrum (v≈v _S), the resonant interaction results in mixing the dispersion laws for the elastic modes. Namely, a surface mode may transform into a volume one and a shear mode, into the Lamb mode or into a shear mode with another number. The resonance interaction of the shear and Lamb elastic modes not only forms the magnetoelastic gaps δω∼b ² but also changes the efficiency of elastic wave coupling with the magnetic subsystem. This may show up as the coexistence of the effects of “repulsing” both the dispersion laws and the damping decrements of the elastic waves at the resonance frequency. It is shown that magnetostriction splits the cutoff frequencies of both transverse Lamb modes and shear modes, as well as the long-wave (q → 0) frequency limits f ₀ of the BVMSW modes. This may cause the resonance interaction between BVMSW modes of equal evenness in a narrow frequency band Δ∼b near f ₀.     

Confinement of polar optical phonons in quasi-one-dimensional Wurtzite GaN-based quantum well wires: propagating and half-space phonon modes

With the aid of the macroscopic dielectric continuum and Loudon’s uniaxial crystal models, the propagating (PR) and half-space (HS) optical phonon modes and corresponding Fröhlich-like electron-phonon interaction Hamiltonians in a quasi-one-dimensionality (Q1D) wurtzite quantum well wire (QWW) structure are derived and studied. Numerical calculations on a wurtzite GaN/A_l0.15Ga_0.85N QWW are performed, and discussion is focused mainly on the dependence of the frequency dispersions of PR and HS modes on the free wave-number k _z in the z-direction and on the azimuthal quantum number m. The calculated results show that, for given k _z and m, there usually exist infinite branches of PR and HS modes in the high-frequency range, and only finite branches of HS modes in the low-frequency range in wurtzite QWW systems. The reducing behaviors of the PR modes to HS modes, and of the HS mode to interface phonon mode have been observed clearly in Q1D wurtzite heterostructures. Moreover, the dispersive properties of the PR and HS modes in Q1D QWWs have been compared with those in Q2D quantum well structures. The underlying physical reasons for these features have also been analyzed in depth.     

A Brillouin study of the temperature-dependence of the acoustic modes across the insulator-metal transitions in V2O3 and Cr-doped V2O3

Brillouin scattering studies have been carried out on high-quality single crystals of undoped and 0.9% Cr-doped V₂O₃. The observed modes in both the samples at ∼12 and ∼60 GHz are associated with the surface Rayleigh wave (SRW) and bulk acoustic wave (BAW), respectively. In the undoped sample, the mode frequencies of the SRW and BAW modes decrease as the temperature is lowered from room temperature to the insulator-metal transition temperature (T_IM=T_N=∼130 K). Below the transition, the modes show hardening. In the doped sample, the SRW mode shows a similar temperature-dependence as the undoped one, but the BAW mode shows hardening from room temperature down to the lowest temperature (50 K). This is the first measurement of the sound velocity below T_IM in the V₂O₃ system. The softening of the SRW frequency from 330 K to T_IM can be qualitatively understood on the basis of the temperature-dependence of C₄₄, which, in turn, is related to the orbital fluctuations in the paramagnetic metallic phase. The hardening of the mode frequencies below T_IM suggests that C₄₄ must increase in the antiferromagnetic insulating phase, possibly due to the orbital ordering.     

Phonon spectrum and interaction between nanotubes in single-walled carbon nanotube bundles at high pressures and temperatures

The Raman spectra of single-walled carbon nanotubes at temperatures up to 730 K and pressures up to 7 GPa have been measured. The behavior of phonon modes and the interaction between nanotubes in bundles have been studied. It has been found that the temperature shift of the vibrational G mode is completely reversible, whereas the temperature shift of radial breathing modes is partially irreversible and the softening of the modes and narrowing of phonon bands are observed. The temperature shift and softening of radial breathing modes are also observed when samples are irradiated by laser radiation with a power density of 6.5 kW/mm². The dependence of the relative frequency Ω/Ω₀ for G ⁺ and G ^? phonon modes on the relative change A ₀/A in the triangular lattice constant of bundles of nanotubes calculated using the thermal expansion coefficient and compressibility coefficient of nanotube bundles shows that the temperature shift of the G mode is determined by the softening of the C-C bond in nanotubes. An increase in the equilibrium distances between nanotubes at the breaking of random covalent C-C bonds between nanotubes in bundles of nanotubes is in my opinion the main reason for the softening of the radial breathing modes.