Higher-order Wave Modes Research Articles

Determination of dispersion curves of higher order guided ultrasonic waves based on experimental data by a 2D-DFT

Guided ultrasonic wave based structural health monitoring has been subject to research over the last decades. In order to analyze the wave propagation data correctly, knowledge about the fundamental wave propagation properties is indispensable. Due to the multimodal and dispersive nature of guided ultrasonic waves these properties are characterized by dispersion diagrams. In previous work by the authors [1] the dispersion behavior of the guided ultrasonic waves is extracted by an adapted non-uniform 2D-DFT algorithm based on [2]. With this algorithm the dispersion curves can be computed from experimental data in an accurate and highly automated fashion. So far the application is limited to the fundamental wave modes over large frequency ranges. In this work the approach is extended to higher-order wave modes, which are of special interest in particular for the nonlinear wave propagation. To analyze the robustness of the presented data acquisition algorithm the procedure is applied first to isotropic waveguides and second to more complex material systems like fiber metal laminates. The results indicate that the presented approach enables one to derive the dispersion curves over large frequency ranges from experimental data not only for the fundamental A0 and S0 wave modes but also for higher-order modes.

Experimental and Computational Investigation of Guided Waves in a Human Skull

We investigate guided (Lamb) waves in a human cadaver skull through experiments and computational simulations. Ultrasonic wedge transducers and scanning laser Doppler vibrometry are used respectively to excite and measure Lamb waves propagating in the cranial bone of a degassed skull. Measurements are performed over a section of the parietal bone and temporal bone spanning the squamous suture. The experimental data are analyzed for the identification of wave modes and the characterization of dispersion properties. In the parietal bone, for instance, the A0 wave mode is excited between 200 and 600 kHz, and higher-order Lamb waves are excited from 1 to 1.8 MHz. From the experimental dispersion curves and average thickness extracted from the skull computed tomography scan, we estimate average isotropic material properties that capture the essential dispersion characteristics using a semi-analytical finite-element model. We also explore the leaky and non-leaky wave behavior of the degassed skull with water loading in the cranial cavity. Successful excitation of leaky Lamb waves is confirmed (for higher-order wave modes with phase velocity faster than the speed of sound in water) from 500 kHz to 1.5 MHz, which may find applications in imaging and therapeutics at the brain periphery or skull–brain interface (e.g., for metastases). The non-leaky A0 Lamb wave mode propagates between 200 and 600 kHz, with or without fluid loading, for potential use in skull-related diagnostics and imaging (e.g., for sutures).

Sensitivity of MCS Low-Frequency Gravity Waves to Microphysical Variations

AbstractThe sensitivity of low-frequency gravity waves generated during the development and mature stages of an MCS to variations in the characteristics of the rimed ice parameterization were tested through idealized numerical simulations over a range of environment shears and instabilities. Latent cooling in the simulations with less dense, graupel-like rimed ice was more concentrated aloft near the melting level, while cooling in simulations with denser, hail-like rimed ice extended from the melting level to the surface. However, the cooling profiles still had significant internal variability across different environments and over each simulation’s duration. Initial wave production during the MCS developing stage was fairly similar in the hail and graupel simulations. During the mature stages, graupel simulations showed stronger perturbations in CAPE due to the cooling and associated wave vertical motion being farther aloft; hail simulations showed stronger perturbations in LFC due to cooling and wave vertical motion being concentrated at lower levels. The differences in the cooling profiles were not uniform enough to produce consistently different higher-order wave modes. However, the initiation of discrete cells ahead of the convective line was found to be highly sensitive to the nature of the prior destabilizing wave. Individual events of discrete propagation were suppressed in some of the graupel simulations due to the higher location of both peak cooling and vertical wave motion. Such results underscore the need to fully characterize MCS microphysical heating profiles and their low-frequency gravity waves to understand their structure and development.

Impact of Convectively Generated Low-Frequency Gravity Waves on Evolution of Mesoscale Convective Systems

AbstractIdealized numerical simulations of mesoscale convective systems (MCSs) over a range of instabilities and shears were conducted to examine low-frequency gravity waves generated during initial and mature stages of convection. In all simulations, at initial updraft development a first-order wave was generated by heating extending through the depth of the troposphere. Additional first-order wave modes were generated each time the convective updraft reintensified. Each of these waves stabilized the environment in advance of the system. As precipitation descended below cloud base, and as a stratiform precipitation region developed, second-order wave modes were generated by cooling extending from the midlevels to the surface. These waves destabilized the environment ahead of the system but weakened the 0–5 km shear. Third-order wave modes could be generated by midlevel cooling caused by rear inflow intensification; these wave modes cooled the midlevels destabilizing the environment. The developing stage of each MCS was characterized by a cyclical process: developing updraft, generation of n = 1 wave, increase in precipitation, generation of n = 2 wave, and subsequent environmental destabilization reinvigorating the updraft. After rearward expansion of the stratiform region, the MCSs entered their mature stage and the method of updraft reinvigoration shifted to absorbing discrete convective cells produced in advance of each system. Higher-order wave modes destabilized the environment, making it more favorable to development of these cells and maintenance of the MCS. As initial simulation shear or instability increased, the transition from cyclical wave/updraft development to discrete cell/updraft development occurred more quickly.

Quantifying excess power from radio frequency interference in Epoch of Reionization measurements

ABSTRACT We quantify the effect of radio frequency interference (RFI) on measurements of the 21-cm power spectrum during the Epoch of Reionization (EoR). Specifically, we investigate how the frequency structure of RFI source emission generates contamination in higher order wave modes, which is much more problematic than smooth-spectrum foreground sources. Using a relatively optimistic EoR model, we find that even a single relatively dim RFI source can overwhelm the EoR power spectrum signal of $\sim 10\, {\rm mK}^2$ for modes $0.1 \ \lt k \lt 2 \, h\, {\rm Mpc}^{-1}$. If the total apparent RFI flux density in the final power spectrum integration is kept below 1 mJy, an EoR signal resembling this optimistic model should be detectable for modes $k \lt 0.9\, h\, {\rm Mpc}^{-1}$, given no other systematic contaminants and an error tolerance as high as 10 per cent. More pessimistic models will be more restrictive. These results emphasize the need for highly effective RFI mitigation strategies for telescopes used to search for the EoR.

Multimode guided wave extraction capabilities using embedded thin film sensors in a composite laminated beam

A novel method to extract individual wave modes from the ultrasonic multimode guided wave response sensed by embedded piezoelectric sensors is presented. Multimode response involving two fundamental modes, i.e., flexural and axial, and two higher-order wave-modes, i.e., shear and thickness contraction have been considered in the present work. The model is based on higher order beam theory which uses wave kinematics to extract individual wave modes from the multimode response. Further, a numerical finite element model is employed to validate the deformation profile of this analytical model. The embedment of thin film sensors at the same location but within different layers produce signals that exhibit a relative difference in the phase and amplitude due to kinematics. The sensor signals are then post-processed to obtain individual Lamb wave modes. Experiments are carried out to validate the procedure for extracting individual guided wave mode response. The method is independent of sampling rate and works in the presence of complicated mode converted responses. Electronic analog circuits can also be used to perform operations on sensor signals before analog-to-digital conversion, thereby eliminating digital signal processing and the requirement of onboard computers for structural health monitoring especially in aircraft. Such capability minimizes power consumption and weight since we may be able to avoid the use of a computer.

30 GHz surface acoustic wave transducers with extremely high mass sensitivity

A nano-patterning process is reported in this work, which can achieve surface acoustic wave (SAW) devices with an extremely high frequency and a super-high mass sensitivity. An integrated lift-off process with ion beam milling is used to minimize the short-circuiting problem and improve the quality of nanoscale interdigital transducers (IDTs). A specifically designed proximity-effect-correction algorithm is applied to mitigate the proximity effect occurring in the electron-beam lithography process. The IDTs with a period of 160 nm and a finger width of 35 nm are achieved, enabling a frequency of ∼30 GHz on lithium niobate based SAW devices. Both centrosymmetric type and axisymmetric type IDT structures are fabricated, and the results show that the centrosymmetric type tends to excite lower-order Rayleigh waves and the axisymmetric type tends to excite higher-order wave modes. A mass sensitivity of ∼388.2 MHz × mm2/μg is demonstrated, which is ∼109 times larger than that of a conventional quartz crystal balance and ∼50 times higher than a conventional SAW device with a wavelength of 4 μm.

Porous labyrinthine acoustic metamaterials with high transmission loss property

This study systemically investigates a porous labyrinthine type of acoustic metamaterials (LAMs), a sort of acoustic metasurface, analytically, numerically, and in laboratory tests. The LAMs are composed of a series of porous elements, where stainless steel plates with various lengths are inserted into the melamine foam. At the frequency of interest 2000 Hz, porous elements with a thickness smaller than one-eighth of the target wavelength are designed to generate a linearly varied phase gradient on the refracting surface and slightly varied phase responses on the reflecting surface; the elements play key roles in refracted and reflected wave manipulations, respectively. Two porous LAMs with different periodical lengths are designed based on the generalized Snell’s law to study the effect of the periodical length on refraction and reflection phenomena in the scattered sound pressure fields. By reducing the length to smaller than one-half of the target wavelength, the high-order wave modes will disappear in the refracted and reflected sound pressure fields at omnidirectional incidence, resulting in enhancements of transmission loss and also sound absorption coefficient in a wide range of incidence angles compared with the uniform melamine foam with the same thickness. The thin porous LAMs provide a method to improve sound transmission loss and sound absorption properties of an uniform porous material and show potentials to be used in cabins of high-speed trains and aircraft.

Investigation on acoustic reflection logging of LWD using a flexible finite difference technique

ABSTRACTAcoustic reflection logging while drilling (LWD) measurement has overwhelming advantages in detecting reflectors outside the borehole, making it a prominent technology in geosteering during LWD operations. This paper carries out a comprehensive numerical investigation into the acoustic reflection logging responses in LWD environments by combining the analytical real axis integration (RAI) solution and an exquisitely improved finite difference method (FDM). Mutual validation of these two methods using typical and well-known cases ensures the reliability of the modelling methodology. Numerical studies on LWD and wireline acoustic reflection logging reveal that a ring source rather than four azimuthally orthogonal point sources can excite acoustic LWD monopole waves without interference from higher order wave modes. Lower order spatial differential operators are more efficient for FDM simulations of LWD cases when variance in the medium is obvious. Compared with the wireline monopole case, LWD monopole reflection acoustic logging can obtain higher quality reflected waves and has a superior ability to identify the azimuth of a geological reflector away from the borehole.

Inertially induced cyclic solutions in thin-film free-surface flows

AbstractNew mechanisms are discovered regarding the effects of inertia in the transient Moffatt–Pukhnachov problem (J. Méc., vol. 187, 1977, pp. 651–673) on the evolution of the free surface of a viscous film coating the exterior of a rotating horizontal cylinder. Assuming two-dimensional evolution of the film thickness (i.e. neglecting variation in the axial direction), a multiple-timescale procedure is used to obtain explicitly parameterized high-order asymptotic approximations of solutions of the spatio-temporal evolution equation. Novel, hitherto-unexplained transitions from stability to instability are observed as inertia is increased. In particular, a critical Reynolds number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}_c$ is predicted at which occurs a supercritical pitchfork bifurcation in wave amplitude that is fully explained by the new asymptotic theory. For $\mathit{Re}<\mathit{Re}_c$, free-surface profiles converge algebraically-cum-exponentially to a steady state and, for $\mathit{Re}> \mathit{Re}_c$, stable temporally periodic solutions with leading-order amplitudes proportional to $(\mathit{Re}-\mathit{Re}_c)^{1/2}$ are found, i.e. in the régime in which previous related literature predicts exponentially divergent instability. For $\mathit{Re}=\mathit{Re}_c$, stable solutions are found that decay algebraically to a steady state. A model solution is proposed that not only captures qualitatively the interaction between fundamental and higher-order wave modes but also offers an explanation for the formation of the lobes observed in Moffatt’s original experiments. All asymptotic theory is convincingly corroborated by numerical integrations that are spectrally accurate in space and eighth/ninth-order accurate in time.

The effect of hydrostatic pressure fields on the dispersion characteristics of fluid-shell coupled system

The effect of hydrostatic pressure on the vibration dispersion characteristics of fluid-shell coupled structures was studied. Both fluid-loaded cylindrical shells and fluid-filled cylindrical shells were considered. Numerical analysis was applied to solve the dispersion equations for shells filled with or loaded with fluid at various hydrostatic pressures. The results for external pressure showed that non-dimensional axial wave numbers are nearly independent when the pressure is below the critical level. The influence of internal pressure on wave numbers was found significant for the real branch s=1 and the complex branches of dispersion curves. The presence of internal pressure increased the cut on frequencies for the branch s=1 for high order wave modes.

Sound propagation in soundproofing casement windows

Casement windows consisted of two wooden frames that can be opened and closed at various angles are widely used in developing countries with tropical climates. However, an annual increase in a number of motorcycles and automobiles and traffic noise level these countries have rendered these windows to be useless. In this paper, we present a model for manufacturing windows which are suitable for the developing tropical countries. These windows are capable of ventilating, regulating sunlight, protecting against coldness, and reducing traffic noise and fumes from motor vehicles. The ventilation and soundproofing unit hold an importance place in the design of the windows and are calculated using the wave equation and observations of higher-order mode waves. In order to maximize the soundproofing ability, the selection of size and placement of input and output openings in such a way that would minimize the effects of higher-order mode waves are considered in details.

A Study on the Effects of Higher Order Mode Wave on Mufflers Performance

Based on the existence of higher order mode waves (HOMW) in expansion mufflers is proved theoretically, a 3-D FEM is used to obtain the four-pole parameters of a muffler which are in turn used to calculate the transmission loss. With this method, the distribution of sound pressure in a muffler is calculated, the effects of HOMW on the muffler performance are investigated and a technique to improve the muffler performance is put forward. It is shown that, because of HOMW, the sound wave in expansion chamber is not in plane form; HOMW can descent capability of muffler, and the position of inlet and outlet is important to the performance of mufflers.

Propagation Characteristics of Higher-order Mode Electromagnetic Signals in Coaxial GIS Model with Various Conditions of Arch-shaped UHF Sensor

Partial discharge detection using a UHF band signal is a well known advanced insulation diagnosis method in gas insulated switchgear (GIS), and has been well studied. In contrast to conventional diagnosis with lower frequencies in the kHz range, UHF band signal above the cutoff frequency has been detected with higher-order modes that only appear in electromagnetic signal propagating inside the GIS tank. This is because the wavelength of UHF band signals is comparable to the GIS tank size. The authors had observed the characteristics of such higher-order electromagnetic waves with a focus on the resonance characteristics of the TE11 mode, using a disk-shaped UHF sensor with the sensor extending into the inside of the tank. The purpose of this paper is to investigate the propagation characteristics of higher-order mode waves in a coaxial GIS model. Considering application to actual equipment, it was investigated that the output of a sensor with an arch-shape not extending into the inside of the tank, which has less influence on the propagation mode of the inner electromagnetic wave. In the frequency domain below the cutoff frequency of the TE11 mode, the output characteristics were almost independent of the installation position of the UHF sensor, but in the higher frequency domain the output power displayed discontinuous increases at some frequencies. It was also studied that the circumferential dependence of sensor output. For higher-order modes resonant characteristics appeared that depended on the tank length, and it was recognized that the electric field distribution inside the tank influenced the output of the UHF sensor at resonant frequencies. Further, it was found that installing a spacer inside the tank shifted resonant frequencies and the influence of the spacer consistent with the relationship between the spacer position and the electric field distribution inside the tank.

Effects of Cross-Sectional Partitioning on Active Noise Control in Round Ducts

Active noise control (ANC) is particularly useful in hard-walled ducts where plane waves propagate. Higher order mode waves are much more difficult to control. Basic acoustic principles dictate that the cut-on frequency at which higher order modes will first begin to eclipse simple plane waves in a duct will be determined by the cross-sectional diameter of the duct. The lowest frequency for higher order modes will increase as duct diameter decreases. Therefore, the range of frequencies where plane waves dominate will be greater, and effective control using ANC will be better as duct diameter decreases. The result is that somewhat higher frequencies can be controlled with ANC for smaller diameters. If smaller diameters have broader frequency ranges that can be controlled with ANC, perhaps one could extend the frequency range for a large cross section by partitioning it into smaller cross sections using axial vane splitters. This hypothesis was tested by two methods of cross-sectional partitioning. Partitioning was achieved in one design by inserting a smaller duct inside a large duct. In a second design, a cross-shaped splitter was inserted inside the large duct. Summed ANC insertion loss (IL) at low frequencies (≤250 Hz) was at least 16 dB and at least 14 dB at middle frequencies (≥315 Hz). ANC IL results were 1.7 to 2 dB better for the large duct partitioned by a smaller inner duct than the large duct alone (p = 0.0146 for low frequency and p = 0.0333 for middle frequency). ANC insertion loss was 5.6 dB better for the large duct partitioned by a cross-shaped splitter at high frequencies than the large duct alone (p = 0.0003). However, the cross-shaped partition system was 5.8 dB less effective at low frequencies than the large duct ANC IL alone (p < 0.0001).

Effects of Cross-Sectional Dimensions on Active Noise Control in Rectangular and Round Ducts

Active noise control (ANC) works best to reduce low frequency noise. Because many industrial noise sources are broadband, ANC may be used more if it can be successfully applied to higher frequency ranges. This study explored one method to increase ANC effectiveness at higher frequencies. ANC is particularly useful in hard-walled ducts where plane waves propagate. Higher order mode waves are much more difficult to control. Basic acoustic principles dictate that the cut-on frequency at which higher order modes will first begin to eclipse simple plane waves in a duct will be determined by the cross-sectional geometry of the duct. The lowest frequency for higher order modes increases as duct diameter decreases; therefore the range of frequencies where plane waves dominate will be greater and effective control using ANC will be better as duct diameter decreases. The result is that somewhat higher frequencies can be controlled with ANC for smaller diameters. Below the first higher order mode cut-on frequency for the largest size studied, there should be little difference in ANC effectiveness between the duct sizes. To test those suppositions, a commercially available ANC system was used to reduce random noise in rectangular and round ducts having different diameters. Results showed that insertion loss (IL) ranged from 5 dB to 29 dB in frequencies ranging from 40–1000 Hz and varied inversely with cross-sectional size as expected. There was no difference in IL below 280 Hz (p = 0.7751) between the different diameter ducts. There was a significant difference between duct diameters above 280 Hz (p < 0.0001). The same tests were conducted on a rectangular duct with one cross-sectional dimension fixed and one varied at seven different sizes. Results showed similar IL from 5 dB to 29 dB that varied inversely with size.

Radiation from a flanged rectangular waveguide

The radiation from a rectangular waveguide with a perfectly conducting infinite flange is rigorously studied by using the method of the Kobayashi potential (KP). The fields in the waveguide and half-space are expanded in terms of the waveguide modes and the Weber-Schafheitlin discontinuous integrals, respectively. Continuity of the tangential aperture fields yields matrix equations for the expansion coefficients and the matrix elements consist of double infinite integrals and double infinite series of Bessel functions, which are calculated efficiently by applying the asymptotic approximation of the Bessel function. Numerical results are presented for various physical quantities, such as the aperture admittance, reflection coefficient of the incident wave, and magnitudes of higher-order mode waves, as well as the far-radiation pattern and aperture fields. To verify the validity of our method, the results are compared with other methods and excellent agreement is obtained.

Effects of Expansion-Chamber Muffler on High-Frequency Sounds in Circular Duct.

Sound attenuation in a circular duct through an expansion-chamber muffler was studied theoretically and experimentally for high-frequency sounds. In the calculation, the higher-order mode waves, the order of which is sufficiently high, are taken into account even if they are nonpropagating modes. In the frequency range where the plane wave theory is usually applicable, the calculated results using the method in this study were different from the calculated results using the plane wave theory. Upon comparsion with the measured values, the accuracy of the calculated results in this study was confirmed. We also examined the effects of the expansion-chamber muffler in the frequency range where the plane wave theory is not applicable and in the case that the higher-order mode wave enters the expansion-chamber muffler. In both cases, the calculated results were sufficiently consistent with the measured values. The method of calculation in this study is expected to be valid for the design of an expansion-chamber muffler for high-frequency sounds.

Attenuation of Sound Including Higher-Order Mode Waves in Circular Duct Using a Narrow Slit on the Duct Wall.

Sound attenuation in a circular duct through a slit on the duct wall was studied for the plane wave and the higher-order mode waves. The slit is the duct expanision with very short axial length. The transmission property through the slit was calculated numerically using a computer. The transmission coefficient through the slit was measured using the apparatus with the sound source that can generate the plane wave, the (1, 1) mode wave and the (2, 1) mode wave. Both the calculated and the measured sound attenuation by the slit ocurred at a specific frequency. This frequency strongly depends on the slit depth. The prediction of this frequency by the calculation is approximately accurate. Because the slit width is very narrow, the slit is not likely to disturb fluid in a duct. Hence the slit is expected to be an effective sound attenuator for the noise in a duct with flow.

Dynamos and angular momentum transport in accretion disks

The transport of angular momentum in astrophysical disks is one of the major issues in modern astrophysics. Here, recent work [Astrophys. J. 347, 435 (1989); 365, 648 (1990)] will be reviewed that suggests that internal waves, analogous to deep ocean waves, play a critical role in transporting angular momentum in neutral disks and generating a magnetic dynamo in ionized disks. Previously, it was shown that low-frequency, slightly nonaxisymmetric (‖m‖=1) waves in thin accretion disks could penetrate to small radii with a unique amplitude because of nonlinear saturation. Here, the ability of these waves to drive an α-Ω dynamo in a disk of thickness H and radius r and keplerian rotational frequency Ω(r)∝r−3/2 is examined. The asymmetry in the wave distribution that creates a nonzero helicity follows from the fact that the fundamental waves all have a positive angular momentum flux. As a result, there will be a large-scale magnetic field driven by an α-Ω dynamo. It is also likely that small-scale fields, driven by higher-order wave modes, will contribute significantly to the local value of BrBφ. It is argued that the magnetic field saturates when its pressure is comparable to the thermal pressure and a crude model of the nonlinear transfer of power to small-scale turbulence is presented. The dynamo process creates a large-scale, axisymmetric toroidal field with Br∼(H/r)3/2Bφ. Smaller-scale waves create small-scale fields with a maximum brbφ∼(H/r)6/5P. In this model, viscous and thermal instabilities in radiation pressure dominated, and electron scattering regions in accretion disks appear to be substantially suppressed.