A study of damping factors in perfectly matched layers for the numerical simulation of seismic waves

When simulating seismic wave propagation in free space, it is essential to introduce absorbing boundary conditions to eliminate reflections from artificially trtmcated boundaries. In this paper, a damping factor referred to as the Gaussian dmping factor is proposed. The Gaussian damping factor is based on the idea of perfectly matched layers （PMLs）. This work presents a detailed analysis of the theoretical foundations and advantages of the Gaussian damping factor. Additionally, numerical experiments for the simulation of seismic waves are presented based on two numerical models： a homogeneous model and a multi-layer model. The results show that the proposed factor works better. The Gaussian damping factor achieves a higher Signal-to-Noise Ratio （SNR） than previously used factors when using same number of PMLs, and requires less PMLs than other methods to achieve an identical SNR.

The damping model for sea waves covered by oil films of a finite thickness

In combination with a wave action balance equation, a damping model for sea waves covered by oil films of a finite thickness is proposed. The damping model is not only related to the physical parameters of the oil film, but also related to environment parameters. Meanwhile, the parametric analyses have been also conducted to understand the sensitivity of the damping model to these parameters. And numerical simulations demonstrate that a kinematic viscosity, a surface/interfacial elasticity, a thickness, and a fractional filling factor cause more significant effects on a damping ratio than the other physical parameters of the oil film. From the simulation it is also found that the influences induced by a wind speed and a wind direction are also remarkable. On the other hand, for a thick emulsified oil film, the damping effect on the radar signal induced by the reduction of an effective dielectric constant should also be taken into account. The simulated results are compared with the damping ratio evaluated by the 15 ENVISAT ASAR images acquired during the Gulf of Mexico oil spill accident.

Energy decay for a class of nonlinear wave equations with a critical potential type of damping

The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions are obtained by using multiplier techniques to establish identity ddtE（t）＋F（t）=0 and skillfully selecting f（t）,g（t）,h（t）when the initial data have a compact support.Using the similar method,the Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│＋t）-1 and a nonlinearity │u│p-1u is studied,similar solutions are obtained when the initial data have a compact support.

Symmetry Reductions, Integrability and Solitary Wave Solutions to High-Order Modified Boussinesq Equations with Damping Term

Both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou are extended to reduce the high-order modified Boussinesq equation with the damping term (HMBEDT) arising in the general Fermi-Pasta-Ulam model. As a result, several types of similarity reductions are obtained. It is easy to show that the nonlinear wave equation is not integrable under the sense of AblowRz's conjecture from the reduction results obtained. In addition, kink-shaped solitary wave solutions, which are of important physical significance, are found for HMBEDT based on the obtained reduction equation.

General Energy Decay of Solutions for A Wave Equation with Nonlocal Nonlinear Damping and Source Terms

We consider a wave equation with nonlocal nonlinear damping and source terms.We prove a general energy decay property for solutions by constructing a stable set and using the multiplier technique.The main difficult is how to handle with the nonlocal nonlinear damping term.Our result extends and improves the result in the literature such as the work by Jorge Silva and Narciso(Evolution Equation and Control Theory,2017(6):437-470)and Narciso(Evolution Equations and Control Theory,2020,9(2):487-508).

Numerical Research on The Nozzle Damping Effect by A Wave Attenuation Method

Nozzle damping is one of the most important factors in the suppression of combustion instability in solid rocket motors.For an engineering solid rocket motor that experiences combustion instability at the end of burning,a wave attenuation method is proposed to assess the nozzle damping characteristics numerically.In this method,a periodic pressure oscillation signal which frequency equals to the first acoustic mode is superimposed on a steady flow at the head end of the chamber.When the pressure oscillation is turned off,the decay rate of the pressure can be used to determine the nozzle attenuation constant.The damping characteristics of three other nozzle geometries are numerically studied with this method under the same operating condition.The results show that the convex nozzle provides more damping than the conical nozzle which in turn provides more damping than the concave nozzle.All the three nozzles have better damping effect than that of basic nozzle geometry.At last,the phase difference in the chamber is analyzed,and the numerical pressure distribution satisfies well with theoretical distribution.

Fractional-order Maxwell model of seabed mud and its effect on surface-wave damping

A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the traditional model. The model is then used to investigate the effect of the mud on the surface-wave damping. The damping rate of a linear monochromatic wave is obtained. The elastic resonance of the mud layer is observed, which leads to the peaks in the damping rate. The damping rate is a sum of the modal damping rates, which indicates the wave damping induced by the mud motion of particular modes. The analysis shows that near the resonance, the total damping rate is dominated by the damping rate of the corresponding mode.

Nonlinear Landau damping of high frequency waves in non-Maxwellian plasmas

Space plasmas often possess non-Maxwellian distribution functions which have a significant effect on the plasma waves. When a laser or electron beam passes through a dense plasma, hot low density electron populations can be generated to alter the wave damping/growth rate. In this paper, we present theoretical analysis of the nonlinear Landau damping for Langmuir waves in a plasma where two electron populations are found. The results show a marked difference between the Maxwellian and non-Maxwellian instantaneous damping rates when we employ a non-Maxwellian distribution function called the generalized （r, q） distribution function, which is the generalized form of the kappa and Maxwellian distribution functions. In the limiting case of r = 0 and q→∞, it reduces to the classical Maxwellian distribution function, and when r = 0 and q→k ＋1, it reduces to the kappa distribution function.

Rudder Roll Damping Autopilot Using Dual Extended Kalman Filter–Trained Neural Networks for Ships in Waves

The roll motions of ships advancing in heavy seas have severe impacts on the safety of crews,vessels,and cargoes;thus,it must be damped.This study presents the design of a rudder roll damping autopilot by utilizing the dual extended Kalman filter(DEKF)trained radial basis function neural networks(RBFNN)for the surface vessels.The autopilot system constitutes the roll reduction controller and the yaw motion controller implemented in parallel.After analyzing the advantages of the DEKF-trained RBFNN control method theoretically,the ship’s nonlinear model with environmental disturbances was employed to verify the performance of the proposed stabilization system.Different sailing scenarios were conducted to investigate the motion responses of the ship in waves.The results demonstrate that the DEKF RBFNN based control system is efficient and practical in reducing roll motions and following the path for the ship sailing in waves only through rudder actions.

Dispersion and damping rate of Langmuir wave in space plasma with regularized Kappa distributed electrons

The dispersion of Langmuir wave(LW)in an unmagnetized collisionless plasma with regularized Kappa distributed electrons is investigated from the kinetic theory.The frequency and damping rate of LW are analyzed for the parameters relating to the source region of a typeⅢsolar radio burst.It is found that the linear behavior of LW is greatly modified by the suprathermal indexκand the exponential cutoff parameterα.In the regionκ<1.5,the damping rate of LW will be much larger than the one with Maxwellian distributed electrons.Hence,the nonlinear process of LW in lowκregion may exhibit different properties in comparison with the one in largeκregion.

Exponential Growth of Solutions for Nonlinear Coupled Viscoelastic Wave Equations with Degenerate Nonlocal Damping and Source Terms

This paper is concerned with a system of nonlinear viscoelastic wave equations with degenerate nonlocal damping and memory terms.We will prove that the energy associated to the system is unbounded.In fact,it will be proved that the energy will grow up as an exponential function as time goes to infinity,provided that the initial data are positive initial energy.

Damping Solitary Wave in a Three-Dimensional Rectangular Geometry Plasma

The solitary waves of a viscous plasma confined in a cuboid under the three types of boundary condition are theoretically investigated in the present paper.By introducing a threedimensional rectangular geometry and employing the reductive perturbation theory,a quasi-Kd V equation is derived in the viscous plasma and a damping solitary wave is obtained.It is found that the damping rate increases as the viscosity coefficient increases,or increases as the length and width of the rectangle decrease,for all kinds of boundary condition.Nevertheless,the magnitude of the damping rate is dominated by the types of boundary condition.We thus observe the existence of a damping solitary wave from the fact that its amplitude disappears rapidly for a → 0and b → 0,or ν→ ＋∞.

Seismic isolation effect of lined circular tunnels with damping treatments

The Havriliak-Negami model for dynamic viscoelastic material behavior and Biot＇s theory of poroelasticity are employed to develop an exact solution for three-dimensional scattering effect of harmonic plane P-SV waves from a circular cavity lined with a multilayered fluid-filled shell of infinite length containing viscoelastic damping materials and embedded within a fluid-saturated permeable surrounding soil medium. The analytical results are illustrated with numerical examples where the effects of liner/coating structural arrangement, viscoelastic material properties, liner-soil interface bonding condition, seismic excitation frequency, and angle of incidence on the induced dynamic stress concentrations are evaluated and discussed to obtain representative values of the parameters that characterize the system. It is demonstrated that incorporating viscoelastic damping materials with a low shear modulus in the constrained layer configuration is an efficient means of enhancing the overall seismic isolation performance, especially for near-normally incident seismic shear waves where the amplitudes of induced dynamic stresses may be reduced by up to one-third of those without isolation in a relatively wide frequency range. Some additional cases are considered and good agreements with solutions available in the literature are obtained.

A hybrid inversion method of damped least squares with simulated annealing used for Rayleigh wave dispersion curve inversion

Surface wave methods are becoming increasingly popular in many geotechnical applications and in earthquake seismology due to their noninvasive characteristics.Inverse surface wave dispersion curves are a crucial step in most surface wave methods.Many inversion methods have been applied to surface wave dispersion curve inversion,including linearized inversion and nonlinearized inversion methods.In this study,a hybrid inversion method of Damped Least Squares(DLS) with Very Fast Simulated Annealing(VFSA) is developed for multi-mode Rayleigh wave dispersion curve inversion.Both synthetic and in situ fi eld data were used to verify the validity of the proposed method.The results show that the proposed method is superior to the conventional VFSA method in aiming at global minimum,especially when parameter searching space is adjacent to real values of the parameters.The advantage of the new method is that it retains both the merits of VFSA for global search and DLS for local search.At high temperatures,the global search dominates the runs,while at a low temperatures,the local search dominates the runs.Thus,at low temperatures,the proposed method can almost directly approach the actual model.

Asymptotic Behavior of Stochastic Strongly Damped Wave Equation with Multiplicative Noise

In this paper we study the asymptotic dynamics of the stochastic strongly damped wave equation with multiplicative noise under homogeneous Dirichlet boundary condition. We investigate the existence of a compact random attractor for the random dynamical system associated with the equation.

Ion Heating from Nonlinear Landau Damping of High Mode Number Toroidal Alfvén Eigenmodes

Bulk ion heating rate from nonlinear Landau damping of high mode number Toroidal Alfven Eigenmodes （TAEs） is calculated in the frame work of weak turbulence theory. The heating rate is lower than the nonlinear spectral transfer rate to more stable modes, but relatively insensitive to the details of linear damping mechanisms.

Influence of AlTi3C0.15 modification treatment on damping properties of ZnAl10 alloy

Zn-Al alloys constitute an interesting group of foundry alloys. Due to a relatively low melting temperature, they allow a decrease in energy-consumption of the melting process and alloy preparation. The vibration damping ability is one of the most interesting properties of the Zn-Al alloys. Zn-Al alloys are divided into two groups: the low-aluminium and high-aluminium alloys. The investigated Zn-10 wt.% Al(ZnAl10) alloy is representative of the high-aluminium alloys, which, on account of its tendency of forming coarse-grained structures, has rather low plastic properties, including elongation. In order to improve the plastic properties, a modification treatment is usually applied. The dependence of the damping coefficient of the ultrasound wave on the amount of the introduced inoculant was studied. Investigations were performed using the AlT i3C0.15 inoculant as the modifier of the ZnAl10 alloy. It was found that titanium additions, in a range from 25 to 100 ppm in relation to the melted charge mass, can reduce the damping coefficient value. An increase of the inoculant addition causes a rise of the damping coefficient, which is probably related to the scattering of the ultrasound wave on Al_3Ti and TiC particles introduced with the inoculant.

Uniform Exponential Attractors for Non-Autonomous Strongly Damped Wave Equations

In this paper, we study the existence of exponential attractors for strongly damped wave equations with a time-dependent driving force. To this end, the uniform H?lder continuity is established to the variation of the process in the phase apace. In a certain parameter region, the exponential attractor is a uniformly exponentially attracting time-dependent set in the phase apace, and is finite-dimensional no matter how complex the dependence of the external forces on time is. On this basis, we also obtain the existence of the infinite-dimensional uniform exponential attractor for the system.

A Simple Prediction Formula of Roll Damping of Conventional Cargo Ships on the Basis of Ikeda＇s Method and Its Limitation

Since the roll damping of ships has significant effects of viscosity, it is difficult to calculate it theoretically. Therefore, experimental results or some prediction methods are used to get the roll damping in design stage of ships. Among some prediction methods, Ikeda＇s one is widely used in many ship motion computer programs. Using the method, the roll damping of various ship hulls with various bilge keels can be calculated to investigate its characteristics. To calculate the roll damping of each ship, detailed data of the ship are needed to input. Therefore, a simpler prediction method is expected in primary design stage. Such a simple method must be useful to validate the results obtained by a computer code to predict it on the basis of Ikeda＇s method, too. On the basis of the predicted roll damping by Ikeda＇s method for various ships, a very simple prediction formula of the roll damping of ships is deduced in the present paper. Ship hull forms are systematically changed by changing length, beam, draft, mid-ship sectional coefficient and prismatic coefficient. It is found, however, that this simple formula can not be used for ships that have high position of the center of gravity. A modified method to improve accuracy for such ships is proposed.

Effect of kappa distribution on the damping rate of the obliquely propagating magnetosonic mode

Data from spacecrafts suggest that space plasma has an abundance of suprathermal particles which are controlled by the spectral index κ when modeled on kappa particle velocity distribution. In this paper, considering homogeneous plasma, the effect of integer values of κ on the damping rate of an obliquely propagating magnetosonic（MS） wave is studied. The frequency of the MS wave is assumed to be less than ion cyclotron frequency, i.e.,iw（28）w. Under this assumption, the dispersion relation is investigated both numerically and analytically, and it is found that the real frequency of the wave is not a sensitive function of κ, but the imaginary part of the frequency is. It is also shown that for those values of κ where a large number of resonant particles participate in wave–particle interaction, the wave is heavily damped, as expected. The possible application of the results to the solar wind is discussed.