Multiple Wave Types Research Articles

Experimental and numerical validation of Advanced Statistical Energy Analysis to incorporate tunneling mechanisms for vibration transmission across a grillage of beams

Advanced Statistical Energy Analysis (ASEA) is used to predict vibrational response on a three-bay linear grillage of beams that supports multiple wave types when there is significant indirect coupling through tunneling mechanisms. For bending wave excitation where the component beams have identical material properties, there was agreement between measurements, ASEA and FEM (Finite Element Methods). The importance of indirect coupling was confirmed for bending-longitudinal and bending-torsional models due to ASEA predicting a higher response than SEA on beams that were distant from the source, and closer agreement between FEM and ASEA (rather than SEA) with only bending modes on all the beams or where beams supported longitudinal or torsional modes as well as bending modes. To investigate an imperfectly periodic, finite grillage that could exist due to engineering tolerances, numerical experiments with FEM were used to introduce uncertainty into the Young’s modulus for each beam. For beams modelled with Euler-Bernoulli or Timoshenko theory, the effect of this uncertainty was to reduce differences between FEM and ASEA to less than ≈3 dB. The results confirm the ability of ASEA to predict vibration transmission with significant indirect coupling across frameworks of beams that support local modes with multiple wave types.

A new spectral parameter to predict dominant wave breaking based on the JONSWAP spectrum

Finding a robust and universal diagnostic parameter that determines the onset of deep-water breaking and its strength has been challenging in wave breaking research. In this paper, a new diagnostic parameter (wave-breaking spectral parameter, WSP) is defined based on the significant steepness of the spectral peak ϵp that was initially proposed by Banner et al. (2000) and Babanin et al. (2001). In addition, the WSP formula contains the spectral peakedness parameter Qp and spectral width ν for taking into account the effect of spectral shape on the value of breaking threshold. To derive the WSP formula and verify the prediction ability of this diagnostic parameter, multiple wave types including nonbreaking waves, critical waves, and single and multiple breaking wave trains were generated in our experiments. The wave trains were generated using a linear focusing theory with components following the JONSWAP distribution. Results show that the threshold value of the new WSP, which distinguishes single and multiple breaking events from non-breaking waves, is found to be 0.042. Furthermore, WSP is used in isolated deep-water spilling breaking packets, and its prediction accuracy is compared with that of the kinematic criterion parameter Bx. The results show that WSP has advantages in predicting the onset of wave breaking, especially for non-sharp wave conditions. Finally, the spatial variation of the total loss rate of the wave energy flux ΔFbrE¯¯ΔFbE¯¯ in deep-water unsteady breaking waves was investigated. It was found that the new WSP has a strong linear correlation with the total loss rate of the wave energy flux. Considering that WSP can be mathematically expressed directly using the spectrum, WSP will be parameterized into the dissipation term of the spectral wind-wave model in our future work. It is expected that the calculation accuracy of the dissipation term will be improved, and the wave model's prediction accuracy of wave parameters will be enhanced because WSP provides a reliable wave-breaking threshold value and has a strong linear relationship with the dissipation rate.

Comparison study of three-component polarization analysis methods for seismic advanced detection in the roadway

Multicomponent seismic exploration makes up for the shortcomings of multiple solutions in conventional single-component seismic exploration for lithological identification and geological structure interpretation. Polarization analysis methods play a key role in the processing of multicomponent seismic data. However, when multiple types of waves are very close to each other, it is very difficult to characterize the polarization distribution of different waveforms using conventional time domain or time-frequency domain polarization analysis. In this paper, a time-frequency domain instantaneous polarization analysis method based on a time-frequency method of generalized S-transform is introduced. The instantaneous polarization parameters (polarization axis, polarizability, and planarization vector) can be calculated based on a time-frequency spectrum and instantaneous phase of multicomponent signal. The numerical simulation of three-component seismic advanced detection in the three-dimensional space shows the following results: the diffracted P-wave from a fault breakpoint has the characteristics of narrow wave train and fast speed, which make it easy to be identified. Besides, it is an effective wave for polarization analysis due to its distinct polarization characteristics. Combining the advantages of the time-frequency domain analysis method, this method is more accurate in waveform identification and more reliable in fault identification. Besides, this method provides better results than the conventional time-domain polarization analysis method.

Modeling and coupling of acoustical layered systems that consist of elements having different transfer matrix dimensions

The transfer matrix method that is often used to model layered or lumped acoustical systems was inspired by a classical methodology commonly used in electrical engineering. To take advantage of that procedure’s accuracy and modeling efficiency, the transfer matrix method has been further adapted here to allow coupling of layered acoustic media having different matrix dimensions. For example, in the case of fluid, or effective fluid, media, the acoustic transfer matrix elements are conventionally modeled using two-by-two matrices. In contrast, a four-by-four matrix is required to model an elastic solid layer, and a six-by-six matrix is required to model a poroelastic layer, since multiple wave types propagate within the latter elements. Here, we introduce a modified transfer matrix calculation process that draws on various matrix operations to couple four-by-four and/or six-by-six matrices with the two-by-two matrices of other acoustical elements. The matrix operations include singular value decomposition and QR decomposition. These tools are used to reduce the order of elastic solid or poroelastic layer matrices from four-by-four or six-by-six to two-by-two, respectively, so that a layered system can be modeled simply by multiplying together a sequence of two-by-two matrices representing all the layered acoustic elements regardless of their complexity, thus finally creating an overall two-by-two matrix. In this article, the proposed method is applied to several different layered or multipanel structures, and the predicted acoustical properties are compared to results obtained by using previously-existing methods in order to validate the modified transfer matrix method.

Tuning coupled wave dispersion in a granular chain on a V-shaped rail

This paper introduces a model for the propagation of multiple types of waves in a compressed granular chain placed on an elastic V-shaped rail. The system possesses translational, rotational, and torsional degrees of freedom, and the different waves interact due to the presence of Hertzian contacts between adjacent spheres and between the spheres and the rail. Additional tangential force and torque between the spheres and the rail governed by the Hertz–Deresiewicz law are accounted for. This allows an exclusive tuning of the shear and torsional stiffness coefficients and leads to a complex coupled wave dynamics. Tunable dispersion relations including zero group velocity mode, accidental degeneracy and mode hybridisation are investigated in the linear regime. It is shown that the tangential force-dependent shear stiffness between the spheres and the rail strongly influences the dispersion relations, while the influence of the torque-dependent torsional stiffness is much weaker. The inclination angle of the rail is examined as another tunable degree of freedom, which modifies the wave dispersion not only by changing the shear coupling but also by influencing the coupling among different types of waves. The tunability of the wave dynamics in the granular chain evidenced in this work offers a flexible way of designing acoustic systems for selective vibration filtering and wave manipulation.

A SPH numerical wave flume with non-reflective open boundary conditions

In this paper, a numerical wave flume with full functions of wave generation and absorption is proposed under the framework of Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH). In contrast to the conventional SPH numerical wave flumes using wave paddles and sponge layers, the wave generation and absorption in this paper are implemented using non-reflective open boundary conditions, which are capable of generating multiple types of waves, including solitary waves, linear and second-order regular waves. Passive and active wave absorption are available for transmitting incident waves and preventing secondary reflections. Steady or unsteady flows can also be defined during wave generation and absorption to set up numerical wave-flow flumes. The results on a series of validation cases indicate that this SPH numerical wave flume not only performs satisfactorily in conventional wave generation and absorption and nonlinear wave-structure interaction simulations but also has the following three advantages: 1) It avoids using the sponge layers to shorten the flumes, which improves the efficiency; 2) it keeps the mean water level steady and prevents water level shifting; and 3) it implements steady/unsteady flow and wave-flow interactions to model a wider range of hydrodynamic problems.

Demonstrating structural waves in rods/beams

Structures exhibit some interesting properties in that multiple types of waves can propagate, and the behavior of those waves is different. This demonstration focuses specifically on the difference between longitudinal waves in rods and bending waves in beams. As used here, rods and beams can be the same structure, in practice, but the terms are used to help distinguish between the particular type of wave propagation. For these wave types, the theory of wave propagation for rods and beams is quite accurate in predicting the experimental response, and can be readily demonstrated if near-ideal boundary conditions are used. This demonstration uses a rod/beam that has free-free boundary conditions. For longitudinal waves, the resonances of the rod should be perfectly harmonic. For bending waves, the resonances of the beam are unevenly spaced due to the dispersive nature of the bending waves. It will be shown how the results from a simple experimental apparatus match theory very well, and how the two types of ...

A 3D parallel Particle-In-Cell solver for wave interaction with vertical cylinders

In this paper, the Particle-In-Cell (PIC) based PICIN solver is extended to three spatial dimensions and parallelised using the Message Passing Interface (MPI) approach. The PICIN solver employs both Eulerian grid and Lagrangian particles to solve the incompressible Navier-Stokes equations for free-surface flows. The particles are employed to carry all the fluid properties, solve the non-linear advection term and track the free-surface, while the grid is used solely for computational efficiency in solving the non-advection terms. Validation of the new 3D model concentrates on test cases involving multiple wave types (including regular waves, focused waves and solitary waves) interacting with vertical cylinders in several spatial configurations. The results are compared with laboratory data and numerical results from state-of-the-art Volume of Fluid (VOF) based Eulerian solvers such as those from the OpenFOAM® suite. It is shown that the 3D parallel PICIN model is able to well simulate highly non-linear water waves, and the interaction of such waves with vertical cylinders, with a CPU efficiency similar to Eulerian solvers. Moreover, the innovative use of particles in PICIN, akin to meshless Lagrangian solvers, gives the model a particular flexibility in handling complex, full 3D, water-wave scenarios involving large free-surface deformations.

Finite difference time domain modelling of a point-excited elastic plate radiating into an acoustic cavity.

Finite difference time domain (FDTD) models are developed to solve the vibroacoustic problem of a thin elastic plate undergoing point force excitation and radiating into an acoustic cavity. Vibroacoustic modelling using FDTD can be computationally expensive because structure-borne sound wavespeeds are relatively high and a fine spatial resolution is often required. In this paper a scaling approach is proposed and validated to overcome this problem through modifications to the geometry and physical properties. This allows much larger time steps to be used in the model which significantly reduces the computation time. Additional reductions in computation time are achieved by introducing an alternative approach to model the boundaries between the air and the solid media. Experimental validation is carried out using a thin metal plate inside a small reverberant room. The agreement between FDTD and measurements confirms the validity of both approaches as well as the FDTD implementation of a thin plate as a three-dimensional solid that can support multiple wave types. Below the lowest room mode, there are large spatial variations in the sound field within the cavity due to the radiating plate; this indicates the importance of having a validated FDTD model for low-frequency vibroacoustic problems.

Bending, longitudinal and torsional wave transmission on Euler-Bernoulli and Timoshenko beams with high propagation losses.

Advanced Statistical Energy Analysis (ASEA) is used to predict vibration transmission across coupled beams which support multiple wave types up to high frequencies where Timoshenko theory is valid. Bending-longitudinal and bending-torsional models are considered for an L-junction and rectangular beam frame. Comparisons are made with measurements, Finite Element Methods (FEM) and Statistical Energy Analysis (SEA). When beams support at least two local modes for each wave type in a frequency band and the modal overlap factor is at least 0.1, measurements and FEM have relatively smooth curves. Agreement between measurements, FEM, and ASEA demonstrates that ASEA is able to predict high propagation losses which are not accounted for with SEA. These propagation losses tend to become more important at high frequencies with relatively high internal loss factors and can occur when there is more than one wave type. At such high frequencies, Timoshenko theory, rather than Euler-Bernoulli theory, is often required. Timoshenko theory is incorporated in ASEA and SEA using wave theory transmission coefficients derived assuming Euler-Bernoulli theory, but using Timoshenko group velocity when calculating coupling loss factors. The changeover between theories is appropriate above the frequency where there is a 26% difference between Euler-Bernoulli and Timoshenko group velocities.

Statistical study of low‐frequency magnetic field fluctuations near Venus under the different interplanetary magnetic field orientations

The magnetic field fluctuations near Venus are investigated in the frequency range 0.03–0.3 Hz on the basis of the measurements observed by Venus Express from April 2006 to December 2008. The data are sorted by the angle between interplanetary magnetic field (IMF) and solar wind flow. The spatial distributions of fluctuation properties under the different IMF orientations are presented and a comparative study is performed. In the mantle and tail regions, the magnetic field is fairly quiet and the fluctuations are almost linearly polarized. There are two possible sources for the fluctuations in the magnetosheath: convection from the upstream foreshock and local generation. When the IMF is nearly perpendicular to the solar wind flow, the fluctuations in the magnetosheath are mainly generated locally by an ion cyclotron instability due to planetary ion pickup. The wave intensity is relatively low and the transverse component is dominant. The waves are left‐handed, elliptically polarized, and propagating parallel to the mean magnetic field. When the IMF is nearly aligned to the solar wind flow, foreshock waves are convected into the magnetosheath. The fluctuations in the magnetosheath become more intensive. Their polarization properties are very mixed and there is no clear tendency. It indicates that the waves convected from the foreshock may be the mixture of multiple wave types and incoherent noise.

Three‐dimensional simulation of energetic outer zone electron dynamics due to wave‐particle interaction and azimuthal advection

We present a three‐dimensional code treating the local resonant interaction with various waves and azimuthal advection around the Earth to evaluate storm‐time energetic outer zone electron phase space density (PSD) evolution at a constant L shell without radial diffusion. Assuming a model distribution of wave characteristics at L = 4.5, we show that energetic (∼MeV) electron PSD can decrease by about three orders over all pitch angles with a visible azimuthal asymmetry during the main phase and enhance by about 30 times of magnitude with a weak azimuthal asymmetry during the recovery phase. The differences between magnetic local time (MLT)‐dependent and MLT‐averaged simulations are also investigated in detail under cases of different wave characteristics. When a single type of wave is present, the differences between MLT‐averaged and MLT‐dependent simulations are fairly small. Energetic (∼MeV) electron PSD is found to be overestimated by a factor of 2 at larger pitch angles for chorus or hiss alone, and underestimated by a factor of 5–10 near the loss cone for electromagnetic ion cyclotron (EMIC) waves alone under the MLT‐averaged approximation. When multiple types of waves are taken into account, there are considerable differences between MLT‐averaged and MLT‐dependent simulations. MLT‐averaged simulations can overestimate the energetic (∼MeV) electron PSD by a factor of 5–50 during the main phase and 9–13 during the recovery phase. Additional control experiments show that larger drift speed tends to diminish the azimuthal asymmetry of MLT‐dependent simulations as well as the difference between MLT‐dependent and MLT‐averaged simulations. These numerical results suggest that azimuthal advection can play an important role in the radiation belt electron dynamics, which should be incorporated in future radiation belt models for space weather application.

Large-Scale Meteorology and Deep Convection during TRMM KWAJEX*

An overview of the large-scale behavior of the atmosphere during the Tropical Rainfall Measuring Mission (TRMM) Kwajalein Experiment (KWAJEX) is presented. Sounding and ground radar data collected during KWAJEX, and several routinely available datasets including the Geostationary Meteorological Satellite (GMS), NOAA outgoing longwave radiation (OLR), the Special Sensor Microwave Imager (SSM/I), and ECMWF operational analyses are used. One focus is on the dynamical characterization of synoptic-scale systems in the western/central tropical Pacific during KWAJEX, particularly those that produced the largest rainfall at Kwajalein. Another is the local relationships observed on daily time scales among various thermodynamic variables and areal average rain rate. These relationships provide evidence regarding the degree and kind of local thermodynamic control of convection. Although convection in the Marshall Islands and surrounding regions often appears chaotic when viewed in satellite imagery, the largest rain events at Kwajalein during the experiment were clearly associated with large-scale envelopes of convection, which propagated coherently over several days and thousands of kilometers, had clear signals in the lower-level large-scale wind field, and are classifiable in terms of known wave modes. Spectral filtering identifies mixed Rossby–gravity (MRG) and Kelvin waves prominently in the OLR data. “Tropical depression–type” disturbances are also evident. In some cases multiple wave types may be associated with a single event. Three brief case studies involving different wave types are presented. Daily-mean sounding data averaged over the five sounding sites show evidence of shallow convective adjustment, in that near-surface moist static energy variations correlate closely with lower-tropospheric temperature. Evidence of thermodynamic control of deep convection on daily time scales is weaker. Upper-tropospheric temperature is weakly correlated with near-surface moist static energy. There are correlations of relative humidity (RH) with deep convection. Significant area-averaged rainfall occurs only above a lower-tropospheric RH threshold of near 80%. Above this threshold there is a weak but significant correlation of further lower-tropospheric RH increases with enhanced rain rate. Upper-tropospheric RH increases more consistently with rain rate. Lag correlations suggest that higher lower-tropospheric RH favors subsequent convection while higher upper-tropospheric RH is a result of previous or current convection. Convective available potential energy and surface wind speed have weak negative and positive relationships to rain rate, respectively. A strong relationship between surface wind speed (a proxy for latent heat flux) and rain rate has been recently observed in the eastern Pacific. It is suggested that in the KWAJEX region, this relationship is weaker because there are strong zonal gradients of vertically integrated water vapor. The strongest surface winds tend to be easterlies, so that strong surface fluxes are accompanied by strong dry-air advection from the east of Kwajalein. These two effects are of opposite sign in the moist static energy budget, reducing the tendency for strong surface fluxes to promote rainfall.

Power flow analysis of beam members with multiple wave types

A power flow finite element method (PFFEM) is developed by Nefske and Sung ( ASME J. Vib. Stress Reliability Des. 111, 1989) for the steady state high frequency vibration analysis of beams in which there is propagation of one wave type (bending). A finite element thermal analog presented herein for power flow analysis of beam members in which both bending and longitudinal waves are present is a further development of the PFFEM. Conducting bar elements model mechanical power flow in the beam and also power transmission, reflection and conversion at structural joints. Convection elements model internal power dissipation. Properties of joint elements are in general non-linear and depend upon the power level at the joint as well as transmission and reflection coefficients. The thermal analog is verified for particular linear cases wherein properties of the joint elements are dependent only upon the transmission and reflection coefficients.

Localization and wave conversion phenomena in multi-coupled nearly periodic structural systems

For disordered mono-coupled systems, wave localization causes an exponential spatial wave amplitude decay, with the associated decay constant known as the localization factor. In multi-coupled structural systems, with multiple wave types, wave conversions complicate the analysis of localization phenomena. In this work, Lyapunov exponents of the system wave transfer matrix are used to analyze localization in multi-coupled disordered systems. Lyapunov exponents are a measure of the exponential growth rate of wave vectors. In a mono-coupled system, the largest Lyapunov exponent is equivalent to the localization factor. Lyapunov exponents are calculated numerically and, for the case of weak disorder, approximated by perturbation techniques. Three examples are presented. First, a representative mono-coupled system is considered. The largest Lyapunov exponent is calculated and compared with localization factors found by Monte Carlo as well as perturbation methods. Then bi-coupled system, a multi-span beam resting on flexible supports, is examined. Lyapunov exponents are calculated and compared with the wave amplitude decay found in a single realization of the disordered system. Finally, a truss beam, which features four types of waves is examined, and the physical significance of the Lyapunov exponents is discussed.

An experimental study of the active control of multiple-wave types in an elastic beam

In many practical situations, different types of waves may coexist within a structure. If control is limited to a single wave type, other kinds of waves may be generated unintentionally by the action of the control forces. In this paper an experimental study of the simultaneous control of multiple wave types in a semi-infinite beam has been undertaken. The ability of the piezoelectric control sources to provide adequate system control and the ability of the accelerometer error sensors to provide adequate observability of the power flow associated with each wave type was also evaluated.

Power flow finite element analysis of beam networks

A power flow analysis was previously developed for predicting the vibration response of structural and acoustic systems to high frequencies at which the traditional finite element method is no longer practical [D. J. Nefske and S. H. Sung, ASME NCA 3, 47–54 (1987)]. As compared to statistical energy analysis, which predicts an overall vibration response of each individual subsystem, the power flow analysis enables one to predict the spatial variation of the vibration response within each subsystem, as well as the power flow and vibration response throughout the entire system. The present paper considers application of the power flow method to built‐up frame structures in the form of beam networks. The power flow analysis considers excitation of multiple wave types in the individual beams and utilizes transmission efficiencies to couple the wavetypes at the beam junctions. The power flow solution is obtained by modifying the properties of a standard structural finite element model to form a power flow fini...

Multiple chemical waves induced by applied electric field

In the most common chemical wave medium, the Belousov–Zaikin–Zhabotinsky reaction, most relevant species are ionic. We show that when an electric field is imposed across nonlinear chemical waves in ionic media the system may support multiple types of waves not present when the applied fields is turned off. It is demonstrated that waves may be stopped (i.e., have zero velocity) or that as the applied field is changed beyond a critical level, waves may change discontinuously in character and even reverse their direction of propagation. The potentiality of the induction of a variety of phenomena due to the presence of applied fields seems great.

Ray Methods for Trapped and Slightly Leaky Modes in Multilayered or Multiwave Regions

Ray-optical techniques presented previously by the authors for study of mode propagation in homogeneously filled waveguides are extended to accommodate multilayered regions and regions capable of supporting multiple wave species. Emphasis is placed on a self-consistent ray treatment which illustrates alternative methods for dealing with ray coupling at boundaries and with the presence of multiple wave types, either in a single layer or in adjacent regions. Both closed and open structures are analyzed, with discussion of the latter limited to modes with small leakage due either to duct inhomogeneities or to curvature. Examples include layered dielectric waveguides with a straight or circular axis, and compressible plasma waveguides which are illustrative of media wherein two wave species (electromagnetic and electroacoustic) can propagate.