Time-domain Finite Element Model Research Articles

Crack length directivity effects on guided-wave acoustic emission: Numerical investigation of radiation patterns

This paper investigates the effect of a finite-sized crack surface on acoustic emission (AE) generated at the crack tip in a thin metallic plate using a 3D time-domain finite element model. Directivity effects on the first arrivals are of particular focus, and the AE is interpreted in terms of a guided mode decomposition. Crack lengths from 0–10 plate thicknesses are studied, in addition to a semi-infinite crack surface, for frequency content in the neighborhood of 0.1–0.4 MHz-mm. Far-field radiation patterns for the fundamental symmetric (S0) and shear horizontal (SH0) guided modes are measured as a function of crack length. The results show an increase in radiation behind the crack tip for both modes and across all considered crack lengths. The surface wave traveling along the crack length appears to be one of the main drivers behind this increase, due to mode conversion after reaching the opposite end of the crack. However, a similar increase is also observed for the semi-infinite crack case, in which there is no mode conversion (the opposite end of the crack is never reached). A radiation offset (RO) metric is introduced to capture this behavior. Parametric studies of the RO across center frequency and bandwidth are presented. Findings suggest that this metric may be of use for AE-based crack length estimation.

Effect of long-term lateral cyclic loading on the dynamic response and fatigue life of monopile-supported offshore wind turbines

Offshore wind turbines are often supported on monopiles and are always subjected to long-term cyclic loading during their service life. This cyclic loading induces changes in the damping, stiffness and permanent accumulated rotation of the monopile foundation. The main purpose of this paper is to investigate the effect of these three changes occurring simultaneously on the dynamic response and fatigue life of offshore wind turbines in sand. To this end, an integrated methodology is presented based on time-domain finite element model and small-scale model tests of rigid piles. Three states of the monopile foundation are selected and defined based on the operational time of the turbine. The results show that these three changes have a slight effect on the dynamic response of offshore wind turbines, but have a significant effect on the fatigue life. The fatigue life decreased from 23.3 years for the initial state to 20.99 years for the medium state and 19.45 years for the ultimate state, a decrease of 10% and 16.5%, respectively, indicating that these changes should be addressed in the design of the fatigue life calculation of offshore wind turbine structures. The systematic parametric analysis shows that soil damping has the greatest effect on the dynamic response and fatigue life, followed by soil stiffness, which is less affected by permanent accumulated rotation.

Time-Domain Finite Element Model Updating for Operational Monitoring and Damage Identification of Bridges

The well-known limitations of modal system identification methods have led to a broad exploration of alternative solutions for operational monitoring and damage diagnosis of structures. This study presents a time-domain Bayesian finite element model updating approach to jointly identify the vehicular loads and finite element modeling parameters of bridges using the vibration data and the location of vehicles traversing the bridge as input. A Bayesian model updating is devised and verified through a series of case studies based on numerically simulated data from a prestressed reinforced concrete box-girder bridge model. Damage states are defined for concrete degradation and delamination, steel corrosion, and loss of prestressing force. Ten different damage scenarios, encompassing the range from minor localized to major distributed damage, are examined. The responses of the damaged bridge are simulated under random traffic scenarios. The acceleration responses, along with the location of the vehicles on the bridge, are used for jointly estimating the model parameters and vehicular loads. The estimated model parameters are then used to infer the location and extent of damage within the bridge. The results show the successful performance of the proposed approach in a numerically simulated environment.

Influence of unilateral low adhesion on transient wheel-rail rolling contact and wheel damages

A time-domain finite element model is developed to study the transient rolling contact of a driving wheelset over a curved track with Low Adhesion Zones (LAZs) shorter than 1.0 m. LAZs on one rail, i.e., unilateral LAZs occurring more likely, is treated for a speed up to 500 km/h. Structural vibrations of wheelset are analyzed to explain the transient contact forces, creepages and the resulting irregular wear. LAZs on high rails are found more detrimental than those on low rails. The results explain the occurrence of flats and rolling contact fatigue in bad weather, although significant wheel idling is absent.

An integrated model for offshore wind turbine monopile in porous seabed under multi-directional seismic excitations

This study proposes an integrated three-dimensional time-domain finite element model for offshore wind turbine (OWT) monopile in porous seabed under multi-directional seismic excitations. Biot's u-p formulation is used to describe the dynamic interaction between the soil skeleton and pore water. Potential-based fluid elements are used for seawater to accurately model fluid–structure interaction (FSI). Moreover, FSI interface elements are applied to the interface of seawater and pile and to the interface of seawater and mud line. To analyze the response of the OWT-monopile-seabed-seawater system to multi-directional seismic excitations, a viscous-spring artificial boundary is implemented in the finite element model. The integrated model was sufficiently verified in terms of the vibration characteristics of OWTs, the displacement and the excess pore water pressure using implemented viscoelastic artificial boundary, and the FSI interaction under both horizontal and vertical excitation. The results indicated that: (1) The hydrodynamic pressure and the excess pore water pressure varied with different positions along the OWT and the pile; (2) Adding the excitation of the EW component ground motion caused the change of the distribution of transient liquefaction with respect to that under the excitation of only NS component ground motion; (3) The vertical ground motion caused a substantial fluctuation of the vertical displacement of the OWT and larger area of transient liquefaction near the surface of the seabed and near the tip of the pile; (4) resonance occurred when the frequency of input motion was approaching to the first natural frequency of OWT, leading to extremely large acceleration and displacement of OWT.

Sound diffusion with spatiotemporally modulated acoustic metasurfaces

Traditional sound diffusers are quasi-random phase gratings attached to reflecting surfaces to introduce spatiotemporal incoherence into the backscattered acoustic field. Early designs consisted of periodically tiled diffuser grating unit cells to cover large surfaces. However, spatial periodicity leads to coherent constructive and destructive interference, which is undesirable for achieving acoustic diffusivity. This problem was partially addressed by using aperiodic tiling of unit cells based on pseudorandom sequences. While an aperiodic diffuser spacing can overcome the problems introduced by spatial periodicity, the improvements in performance come at the expense of increased thickness. In this work, we investigate spatiotemporal modulation of the surface acoustic admittance of a metasurface diffuser to improve sound diffusion. Using semi-analytical and finite element models, we demonstrate that the effects of the spatial periodicity can be mitigated without introducing an aperiodic spatial spacing, thus simultaneously minimizing diffuser thickness and improving diffusivity of the backscattered field. We develop a semi-analytical model that employs Fourier series expansion to determine the scattered sound field from a surface admittance consisting of a quadratic residue diffuser whose individual well admittances are modulated in a traveling wave fashion with modulation frequency, ωm, amplitude, Ym, and a wavenumber that matches the unit cell length, Λ. We observe significant improvement in diffusion due to the fact that the spatiotemporal modulation scatters sound into additional frequency-wavenumber pairs associated with harmonics of ωm and their diffraction orders. The semi-analytical model results are verified using a time-domain finite element model and compared with periodic and aperiodic diffuser designs.

A model-driven approach to ultrasonic detection of state of charge in lithium-ion batteries

Ultrasonic inspection is one non-destructive method to monitor the internal state of lithium-ion battery (LIB) cells. During charging, lithium ions intercalate into the graphite anode, causing moderate volumetric expansion (approximately 10%) and as much as a three-fold increase in Young’s modulus of the anode. Many researchers have observed changes in the time-of-flight (TOF) of through-thickness ultrasonic waves that correlate with changes in the state of charge (SOC). We introduce a transfer matrix method and Bloch-wave formalism for periodically layered media to show that the observed changes in TOF are partially due to the associated changes in anode stiffness. However, more detailed models that consider battery heterogeneity in structure and properties are needed to predict changes in TOF and signal amplitude (SA) for sophisticated ultrasonic measurement configurations and different cell chemistries. We therefore employ a quasi-static homogenization scheme for layered media to estimate the effective anisotropic stiffness of LIB pouch cells as a function of SOC as an input to a time-domain finite element model to determine the influence of changes in the anode, cathode, and separator on the direction-dependent propagation modes. This model is then employed to interpret experimentally obtained TOF and SA data for more robust SOC detection.

A coupled frequency and time domain approach for hydroelastic analysis of very large floating structures under focused wave groups

This paper presents a Python-based scheme for simulating the hydroelastic response of very large floating structures (VLFS) under extreme conditions which are represented by focused wave groups. Applying the modal expansion method, we decouple the fluid-structure problem into a hydrodynamic problem in terms of velocity potentials for the fluid and a mechanical problem for the structure. The hydrodynamic problem is solved by the higher-order boundary element method in the frequency domain, while the structural analysis is performed by a time-domain finite element model. In order to validate the proposed scheme, numerical simulations are carried out on a scaled model of VLFS in regular and random waves. Both analytical and discrete numerical modal shape functions are used for representing the elastic deformations. The Mindlin plate theory is used for the finite element model. Extensive convergence studies of finite element model meshes, hydrodynamic model meshes and elastic mode numbers are carefully carried out. Good agreements of the vertical displacement, bending moment and shear force amplitudes of the floating plate are found between the predictions of the present model, and experimental data and numerical results in the literature for regular and random waves. The hydroelastic responses of the scaled model in focused wave groups are then investigated. A modified NewWave model is proposed to generate focused pressure in linear wave groups, and the results show the effectiveness of the proposed model. Influence of the focal position, water depth, incident wave angle, and peak spectrum frequency and bandwidth of the focused wave groups on the hydroelastic response of the plate is also studied. The proposed approach is shown promising for hydroelastic analysis for more complex VLFS in realistic sea states.

Wave propagation in a continuum phononic material with geomaterial-inspired nonlinearity

This presentation discusses the nonlinear wave propagation in a continuum phononic material with nonlinear mechanisms inspired by geomaterials. Geomaterials can exhibit nonlinear wave responses due to mechanisms such as material nonlinearity or lack of bonding between phases of material. We study the interaction of nonlinear and phononic behavior by introducing two geomaterial-inspired nonlinear mechanisms into a phononic material. The influence of material nonlinearity and nonlinearity due to delaminations between material phases are studied in a bilayer finite element model composed of alternating layers of stiff linear elastic material and soft hyperelastic material. To model delaminations, a binary contact condition is applied at the interface between layers. Measurements of the quasi-static nonlinear mechanical response of delaminations of different lengths are used as inputs into the finite element method simulations. The influence of the delamination nonlinearity plus material nonlinearity on the phononic material is studied in a full-scale time-domainfinite element model. This model is used to further probe the interaction between phononic band gaps and nonlinear wave response, as well as the dependence of delamination size and location on the nonlinear wave response.

Numerical modeling of ground-borne vibrations induced by pile driving with a simple and direct material damping approach

Ground-borne vibrations are an increasingly common problem in large cities due to its considerable disturbance in terms of human comfort and health. In this sense, construction operations stand as a significant source of vibrations and may be critical since construction sites are frequently adjacent to existing buildings. In the present work, vibrations induced by pile driving are studied. A time-domain finite element model is developed and a post-processing approach is proposed to simulate the material damping of the soil. This damping formulation stands as a simple and direct approximation of the material damping in the system. In order to do so, the numerical response is computed without material damping, which is introduced as a post-processing procedure. An explicit and highly efficient method is applied for the time integration of the equation of motion, considering an axisymmetric formulation. A numerical application is carried out and the obtained results are compared to previous numerical and in-situ measurements available in the literature, indicating a good agreement with previous studies.

An Efficient Unsplit Perfectly Matched Layer for Finite-Element Time-Domain Modeling of Elastodynamics in Cylindrical Coordinates

The truncation of an unbounded medium into a finite domain and the elimination of reflections from artificial medium boundaries is important in numerical simulations of elastodynamic equations. The perfectly matched layer (PML) technique as a novel absorbing boundary has demonstrated very high efficiency for elastic wave equation models. Based on the stretched coordinate concept, an efficient and unsplit-field perfectly matched layer equation for elastic waves is formulated in a cylindrical coordinate system. By introducing integrated complex variables for radial direction and auxiliary functions, the PML formulation is extended in cylindrical coordinates based on the second-order elastic wave equation with displacements as basic unknowns. Finite-element time-domain modeling of the second-order unsplit PML for the elastodynamic equation is presented, which is a standard displacement-based formulation for the computational domain including a PML region. The formulas for the special cases with 2-D axisymmetric coordinates and polar coordinates are also given. The efficiency of the proposed formulations is illustrated by a numerical example using the finite-element method.

Non-Split PML Boundary Condition for Finite Element Time-Domain Modeling of Ground Penetrating Radar

As a highly efficient absorbing boundary condition, Perfectly Matched Layer (PML) has been widely used in Finite Difference Time Domain (FDTD) simulation of Ground Penetrating Radar (GPR) based on the first order electromagnetic wave equation. However, the PML boundary condition is difficult to apply in GPR Finite Element Time Domain (FETD) simulation based on the second order electromagnetic wave equation. This paper developed a non-split perfectly matched layer (NPML) boundary condition for GPR FETD simulation based on the second order electromagnetic wave equation. Taking two-dimensional TM wave equation as an example, the second order frequency domain equation of GPR was derived according to the definition of complex extending coordinate transformation. Then it transformed into time domain by means of auxiliary differential equation method, and its FETD equation is derived based on Galerkin method. On this basis, a GPR FETD forward program based on NPML boundary condition is developed. The merits of NPML boundary condition are certified by compared with wave field snapshots, signal and reflection errors of homogeneous medium model with split and non-split PML boundary conditions. The comparison demonstrated that the NPML algorithm can reduce memory occupation and improve calculation efficiency. Furthermore, numerical simulation of a complex model verifies the good absorption effects of the NPML boundary condition in complex structures.

Comparative analysis of numerically simulated and experimentally measured motions and sectional forces and moments in a floating wind turbine hull structure subjected to combined wind and wave loads

Multi-body time-domain finite element models, which implement a recently developed numerical approach for determining forces and moments in floaters, are developed to simulate rigid-body motions and sectional forces and moments of a reference 5-MW braceless semi-submersible wind turbine in turbulent winds and irregular waves corresponding to below rated, at rated and above rated conditions. The simulated responses are compared with measurements of a 1:30 scaled model test using a real-time hybrid testing approach. In general, agreement between simulations and measurements are very good. Differences in spectral densities of the measurements and simulations have been quantified while the reasons for the differences have been thoroughly analyzed and discussed based on comparisons of measurements in different conditions and numerical parametrical study. Effects of non-linear wave excitation loads and drag forces on the rigid-body motions and sectional forces and moments are analyzed while dominant load components in fore-aft bending moments in five cross-sections in the hull of the reference model are identified. The interface between the pontoons and central column of the reference model is identified as the most critical part. Both low frequency and wave frequency load effect should be accounted for. Mean forces and moments from wind and waves result in a change in configuration of mean wetted body surface of the hull when compared to its configuration in calm water. This may result in a considerable change in resultant sectional forces and moments even though change in resultant of the hydro pressure forces on whole of the wetted body surface could be very limited. For the analyzed model, simulated fore-aft bending moments of the model in wind and waves could be obtained by superimposing the results for wind only condition, and wave only condition except that the corresponding averaged wind induced forces and moments should be applied on the numerical model. This simplification can significantly reduce number of cases of short-term analysis required in long-term analysis. However, applicability of the simplification should be analyzed case by case in particular for a blunt structure with relatively large volume of displaced water in waves with relatively small wave length. Analysis and discussions given in this paper are based on available measurements of the model test. Hydroelastisity and structural vibration of the columns and pontoons of the hull are not accounted for by the numerical and experimental models. Suggestions for design of future model tests are given in this paper.

Investigation of nonlinear ultrasonic guided waves in open waveguides based on perfectly matched layers.

Nonlinear ultrasonic guided waves have been investigated widely in closed waveguides such as plates, pipes, etc. However, the description of nonlinear ultrasonic guided waves remains challenging for open waveguides, as energy may leak into the surrounding medium. In this work, the properties of nonlinear ultrasonic guided waves in open waveguides are investigated. Mathematical framework is first established based on real reciprocity relation and modal expansion with perfectly matched layers. Numerical models are then implemented, including nonlinear semi-analytical finite element (SAFE) method to predict the properties of nonlinear ultrasonic guided waves, and time domain finite element models to simulate the nonlinear guided wave propagation and cross validate the predictions from the nonlinear SAFE method. Two examples, an aluminum plate attached to an elastomer and an aluminum plate with water loaded on one side, are studied to demonstrate the proposed methods and reveal some interesting phenomena that only exist in open waveguides. It is interesting to find out that the amplitude of the attenuated second harmonic wave in immersed waveguides can keep constant with propagation distance, only if the primary wave is non-leaky, which may bring potential non-destructive test applications for underwater inspections. Such a feature is validated by well-designed experiments in one-sidedly immersed plates.

Numerical time-domain modelling of hoof-ground interaction during the stance phase.

Hoof-ground interaction impacts on the health and performance characteristics of horses. Due to complex interactions between hoof and ground during the stance phase, previous experimentally dominated studies concentrated on subproblems of the phenomena observed. A multidisciplinary methodology with mathematical modelling, material testing and in vivo experimental measurements seems promising. With the help of a mathematical approach, this contribution aims to explain from a biomechanical point of view the phenomena observed during experimental investigations (hoof acceleration, interacting forces) and aims to contribute to an overall experimental-mathematical multidisciplinary approach. In silico modelling of hoof-ground interaction (limb, hoof and horizontally unbounded ground). Hoof-ground interaction is represented by a time-domain finite element model including the limb, the hoof and the unbounded representation of the ground via the scaled boundary finite element method to capture radiation damping during the stance phase. Motoric forces (driving forces) of the horse during locomotion are included. Numerical model results for acceleration-time relations (hoof) at different trotting velocities are compared with previously published acceleration-time relations and show qualitative agreement. From the model approach, power loss due to different ground properties and ground damping is computed in combination with the maximum limb force during the stance phase. Intentionally, a simplified model approach for the material and structural representation of the limb, the hoof and the ground in terms of material features and spatial resolution has been used for this study, which might be the basis for a model refinement in terms of contact properties as well as the integration of bone and joint structures. The comparison to experimentally obtained results demonstrates the applicability of the model, which, in turn, enables an insight into the processes taking place during hoof-ground interaction.

Finite-element time-domain modeling of electromagnetic data in general dispersive medium using adaptive Padé series

The induced polarization (IP) method has been widely used in geophysical exploration to identify the chargeable targets such as mineral deposits. The inversion of the IP data requires modeling the IP response of 3D dispersive conductive structures. We have developed an edge-based finite-element time-domain (FETD) modeling method to simulate the electromagnetic (EM) fields in 3D dispersive medium. We solve the vector Helmholtz equation for total electric field using the edge-based finite-element method with an unstructured tetrahedral mesh. We adopt the backward propagation Euler method, which is unconditionally stable, with semi-adaptive time stepping for the time domain discretization. We use the direct solver based on a sparse LU decomposition to solve the system of equations. We consider the Cole-Cole model in order to take into account the frequency-dependent conductivity dispersion. The Cole-Cole conductivity model in frequency domain is expanded using a truncated Padé series with adaptive selection of the center frequency of the series for early and late time. This approach can significantly increase the accuracy of FETD modeling.

Finite element time domain modeling of controlled-source electromagnetic data with a hybrid boundary condition

We implemented an edge-based finite element time domain (FETD) modeling algorithm for simulating controlled-source electromagnetic (CSEM) data. The modeling domain is discretized using unstructured tetrahedral mesh and we consider a finite difference discretization of time using the backward Euler method which is unconditionally stable. We solve the diffusion equation for the electric field with a total field formulation. The finite element system of equation is solved using the direct method. The solutions of electric field, at different time, can be obtained using the effective time stepping method with trivial computation cost once the matrix is factorized. We try to keep the same time step size for a fixed number of steps using an adaptive time step doubling (ATSD) method. The finite element modeling domain is also truncated using a semi-adaptive method. We proposed a new boundary condition based on approximating the total field on the modeling boundary using the primary field corresponding to a layered background model. We validate our algorithm using several synthetic model studies.

Chatter reduction in slender boring bar via a tunable holder with variable mass and stiffness

In this study, a new strategy is presented to increase the machining stability due to chatter suppression for boring and turning machining processes. The proposed approach is based on varying the position of stability lobes via changing mechanical properties of the tool body such as the mass and stiffness. Because of the shape of stability lobe diagrams, having a tool with a tunable stability lobe diagram can be useful to alter an unstable condition to a stable condition. For this purpose, a structure for the tool body is designed that is consisted of a hollow body with a core as a tunable screw inside it. As the core gets in or out, it changes the mass and stiffness of the tool body that leads to change the position of stability lobe diagram. In order to study the effect of designed structure on stability, the structure is simulated using a validated finite element time domain model. The time domain simulation shows a considerable improvement in stability of process. The strategy is experimentally applied to the process via modulation of the tool structure in the machining process to validate the simulation results. The experimental results have a high coincidence with theory and show a good improvement in stability.

A time-domain finite element model reduction method for viscoelastic linear and nonlinear systems

MANY AUTHORS HAVE SHOWN THAT THE EFFECTIVE DESIGN OF VISCOELASTIC SYSTEMS CAN BE CONVENIENTLY CARRIED OUT BY USING MODERN MATHEMATICAL MODELS TO REPRESENT THE FREQUENCY- AND TEMPERATURE-DEPENDENT BEHAVIOR OF VISCOELASTIC MATERIALS. HOWEVER, IN THE QUEST FOR DESIGN PROCEDURES OF REAL-WORD ENGINEERING STRUCTURES, THE LARGE NUMBER OF EXACT EVALUATIONS OF THE DYNAMIC RESPONSES DURING ITERATIVE PROCEDURES, COMBINED WITH THE TYPICALLY HIGH DIMENSIONS OF LARGE FINITE ELEMENT MODELS, MAKES THE NUMERICAL ANALYSIS VERY COSTLY, SOMETIMES UNFEASIBLE. IT IS ESPECIALLY TRUE WHEN THE VISCOELASTIC MATERIALS ARE USED TO REDUCE VIBRATIONS OF NONLINEAR SYSTEMS. AS A MATTER OF FACT, WHICH THE RESOLUTION OF THE RESULTING NONLINEAR EQUATIONS OF MOTION WITH FREQUENCY- AND TEMPERATURE-DEPENDENT VISCOELASTIC DAMPING FORCES IS AN INTERESTING, BUT HARD-TO-SOLVE PROBLEM. THOSE DIFFICULTIES MOTIVATE THE PRESENT STUDY, IN WHICH A TIME-DOMAIN CONDENSATION STRATEGY OF VISCOELASTIC SYSTEMS IS ADDRESSED, WHERE THE VISCOELASTIC BEHAVIOR IS MODELED BY USING A FOUR PARAMETER FRACTIONAL DERIVATIVE MODEL. AFTER THE DISCUSSION OF VARIOUS THEORETICAL ASPECTS, THE EXACT AND REDUCED TIME RESPONSES ARE CALCULATED FOR A THREE-LAYER SANDWICH PLATE BY CONSIDERING NONLINEAR BOUNDARY CONDITIONS.

Transient analysis of coupled non‐uniform transmission line using finite element method

SummaryThis paper presents a finite element time domain model for a numerical solution of a coupled non‐uniform transmission line problem. On the basis of the finite element method, a novel numerical procedure for the solution of a system of the non‐uniform multi‐conductor transmission line equations in the time domain is presented. The results obtained by the proposed method have been compared with the solution obtained using the finite difference time domain method, and an excellent correlation has been demonstrated. Copyright © 2014 John Wiley & Sons, Ltd.