Time-domain Boundary Element Method Research Articles

Deep Learning for Scattered Waves Obtained by Time-domain Boundary Element Method and an Attempt to Classify Defect Types

Deep Learning for Scattered Waves Obtained by Time-domain Boundary Element Method and an Attempt to Classify Defect Types

Introducing an effective coherence function to generate non-uniform ground motion on topographic site using time-domain boundary element method

In this study, a comprehensive parametric analysis was performed on non-uniform excitation of V-shaped topography using the boundary element method in time domain. For this purpose, wave scattering analysis was carried out on a topography subjected to the SV-wave for different predominant frequencies and shape ratios. Based on the numerical results, new coherence and time delay functions are proposed to generate non-uniform ground motion for topographic irregularities. The efficiency and accuracy of the proposed functions for real engineering problems are indicated by comparison with observations reported in previous literature.

Basic investigation to develop a fast time-domain boundary element method for electromagnetic scattering problems in 3D

Basic investigation to develop a fast time-domain boundary element method for electromagnetic scattering problems in 3D

Convolution quadrature time-domain boundary element method for anisotropic pure SH wave with viscosity

Convolution quadrature time-domain boundary element method for anisotropic pure SH wave with viscosity

A shape optimization for 3D unsteady acoustic problems using the fast time-domain boundary element method

A shape optimization for 3D unsteady acoustic problems using the fast time-domain boundary element method

Development of TD-BEM Formulation for Dynamic Analysis for Twin-Parallel Circular Tunnels in an Elastic Semi-Innite Medium

In order to simulate the propagation process of subway vibration of parallel tunnels in semi-infinite rocks or soils, time domain boundary element method (TD-BEM) formulation for analyzing the dynamic response of twin-parallel circular tunnels in an elastic semi-infinite medium is developed in this paper. The time domain boundary integral equations of displacement and stress for the elastodynamic problem are presented based on Betti’s reciprocal work theorem, ignoring contributions from initial conditions and body forces. In the process of establishing time domain boundary integral equations, some virtual boundaries are constructed between finite boundaries and the free boundary to form a boundary to refer to the time domain boundary integral equations for a single circular tunnel under dynamic loads. The numerical treatment and solving process of time domain boundary integral equations are given in detail, including temporal discretization, spatial discretization and the assembly of the influencing coefficients. In the process of the numerical implementation, infinite boundary elements are incorporated in time domain boundary element method formulation to satisfy stress free conditions on the ground surface, in addition, to reduce the discretization of the boundary of the ground surface. The applicability and efficiency of the presented time domain boundary element formulation are verified by a deliberately designed example.

On the Comparative Seakeeping Analysis of the Full Scale KCS by Several Hydrodynamic Approaches

The main transport channel of the global economy is represented by shipping. Engineers and hull designers are more preoccupied in ensuring fleet safety, the proper operation of the ships, and, more recently, compliance with International Maritime Organization (IMO) regulatory incentives. Considerable efforts have been devoted to in-depth understanding of the hydrodynamics mechanism and prediction of ship behavior in waves. Prediction of seakeeping performances with a certain degree of accuracy is a demanding task for naval architects and researchers. In this paper, a fully numerical approach of the seakeeping performance of a KRISO (Korea Research Institute of Ships and Ocean Engineering, Daejeon, South Korea) container ship (KCS) container vessel is presented. Several hydrodynamic methods have been employed in order to obtain accurate results of ship hydrodynamic response in regular waves. First, an in-house code DYN (Dynamic Ship Analysis, “Dunarea de Jos” University of Galati, Romania), based on linear strip theory (ST) was used. Then, a 3D fully nonlinear time-domain Boundary Element Method (BEM) was implemented, using the commercial code SHIPFLOW (FLOWTECH International AB, Gothenburg, Sweden). Finally, the commercial software NUMECA (NUMECA International, Brussels, Belgium) was used in order to solve the incompressible unsteady Reynolds-averaged Navier–Stokes equation (RANSE) flow at ship motions in head waves. The results obtained using these methods are represented and discussed, in order to establish a methodology for estimating the ship response in regular waves with accurate results and the sensitivity of hydrodynamical models.

Numerical analysis of stick–slip induced nonlinear vibration and acoustic responses of composite laminated plates with friction boundaries

This paper is concerned with the development of a numerical model for predicting the nonlinear structural and acoustic responses of a composite laminated plate induced by stick–slip motions. The structural model of the plate is formulated using a higher-order shear deformation zigzag theory for accommodating the analysis of both thin and relatively thick composite plates. A phenomenological macro-slip friction model is adopted to describe the stick and slip motions of the friction boundaries. The nonlinear dynamics model of the composite plate is established based on a finite element method, and the exterior acoustic fluid is modeled using a time-domain boundary element method. The nonlinear vibro-acoustic responses of the plate are calculated by considering the compatibility conditions on the common interface of the plate and the fluid. The role of the frictional forces in the vibration and sound radiation of the plate is explained. It is found that the periodical distortions of the sound pressure waves are mainly due to the stick-to-slip transitions of the friction boundary other than the slip-to-stick transitions. The effects of the preload, friction coefficient and stiffness of the boundary on the nonlinear structural and acoustic responses of composite plates are examined.

On subsurface multiple inclusions model under transient SH-wave propagation

ABSTRACT In this paper, a homogeneous linear elastic half-plane model cluttered with multiple embedded arbitrarily-shaped inclusions is presented. The model was built based on the time-domain boundary element method established via the half-space Green’s functions, subjected to propagating obliquely incident SH-waves. Using this method, the discretization was performed only on the interfaces. The full-contact posture was assumed between the inclusions and the surrounding domain. First, the problem was disintegrated into two parts including a multi-pitted half-plane and a system of randomly shaped closed filled solids. Then, by applying the method to each part, the influence coefficients of the matrices were obtained. Finally, to form a coupled equation for determining unknown boundary values in each time-step, the boundary/continuity conditions were satisfied on the interfaces. By implementing the method in an advanced developed algorithm, its efficiency was investigated by comparing the responses with those of the published works. To complete the obtained results, the synthetic seismograms and three-dimensional amplification patterns of the surface were presented. Also, some snapshots were illustrated to reveal the dispersion of the waves. The proposed method is a powerful tool for modeling various structures at the nano-scale and can be recommended to engineers for transient analysis of composite materials.

Real-time dynamics of plasmonic resonances in nanoparticles described by a boundary element method with generic dielectric function.

Investigating nanoplasmonics in an explicit time-dependent perspective is a natural choice when light pulses are used and may also reveal aspects that are hidden in a frequency-based picture. In the past, we proposed a method time domain-boundary element method (TD-BEM) to simulate the time dependent polarization of nanoparticles based on a boundary element method that is particularly suitable to interface with a quantum atomistic description of nearby molecules. So far, however, metal dielectric functions in TD-BEM have been modeled through analytic expressions, such as those of Debye and Drude-Lorentz, which cannot account for multiple electronic resonances. Our approach allows us to include in the TD-BEM framework also the description of metals with complicate dielectric function profiles in the frequency domain. Particularly, among all metals, gold is a challenging case due to the presence of many transition frequencies. We applied our methods to different metals (gold, silver, and the less commonly investigated rhodium) and different shaped nanoparticles (spheres, ellipsoids, and cubes), the approach has been tested comparing TD-BEM and frequency domain BEM absorption spectra, and it has been used to investigate the time-dependent field acting locally close to nanoparticle vertices.

Seismic analysis of semi-sine shaped alluvial hills above subsurface circular cavity

In this study, a seismic analysis of semi-sine shaped alluvial hills above a circular underground cavity subjected to propagating oblique SH-waves using the half-plane time domain boundary element method (BEM) was carried out. By dividing the problem into a pitted half-plane and an upper closed domain as an alluvial hill and applying continuity/boundary conditions at the interface, coupled equations were constructed and ultimately, the problem was solved step-by-step in the time domain to obtain the boundary values. After solving some verification examples, a semi-sine shaped alluvial hill located on an underground circular cavity was successfully analyzed to determine the amplification ratio of the hill surface. For sensitivity analysis, the effects of the impedance factor and shape ratio of the hill were also considered. The ground surface responses are illustrated as three-dimensional graphs in the time and frequency domains. The results show that the material properties of the hill and their heterogeneity with the underlying half-space had a significant effect on the surface response.

Finite element method and boundary element method iterative coupling algorithm for 2-D elastodynamic analysis

The coupling algorithm of the finite element method (FEM) and boundary element method (BEM) can make maximal use of both methods’ advantages. However, such coupling will reduce the computational efficiency because the systems’ degrees of freedom will increase sharply. Thus, a new coupling algorithm that achieves accuracy and computational efficiency is necessary. This study proposes the Newmark-based precise integration FEM (NBPI-FEM) and analytical-based time domain BEM (ABTD-BEM) coupling algorithm. In this coupling algorithm, the governing equation of the FEM is solved by Newmark-based precise integration, and the governing equation of the BEM is solved by the analytical method. First, the procedures of NBPI-FEM and ABTD-BEM are given. The coupling strategy is then provided, and the relationship between the iteration numbers and the relaxation parameter is investigated. Finally, two illustrative examples—i.e., 1-D rod and a semi-infinite structure—are selected to verify the coupling algorithm proposed in the study. The results show that the numerical solutions agree well with the analytical solutions for the 1-D rod example and coincide with the numerical solutions calculated by FEM. Thus, NBPI-FEM and ABTD-BEM can be applied for solving elastodynamic problems with high accuracy and efficiency.

Krylov Subspace iterative methods for time domain boundary element method based nearfield acoustical holography

In this paper we study the reconstruction of the acoustic field on an arbitrarily shaped vibrating surface using the Time domain Boundary Element Method (TBEM) based Near-field Acoustic Holography technique, or Inverse TBEM (ITBEM). The main focus of our study is the indirect formulation known as the single layer representation and the impact of the dicretization using higher order polynomial basis for both space and time. The solution of the resultant matrix system from this formulation contains a special sparse structure that can be efficiently implemented using Krylov subspace iterative methods like Least Squares QR (LSQR). We show, using numerical data, that the semi-convergent behavior of the LSQR iterations allows the effective mitigation of the ill-posed nature of the numerical solution to this matrix system. Similarly, we provide a numerical study of the ITBEM reconstruction when the signals contain problematic frequencies information. The numerical data is generated over a spherical geometry using Gaussian pulses.

Vortex sound interaction in acoustic resonance of a flow duct containing a plate

Acoustic resonance induced by vortex shedding from a flat plate in a flow duct has been widely concerned in a variety of engineering applications. However, the unsteady vortex sound interaction is still an open issue. A nonlinear physical model is established based on three meshless sub-models, including the discrete vortex method (DVM) for vortex shedding, the vortex sound theory for sound radiation and the time-domain boundary element method (TDBEM) for sound propagation within the duct. Then, the feedback effect of sound wave is considered by adding acoustic particle velocity onto the potential flow of vortex shedding, which makes the coupling process bidirectional. Both the flow field, sound field and their unsteady interaction are obtained simultaneously. The predicted resonant frequency and amplitude results are in accordance with the previous experiment data, especially, the lock-in phenomenon is reasonably captured. By comparing the numerical results with and without acoustic feedback, it reveals that the feedback sound plays a significant role in the onset of lock-in phenomenon, including enhancing the strength and modulating the frequency of vortex shedding. It helps to get a more detailed insight into the underlying physical process of vortex sound interaction for studying control strategy.

Influence of Viscosity and Non-Linearities in Predicting Motions of a Wind Energy Offshore Platform in Regular Waves

AbstractMotion predictions of floating bodies in extreme waves represent a challenging problem in naval hydrodynamics. The solution of the seakeeping problem involves the study of complex non-linear wave-body interactions that require large computational costs. For this reason, over the years, many seakeeping models have been formulated in order to predict ship motions using simplified flow theories, usually based on potential flow theories. Neglecting viscous effects in the wave-induced forces might largely underestimate the energy dissipated by the system. This problem is particularly relevant for unconventional floating bodies at resonance. In these operating conditions, the linear assumption is no longer valid, and conventional boundary element methods, based on potential flow, might predict unrealistic large responses if not corrected with empirical viscous damping coefficients. The application considered in this study is an offshore platform to be operated in a wind farm requiring operability even in extreme meteorological conditions. In this paper, we compare heave and pitch response amplitude operators predicted for an offshore platform using three different seakeeping models of increasing complexity, namely, a frequency-domain boundary element method (BEM), a partly nonlinear time domain BEM, and a non-linear viscous model based on the solution of the unsteady Reynolds-averaged Navier–Stokes (URANS) equations. Results are critically compared in terms of accuracy, applicability, and computational costs.

Free-Surface Effects on the Performance of Flapping-Foil Thruster for Augmenting Ship Propulsion in Waves

Flapping foils located beneath or to the side of the hull of the ship can be used as unsteady thrusters, augmenting ship propulsion in waves. The basic setup is composed of a horizontal wing, which undergoes an induced vertical motion due to the ship’s responses in waves, while the self-pitching motion of the wing is controlled. Flapping foil thrusters can achieve high level of thrust as indicated by measurements and numerical simulations. Due to the relatively small submergence of the above biomimetic ship thrusters, the free-surface effects become significant. In the present work, the effect of the free surface on the performance of flapping foil thruster is assessed by means of two in-house developed computational models. On one hand, a cost-effective time-domain boundary element method (BEM) solver exploiting parallel programming techniques and general purpose programming on graphics processing units (GPGPU) is employed, while on the other hand a higher fidelity RANSE finite volume solver implemented for high performance computing (HPC) is used, and comparative results are presented. BEM and RANSE calculations present quite similar trends with respect to mean submergence depth, presenting 12%, 28%, and 18% of differences concerning the mean values of lift, thrust, and moment coefficients, respectively. The latter differences become very small after enhancement of the BEM model to include viscous corrections. Useful information and data are derived supporting the design of the considered biomimetic thrusters, for moderate submergence depths and conditions characterized by minor flow separation effects.

Vibration and acoustic waves of multilayered cylindrical shells carrying internal components attached by nonlinear compliant mounts

The structural-acoustic interactions of a coupled multilayered composite cylindrical shell and internal equipment system immersed in an infinite fluid medium are analyzed. The internal equipment is installed on the cylindrical shell by a series of nonlinear compliant mounts, which are represented by nonlinear springs and linear viscous dampers. Both the translational and rotational vibrations of the internal equipment are considered, and they are strongly coupled together due to the nonlinear elastic mounts. The nonlinear dynamics model of the coupled cylindrical shell and internal equipment system is established using a modified variational method, and the fluid exterior to the shell is modeled by a time-domain boundary element method. A strongly coupled serially staggered procedure is adopted to solve the governing equations of the structural system and the acoustic fluid as a coupled system. The results of the present analysis are validated by comparing with those obtained from the finite element method. The nonlinear structural vibration and acoustic wave behaviors of the coupled system containing compliant mounts with linear or nonlinear stiffnesses (including quadratic, cubic, quartic, quadratic-quartic types of stiffness) are analyzed. The effects of the translational and rotational motions of the internal equipment as well as their coupling on the nonlinear vibration and acoustic wave responses of the coupled system are examined. Physical insights into the super-harmonics in the vibration and sound pressure responses of the coupled system are provided.

BEM applied to the cup effect on the partially submerged propeller performance prediction and ventilation pattern

This article describes the development of the boundary element method (BEM) to predict the partially submerged propeller (PSP) performance with and without the cup effect, and the 3D unsteady ventilation pattern under an open flow condition. The applied theory is a time-domain BEM, where the perturbation potential is a function of immersion ratio and time. For validation, the unsteady ventilating flow about the 841-B propeller is investigated. It is shown that the formation of the ventilation pattern is captured by the BEM, and the predicted shape of the ventilated surface corresponds well with the experimental observation. Force/moment (components) coefficients are calculated on the key blade of PSP during one cycle in comparison with and without the cup effect. The obtained numerical results are in good agreement with experiments data at high advanced coefficients and in low advanced coefficients reduced.

Construction and application of adaptive semi-Infinite boundary element with dynamic problems on half-plane

For thedynamic problem ofhalf-plane, if the radiation condition at the semi-infinite boundary is not taken into account in the numerical calculation, the accuracy of the result will be affected.In this paper, the basic theory of time-domain boundary element method (TD-BEM) and the propagation characteristics of stress waves in elastic media are used to transform a semi-infinite boundary into a semi-infinite boundary element which can adjust the size of the element automatically with time-space parameters.Enablingthe element to simulate radiative damping effects in the far field.At last, the efficiency of theelement is verified with a half-plane example under dynamic load by comparing its results with the results of the finite element method (FEM). Theverificationshows thatthe adaptive semi-infinite element can effectively simulate the radiation conditions in the far area. And it is convenient to use TD-BEM to solve the half-plane dynamics problem.

On some recent developments of the 3D fast time-domain boundary element method

On some recent developments of the 3D fast time-domain boundary element method