Wave Attenuation Characteristics Research Articles

Lightweight architected lattice phononic crystals with broadband and multiband vibration mitigation characteristics

A novel architected lattice metamaterial with broadband and multiband bandgap characteristics is studied here. A slight structural modification in a regular lattice structure has succeeded to significantly magnify the vibration attenuation capability of these lightweight periodic lattices. The vibration control properties of these lattices are investigated both theoretically and experimentally. The sinusoidal-shaped ligament is found useful in generating a broadband Bragg bandgap with robust wave attenuation characteristics. The embedment of circular masses at the center of these lattices help induce multiband low frequency bandgaps. The properties of sinusoidal-shaped ligament such as the number of sine wave undulations/ligament wavelength and the effect of central mass radius on bandgaps are investigated. Introducing material damping flattens the transmission peaks and it results in a broadband bandgap distributed throughout the frequency spectrum. The experimental results are in good agreement with numerical solutions. The proposed lightweight lattice metamaterial can be effectively applied at any length scale for controlling acoustic/elastic waves propagation.

Damping effects on wave-propagation characteristics of microtubule-based bio-nano-metamaterials

Due to the essential roles of entangled microtubule networks in complicated cellular activities such as mechanotransduction, improving the insight into their mechanical properties and dynamic load-transfer mechanisms can be inspiring to design new bio-nano-metamaterials. Damping effects arising from the polymeric nature of the microtubules as well as the surrounding cytosol in vivo and stabilizing agents in vitro can play significant roles in the dynamic behavior of the individual microtubules and their networks. Hence, this paper presents a comprehensive analysis of damping effects on elastic wave-propagation characteristics of microtubule-based metamaterials. For this purpose, microtubules are taken as the constituting elements of architected periodic structures of various topologies, and the interactions between the structures and their surrounding media are modeled by drag forces and viscous damping. The model is then used to investigate in-plane and out-of-plane motions of the microtubule-based networks. The paper starts with an explanation of the finite element method applied to derive the governing equations of undamped elastic wave propagation from obtaining the dispersion curves of the periodic structures. Also, considering the damping matrix proportional to the stiffness matrix, the equations of damped wave propagation in microtubule-based periodic structures are obtained and solved using the state-space method. The results prove that considering both of the in-plane and out-of-plane motions have significant effects on the formation of the dispersion curves and wave attenuation properties of microtubule networks. Moreover, the damping effects of the surrounding medium can lead to forming different dispersion curves and, consequently, showing different wave attenuation characteristics due to various damping-induced phenomena such as branch overtaking and branch cut-off/cut-on. The results of the current study are counted as the initial steps towards more realistic modeling of bio-nano-filters. They may soon be used as a basis to design bio-nano-metamaterials with unique wave-filtering properties and higher biocompatibility.

Influence of Lateral Constraints on Wave Propagation in Finite Granular Crystals

Abstract In the presented work, wave dynamics of 2D finite granular crystals of polyurethane cylinders under low-velocity impact loading was investigated to gain better understanding of the influence of lateral constraints. The deformation of the individual grains in the granular crystals during the impact loading was recorded by a high-speed camera and digital image correlation (DIC) was used to calculate high fidelity kinematic and strain fields in each grain. These grain-scale kinematic and strain fields were utilized for the computation of the intergranular forces at each contact using a granular element method (GEM) based mathematical framework. Since the polyurethane were viscoelastic in nature, the viscoelasticity constitutive law was implemented in the GEM framework and it was shown that linear elasticity using the strain rate-dependent coefficient of elasticity is sufficient to use instead of a viscoelastic framework. These particle-scale kinematic and strain field measurements in conjunction with the interparticle forces also provided some interesting insight into the directional dependence of the wave scattering and attenuation in finite granular crystals. The directional nature of the wave propagation resulted in strong wave reflection from the walls. It was also noteworthy that the two reflected waves from the two opposite sidewalls result in destructive interference. These lateral constraints at different depths leads to significant differences in wave attenuation characteristics and the finite granular crystals can be divided into two regions: upper region, with exponential wave decay rate, and lower region, with higher decay rate.

Measurement of normal retinal vascular pulse wave attenuation using modified photoplethysmography.

Pulse wave attenuation characteristics reflect compliance and resistance properties of the vessel wall as well as initial pulse generation factors. Recently, it has become possible to measure and map the retinal vessel wall pulse wave amplitudes. Predictable pulse wave amplitude distribution may allow inferences to be made concerning vascular compliance and resistance. Twenty-eight eyes from sixteen subjects (8 male and 8 female) were examined using modified retinal photoplethysmography with simultaneous ophthalmodynamometry. This allowed the assessment of vessel wall pulsation amplitudes under a dynamic range of intraocular pressures. Pulse amplitudes were calculated using harmonic regression analysis. The pulse wave attenuation was measured under different ranges of ophthalmodynamometric force (ODF) as a function of distance along the vessel (VDist), which in turn was calculated in disc diameters (DD) from the center of the optic disc. A linear mixed-effects model with randomized slopes and intercepts was used to estimate the correlations between the logarithmically transformed harmonic regression wave amplitude (HRWa) and the Fourier trigonometric coefficients with the predictors (VDist and ODF). The retinal venous harmonic regression wave attenuation (coefficient value±standard error) -0.40±0.065/DD, (p-value < 0.00001, 95% confidence interval (CI) -0.53 to -0.27), which was approximately twice that of the arterial -0.17±0.048/DD, (p-value < 0.0004, 95% CI = -0.27 to -0.08). There was a positive correlation between attenuation of the harmonic regression wave and ophthalmodynamometric force in both vascular systems. The attenuation of all but the sine coefficient of the second Fourier harmonic (bn2) achieved statistical significance in the correlation with VDist. The cosine coefficient of the first Fourier harmonic an1 was the only coefficient to achieve statistical significance in the correlation with the predictors VDist and ODF in both vascular systems. The an1 coefficient value in the correlation with VDist was -3.79±0.78 and -1.269±0.37 (p < 0.0006), while this coefficient value in the correlation with ODF was 0.026±0.0099 and 0.009±0.04 (p < 0.01) in both the retinal veins and arteries respectively. The predictable attenuation characteristics in normal subjects suggest that this technique may allow the non-invasive quantification of retinal vascular compliance and other hemodynamic parameters.

Experimental investigation of multiple oscillating water column wave energy converters integrated in a floating breakwater: Wave attenuation and motion characteristics

This article is Part B of a study into the proof-of-concept of a floating breakwater integrated with multiple Oscillating Water Column (OWC) Wave Energy Converters (WEC). The structure is designed for nearshore and offshore applications and the investigation was performed through model scale hydrodynamic experimentation. Part A introduced the concept and the experiments performed, followed by an investigation into the energy extraction performance of the installed OWC devices [1]. This paper covers the impact of the OWC WECs on the floating breakwater’s wave attenuation and motion characteristics. As this investigation took a proof-of-concept approach, a soft mooring system was configured to the device in order to establish the general behaviour of the structure. Results indicate that the pitch motion was the most detrimental motion in terms of OWC device performance, but this is expected to be mitigated with incorporation of realistic mooring arrangements. Additionally, findings infer that in majority of cases, OWC device integration has beneficial impacts on both the wave attenuation and motions of the breakwater structure, lending further credence to the economic and performance viability of the concept.

Role of mangroves in wind-wave climate modeling – A review

Globally, there has been dedicated research on mangrove ecosystems, however, the modeling of wave-mangrove interaction is seldom considered in the operational wave prediction for vegetated coastlines. This review work apprises on the significant impact of mangroves on surface gravity wave characteristics. Prediction and quantification of wave attenuation characteristics by mangroves is an essential pre-requisite for coastal zone management activities along a mangrove dominated shoreline. Nevertheless, the dynamic impact of waves on mangroves is missing in the current regional wave forecasting systems. In this review article, the scientific advancements in wave-mangrove interaction studies are elucidated and focus on its significance in an operational wave modeling scheme for the Indian coast. The relevant studies on wave dissipation by mangroves and other vegetation; its nonlinear interaction in the presence of currents and extreme waves, and the need for improving its parameterization are considered distinctly. The study also highlights the importance to predict the futuristic scenarios of wave attenuation characteristics in mangrove dominated regions which are highly sensitive to effects from climate change. The authors believe that the research on dynamics of wave-mangrove interaction in India has an extensive scope, and possible future endeavors towards a realistic nearshore wave modeling along mangrove dominant coasts are presented in the concluding remarks.

Elastic Wave Attenuation Characteristics and Relevance for Rock Microstructures

We investigated elastic wave attenuation characteristics using a PCI-2 acoustic emission system. A lead-break test was employed to carry out attenuation experiments in granite, marble, red sandstone, and limestone. Because the centroid frequency variation of the red sandstone differs significantly from the other rocks, a pendulum steel ball impact test was also performed to study the attenuation characteristics of elastic waves in red sandstone. The results show that the elastic wave signal amplitude decreases with increasing propagation distance for all four rock types. In granite and red sandstone, the peak frequency of the elastic wave declines abruptly after the propagation exceeds 800 and 100 mm, respectively, and remains almost unchanged in marble and limestone. The attenuation of centroid frequency in granite, limestone, and marble shows the same trend; however, in red sandstone, when the elastic wave propagation exceeds a certain distance, the variation of centroid frequency shows an upward tendency. The main influence of elastic wave attenuation in rock is the packing state of mineral particles: less tightly packed rocks consistently have a higher attenuation coefficient. The secondary cause of attenuation is the development of structures such as joints and stratifications. More developed interior structures lead to higher attenuation coefficients. Sensor selection is also very important in rock attenuation tests. We recommend use of a wide resonant frequency sensor or sensors with different resonant frequencies along the elastic wave propagation path.

Experimental investigation of multiple Oscillating Water Column Wave Energy Converters integrated in a floating breakwater: Energy extraction performance

Currently, ocean wave energy technology is in its infancy relative to the mature renewable energy technologies such as wind and solar. Due to its early stage of development, ocean wave energy has high associated Levelised Cost of Electricity (LCOE), a measure of lifetime costs relative to lifetime energy production. Several solutions have been derived in an attempt to reduce this high LCOE, of which breakwater integration of wave energy converters presents a viable option. Current full-scale commercial and demonstration devices indicate that OWC device integrated breakwaters are typically limited to nearshore and onshore operational regions. However, industries such as aquaculture and offshore wind are exploring the viability of placing these structures in deeper waters, where these traditional concepts would not be applicable, providing opportunity for the development of floating offshore multi-purpose structures. This article describes a proof-of-concept for a floating breakwater integrated with Oscillating Water Column (OWC) Wave Energy Converters (WEC). For an integrated device of this type there are multiple key aspects that are inter-related and each must be understood: energy extraction performance, wave attenuation and quantifying platform motions. In order to adequately report on each aspect in a logical manner the study is presented in two parts. This paper covers the energy extraction aspects, while the second part deals with wave attenuation and motion characteristics [1]. The wave energy extraction characteristics of the installed devices are explored across parameters including device configurations, breakwater width, power take-off damping, wave height and motion constraints, all of which was achieved through model scale hydrodynamic experimentation. The major findings indicate that OWC device spacing is a key parameter in the design of multi-device structures, as device-device interaction can have constructive or destructive interferences on the energy extraction. Additionally, the results of the OWC device performance, under the influence of the aforementioned parameters, provides new insights to the development of floating offshore multi-purpose structures and their feasibility.

Cloud‐based difference algorithm using big GPR data for roadbed damage detection

SummaryGround‐penetrating radar (GPR) technology is being widely used for urban roadbed damage detection. In this paper, we present the development of a cloud‐based difference detection method using big GPR data for roadbed damage detection. Unlike many processing methods relying on standalone servers, the proposed method can achieve high accuracy and processing efficiency by distributing the computation over a server cluster. The method includes a difference detection algorithm for GPR image enhancement and damage extraction, the Hadoop Distributed File System, and MapReduce distributed parallel computing framework for big GPR data parallel processing and interpretation. Moreover, to automatize roadbed damage classification, a criterion with seven grades is established based on the wave group shape, amplitude, phase, and attenuation characteristics. We validate the proposed method through a detection experiment that was conducted on the Fourth Ring Road in Beijing, China. The detection revealed 187 damage from the efficient processing of big GPR data, thus suggesting the ability of the proposed method to provide timely support for road safety in cities.

Hydrodynamic performance of a floating breakwater as an oscillating-buoy type wave energy converter

Combined floating breakwater and wave energy converter systems have the potential to provide a cost-effective solution to offshore power supply and coastal protection. This will make wave energy economically competitive and commercial-scale wave power operations possible. This paper investigates the hydrodynamic features of wave energy converters that meet the dual objectives of wave energy extraction and attenuation for such a combined system. A two-dimensional numerical model was established using Star-CCM+ commercial software based on viscous Computational Fluid Dynamics theory to investigate the hydrodynamic performance of an oscillating buoy Wave Energy Converter (WEC) type floating breakwater under regular waves. The model proposed in this paper was verified with published experimental results. The hydrodynamics of symmetric and asymmetric floaters were investigated to demonstrate their wave attenuation and energy extraction performance, including square bottomed, triangular bottomed (with and without a baffle plate), and the Berkley Wedge. The asymmetric floaters were found to have higher power conversion efficiency and better wave attenuation performance, especially the Berkeley Wedge bottom device and the triangular-baffle bottom device. The triangular-baffle bottom device with a simpler geometry achieved similar wave attenuation and energy extraction performance characteristics to that of the Berkeley Wedge device. The maximum energy conversion efficiency of the triangular-baffle bottom floater reached up to 93%, an impressive WEC device among many designs for wave energy conversion. There may be a great potential for this newly proposed triangular-baffle bottom WEC type of floater to be an ideal coastal structure for both coastal protection and wave energy extraction.

Characteristics of wave attenuation due to roughness of stepped obstacles

ABSTRACT In this study, we investigated the energy dissipation characteristics of stepped obstacles by using both the regular and irregular waves in a physical wave flume. The stepped obstacle used in this study is different from those of traditional stepped dikes with fixed horizontal and vertical stage surfaces; here, the angle of the stepped surface varies with the slope of the embankment surface, with various interaction angles between the incident waves and the rough stepped surfaces. The stepped embankments were composed of six types of stepped arrangements and were used to analyse the wave run-up heights and reflection coefficients; in addition, the variations in energy dissipation effects were also studied. The results identify two of the six roughness types that have better mitigation effects on the investigated the energy dissipation characteristics of stepped obstacles. The reflection coefficient is larger for a submerged dike with a rough surface than for one with a smooth surface.

Structural optimization and analysis of surface acoustic wave biosensor based on numerical method

The biosensor based on surface acoustic wave is of great significance for the application of biological clinical detection, but the sensitivity and specificity of surface acoustic wave biosensor still need to be improved. In this article, the structure of surface acoustic wave biosensor and interdigital transducer is designed by studying the theoretical model of surface acoustic wave biosensor. Then the amplitude–frequency response of the device is studied. Later, the simulation model of surface acoustic wave biosensor structure is established, and the performance of surface acoustic wave device is numerically calculated. Meanwhile, the relationship between the applied excitation signal and the resonant frequency is considered, and the performance of the surface wave propagation and attenuation characteristics are analyzed. In addition, the influence of the material of the piezoelectric substrate and the structure of the interdigitated electrode on the surface acoustic wave propagation are studied. The response potential curve and the total displacement of the particle vibration are analyzed, and the structure of the surface acoustic wave device is optimized.

Investigation of coda and body wave attenuation functions in Central Asia

In this study, we evaluate the body and coda wave attenuation characteristics within Kyrgyzstan and Tajikistan as part of Central Asia. The selected database consists of 354 broadband seismograms from 179 local earthquakes recorded by 24 different stations within the period of 2015 through 2018. First, coda Q has been inferred for different coda window lengths of 20, 30, 40, and 50 s using the single-backscattering interpretation. The coda Q values increase by increasing the coda window length. We show that coda attenuation properties in Central Asia are better modeled by multiple-scattering and surface wave regimes for long-distance records without invoking any depth dependence of the attenuation properties in the crust. Furthermore, standard errors and convergence of different components’ QC indicate that we can fit envelope records of coda waves much better using a coda window length of 50 s. Therefore, we evaluate average coda quality factor functions as QC = 261 f0.601 and QC = 219 f0.633 assuming multiple-scattering and surface wave regimes for a coda window length of 50 s in the frequency range of 1 to 20 Hz for distances up to 200 km. We also show that the source to site distance of records has a significant impact on coda Q estimates. For a shorter distance range up to 100 km, attenuation attributes of Central Asia are better captured by a single-scattering model. We reevaluate the average coda quality factor function as QC = 222 f0.692 assuming a single-backscattering model for a coda window length of 50 s in the frequency range of 1 to 20 Hz for distances up to 100 km. Moreover, we determine QP = 158 f0.706 and QS = 152 f0.856 with a geometrical spreading function of R−1 using the multiple-station coda normalization method.

Modeling wave propagation in cracked porous media with penny-shaped inclusions

Understanding acoustic wave dispersion and attenuation induced by local (squirt) fluid flow between pores and cracks (compliant pores) is fundamental for better characterization of the porous rocks. To describe this phenomenon, some squirt-flow models have been developed based on the conservation of the fluid mass in the fluid mechanics. By assuming that the cracks are represented by isotropically distributed (i.e., randomly oriented) penny-shaped inclusions, this study applies the periodically oscillating squirt flow through inclusions based on the Biot-Rayleigh theory, so that the local squirt flow and global wave oscillation of rock are analyzed in the same theoretical framework of Hamilton’s principle. The governing wave-propagation equations are derived by incorporating all of the crack characteristics (such as the crack radius, crack density, and aspect ratio). In comparison with the previous squirt models, our model predicts the similar characteristics of wave velocity dispersion and attenuation, and our results are in agreement with Gassmann equations at the low-frequency limit. In addition, we find that the fluid viscosity and crack radius only affect the relaxation frequency of the squirt-flow attenuation peak, whereas the crack density and aspect ratio also affect the magnitudes of dispersion and attenuation. The application of this study to experimental data demonstrates that when the differential pressure (the difference between confining pressure and pore pressure) increases, the closure of cracks can lead to a decrease of attenuation. The results confirm that our model can be used to analyze and interpret the observed wave dispersion and attenuation of real rocks.

Nearshore modelling of wind-waves and its attenuation characteristics over a mud dominated shelf in the Head Bay of Bengal

The global interest of this study is to comprehend the impact of muddy bottom on the near-shore wave characteristics in the Head Bay of Bengal, and consequently improve the nearshore wave forecasting system for this region. Prediction and quantification of wave attenuation characteristics due to localized processes is an essential pre-requisite for coastal zone management activities. Due to lack of observations as well the difficulty involved in the procurement of direct observations over this region, detailed numerical experiments are conducted to investigate the wave attenuation characteristics and thereby assess the reliability of a spectral wave model SWAN for the area of interest. The study utilized a coupled wave-hydrodynamic model ADCIRC+SWAN to establish and quantify the wave damping effects attributed by bottom mud during an extreme weather event, a case study for SIDR cyclone. Waves propagating over a shallow water environment having muddy bottom decays exponentially with the depth/distance and dissipates completely near to the shoreline. Maximum attenuation rates of 84%, 70% and 33% was estimated during the three different weather events categorized as fair, rough, and extreme respectively. The study signifies that wave dissipation rates are found to be relatively less during extreme weather conditions over a muddy bottom environment.

Frequency-dependent body-Q and coda-Q in Karlıova Triple Junction and its vicinity, Eastern Turkey

A dataset obtained from six broadband stations of 111 small- to moderate-sized local events that occurred between 2010 and 2018 was analyzed to reveal the frequency-dependent seismic body (body-Q) and coda (coda-Q) wave attenuation characteristics of three tectonic branches of the Karlıova Triple Junction: the Varto Fault Zone (VFZ), North Anatolian Fault Zone (NAFZ), and East Anatolian Fault Zone. The magnitude range was between 2.8 and 6.1 with shallow (

Attenuation of short-period body waves in Northwestern Himalayan Region, India

The attenuation of seismic wave is one of the basic physical parameters which is closely related to the seismicity and regional tectonics activity of a particular area. This is also important for seismic hazard measurement. Seismic wave attenuation for local earthquakes is determined from the analysis of direct body waves and coda waves. The dimensionless parameter, Q, is studied in the present work, which is defined as a measure of the rate of decay of the coda waves or body waves within a specific frequency band. Digital seismogram data of 75 earthquakes that occurred in Garhwal Himalaya region during 2004–2006 and recorded at 20 different stations have been analyzed to study the seismic body and coda wave attenuation. Seismic body wave attenuation characteristics are examined by estimating the frequency dependent relationship of quality factors for P-waves, Qα and for S-waves, Qβ in the frequency range 1.5–28 Hz, using 95 seismic observations with hypo central distance less than 100 km. The extended coda normalization method was applied. The average value of Qα is found to be varied from 45.10 at 1.5 Hz to 1400.0 at 28 Hz, while it varies from 109.02 at 1.5 Hz to 3987.0 at 28 Hz for Qs. The estimated frequency dependent relation for quality factors are Qα=(29.077±8.5)f(1.16±0.01) and Qβ=(67.84±13.5)f(1.18±0.02) for P and S-waves, respectively. The rate of increase of Q(f) for P and S waves in this region is comparable with the other regions of the Himalayas. The ratio QβQα is greater than unity in the entire analyzed frequency range. It indicates that scattering is an important factor contributing to the attenuation of body wave in the region. The low Qα,β values or high, attenuation at lower frequencies and high Qα,β values or low attenuation at higher frequency may indicate that the heterogeneity decreases with increasing depth in the study region.

Damage Detection in a Plate Structure based on FBG sensing Technique under a Single-Mode Lamb Wave

Lamb wave is widely acknowledged as one of the most encouraging tools for damage identification in plate structures, and relevant research has been conducted intensively. However Lamb wave modes have different wave structure, frequency dispersion and attenuation characteristics, which are sensitivity to different types of damages and it is difficult to solve such engineering problems by conventional techniques. Although the single pattern detection method has been researched by piezoelectric wafers, there is little research about FBG sensing detection under single-mode ultrasonic Lamb wave technique currently. So this paper puts forward a single-mode Lamb wave technique for crack detection based on Fiber Bragg Grating sensor, which is used to receive the waves in the plate. First of all, measuring principle of single-mode ultrasonic Lamb technique and demodulation principle of the FBG sensor are introduced. And simulation analysis in the acoustic field is devoted, whose results lay the foundation for the damage detection in the plate. Then, the experimental system is built by a single-mode Lamb wave excitation, and the feasibility of fiber Bragg grating sensors in single-mode excitation method is verified by experiments.

Sagittal Plane Waves in Infinitely Periodic Multilayered Composites Composed of Alternating Viscoelastic and Elastic Solids

In order to design phononic crystals whose band-gaps are located in low-frequency ranges, researchers commonly adopt low stiffness polymeric materials as key constituents and exploit the high impedance mismatch between metals and polymers. However, there has been very little research on wave propagation at arbitrary angles in the sagittal plane of viscoelastic-elastic multilayered composites because there exist the intricate wave attenuation characteristics at the layer interfaces. The objective of our investigation is to obtain analytical dispersion relation for oblique wave motion in the sagittal plane of infinitely periodic multilayered composite composed of alternating viscoelastic and elastic solids, where the attenuation of harmonic plane waves is found to occur only in the direction perpendicular to the layers. By using this wave propagation characteristic, we directly apply the semi-analytical approach employed in elastic multilayered composites to calculate the dispersion relation of sagittal plane waves in alternating viscoelastic-elastic multilayered composites. Specifically, we consider a bilayered composite composed of alternating aluminum and polyurethane elastomer, whose complex-valued viscoelastic moduli are experimentally determined by performing dynamic mechanical analysis (DMA). The analysis shows that the alternating viscoelastic-elastic layered composite does not possess a phononic band-gap regardless of incident angles. In addition, wave motions at oblique angles are found to travel with a wide range of frequency contents compared to wave motions perpendicular to the layers. The presented analysis demonstrates that wave dispersion relation in viscoelastic-elastic layered composites is distinctly different from the corresponding elastic counterpart, and highlights the importance of the viscoelastic modeling of polymeric materials in wave dispersion analysis.

Effect of small anisotropy and absorption on metamaterial applications: “non-ideal” features of propagation and tunneling of electromagnetic waves

For cases of isotropic, uniaxial, and biaxial electromagnetic metamaterials (MM), a comparative analysis of the effect of small deviations of local material parameters from “ideal” values on the realization of MM applications (“zero” media, the Veselago-Pendry superlens) has been carried out. On the basis of the detailed investigation of the solutions of dispersion equations, it is established that even a very small dielectric and (or) magnetic anisotropy of a general form is the universal “non-ideal” factor determining (to a much greater extent than small losses) the operability of those MM applications where the wave misphasing in the effective medium is undesirable. The characteristics of wave attenuation in the absorbing isotropic and weakly anisotropic MM are mainly comparable for the applications. Limitations of the traditional approaches using the second-order curves (or surfaces) for analytic modeling of the absorbing MM dispersion equations are shown.