Numerical Simulation of Free Surface-Structure-Interaction with Multi-Regional Mesh Deformation

The Fluid-Structure-Interactions (FSI) for technological constructions on sea are becoming nowadays very important in view of growing consumption of renewable energy sources. Exceptionally the offshore wind farms are exposed to extreme weather conditions due to breaking and non-breaking wave loads. This work presents numerical Finite-Volume-Method (FVM) analysis of fluid and structure interactions with water waves impact on elastic solid structures. We develop a Free Surface-Structure-Interaction (FSSI) solver in OpenFAOM [1] with multi-regional mesh deformation. A two dimensional numerical water impact model on a damping element prototype of an offshore wind turbin tower is investigated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Uniform stabilization to equilibrium of a nonlinear fluid–structure interaction model

We consider uniform stability to a nontrivial equilibrium of a nonlinear fluid–structure interaction (FSI) defined on a two or three dimensional bounded domain. Stabilization is achieved via boundary and/or interior feedback controls implemented on both the fluid and the structure. The interior damping on the fluid combining with the viscosity effect stabilizes the dynamics of fluid. However, this dissipation propagated from the fluid alone is not sufficient to drive uniformly to equilibrium the entire coupled system. Therefore, additional interior damping on the wave component or boundary porous like damping on the interface is considered. A geometric condition on the interface is needed if only boundary damping on the wave is active. The main technical difficulty is the mismatch of regularity of hyperbolic and parabolic component of the coupled system. This is overcome by considering special multipliers constructed from Stokes solvers. The uniform stabilization result obtained in this article is global for the fully coupled FSI model.     

Asymptotic analysis of steady solutions of the KdVB equation with application to resonant sloshing

The forced Korteweg-de Vries equation with Burgers’ damping (fKdVB) on a periodic domain, which arises as a model for water waves in a shallow tank with forcing near resonance, is considered. A method for construction of asymptotic solutions is presented, valid in cases where dispersion and damping are small. Through variation of a detuning parameter, families of resonant solutions are obtained providing detailed insight into the resonant response character of the system and allowing for direct comparison with the experimental results of Chester and Bones (1968).     

An energy flow model for high-frequency vibration analysis of two-dimensional panels in supersonic airflow

Many energy flow models have been proposed for high-frequency forced vibration analysis of structures. In this paper, a novel energy flow model is developed to predict the high-frequency vibration response of panels in supersonic airflow and quantify the effects of supersonic airflow on high-frequency forced vibration characteristics. The additional damping due to supersonic airflow is derived from the motion equation of a two-dimensional panel. The relationship between the wavenumber and the group velocity is introduced to describe the energy transmission property considering the effects of supersonic airflow. Then the energy density governing equation (i.e. energy flow model) is established and solved by the energy flow analysis (EFA) and the energy finite element method (EFEM). Finally, comparing the vibration responses obtained by the present energy flow model with the corresponding exact analytical solutions, the developed energy flow model is verified to be effective for high-frequency vibration analysis of panels in supersonic airflow. Furthermore, the numerical simulations indicate that supersonic airflow can affect the equivalent damping of the propagating elastic waves, and thus change the energy density distribution of the panel.     

Advanced FEM for free surface flow with application to landslides

An advanced space-time finite element method is presented to investigate movements of landslides and their interaction with flexible structures. The mechanics of liquefied soil is described by Navier-Stokes-equations for visco-plastic non-newtonian fluid. Likewise the fluid the kinematics of the structure is described by velocities, taking large rotations into account. This leads to a monolithic fluid-structure interaction approach considering the multi-field problem as a whole. The discretized model equations are assembled in a single set of algebraic equations, which are solved by applying Newton-Raphson scheme. Free surface motion of landslide is described by the level-set method. To reduce computational effort the fragmented finite element method is used, where only active finite elements are evaluated. A pde-based extrapolation of the velocity-field is applied to ensure an accurate transport of distance function, which defines the profile in space and time of the free surfaces. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A FEM-BEM approach for Fluid-Structure Interaction

In an earlier attempt to solve problems of Fluid-Structure Interaction (FSI), a high-order finite element code, which can be applied to solve problems of Computational Structural Dynamics (CSD) has been coupled to a Lattice Boltzmann (LB) fluid solver. In order to extend this approach to maritime applications and to increase the computational efficiency, the CSD solver is coupled to a fluid solver based on the Boundary Element Method (BEM). In this way, the computational effort for the discretisation of the fluid is significantly reduced. In this paper the proposed coupling scheme is discussed and compared to a FSI scheme where the BEM is replaced by a method based on the Reynolds-averaged Navier-Stokes equations (RANSE). Special emphasis is placed on the question of how to exchange the data between the different discretisation schemes and the development of a stable and efficient coupling scheme for FSI simulations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A symplectic analytical wave propagation model for damping and steady state forced vibration of orthotropic composite plate structure

An analytical wave propagation model is proposed in this paper for damping and steady state forced vibration of orthotropic composite plate structure by using the symplectic method. By solving an eigen-problem derived in the symplectic dual system of free bending vibration of orthotropic rectangular thin plates, the wave shape of plate is obtained in symplectic analytical form for any combination of simple boundary conditions along the plate edges. And then the specific damping capacity of wave mode is obtained symplectic analytically by using the strain energy theory. The steady state forced vibration of built-up plates structure is calculated by combining the wave propagation model and the finite element method. The vibration of the uniform plate domain of the built-up plates structure is described using symplectic analytical waves and the connector with discontinuous geometry or material is modeled using finite elements. In the numerical examples, the specific damping capacity of orthotropic rectangular thin plate with three different combinations of boundary condition is first calculated and analyzed. Comparisons of the present method results with respect to the results from the finite element method and from the Rayleigh–Ritz method validate the effectiveness of the present method. The relationship between the specific damping capacity of wave mode and that of modal mode is expounded. At last, the damped steady state forced vibration of a two plates system with a connector is calculated using the hybrid solution technique. The availability of the symplectic analytical wave propagation model is further validated by comparing the forced response from the present method with the results obtained using the finite element method.     

Investigation of constrained-layer technique using exact elasticity theory

It is possible to damp flexural waves in metal plates by means of a layer of elastomeric material with high loss factor. It was found that adding a third layer of metal enhances the damping effect. This may be explained by observing that the constraining layer increases shear in the elastomer layer, and thus increases energy loss due to the loss factor in its shear modulus.The purpose of the present investigation is to extend computational techniques by which one may decide on optimum combinations of layer thickness and material properties for a given damping application. A model proposed by Kerwin in 1959 shows the effect of the various parameters on the attenuation, but it uses thin-plate theory for the base plate and does not account for extensional waves. Kerwin's model is extended to include extentional waves. A hybrid model is presented whereby the base plate is described by exact elasticity theory. Comparison of the results from the hybrid model with those from the extended model shows the consequences of the use of exact elasticity theory.     

Numerical simulation of three-dimensional incompressible fluid in a box flow passage considering fluid–structure interaction by differential quadrature method

A numerical simulation scheme of 3D incompressible viscous fluid in a box flow passage is developed to solve Navier–Stokes (N–S) equations by firstly taking fluid–structure interaction (FSI) into account. This numerical scheme with FSI is based on the polynomial differential quadrature (PDQ) approximation technique, in which motions of both the fluid and the solid boundary structures are well described. The flow passage investigated consists of four rectangular plates, of which two are rigid, while another two are elastic. In the simulation the elastic plates are allowed to vibrate subjected to excitation of the time-dependent dynamical pressure induced by the unsteady flow in the passage. Meanwhile, the vibrating plates change the flow pattern by producing many transient sources and sinks on the plates. The effects of FSI on the flow are evaluated by running numerical examples with the incoming flow’s Reynolds numbers of 3000, 7000 and 10,000, respectively. Numerical computations show that FSI has significant influence on both the velocity and pressure fields, and the DQ method developed here is effective for modelling 3D incompressible viscous fluid with FSI.     

Modeling concept and numerical simulation of ultrasonic wave propagation in a moving fluid-structure domain based on a monolithic approach

In the present study, we propose a novel multiphysics model that merges two time-dependent problems – the Fluid-Structure Interaction (FSI) and the ultrasonic wave propagation in a fluid-structure domain with a one directional coupling from the FSI problem to the ultrasonic wave propagation problem. This model is referred to as the “eXtended fluid-structure interaction (eXFSI)” problem. This model comprises isothermal, incompressible Navier–Stokes equations with nonlinear elastodynamics using the Saint-Venant Kirchhoff solid model. The ultrasonic wave propagation problem comprises monolithically coupled acoustic and elastic wave equations. To ensure that the fluid and structure domains are conforming, we use the ALE technique. The solution principle for the coupled problem is to first solve the FSI problem and then to solve the wave propagation problem. Accordingly, the boundary conditions for the wave propagation problem are automatically adopted from the FSI problem at each time step. The overall problem is highly nonlinear, which is tackled via a Newton-like method. The model is verified using several alternative domain configurations. To ensure the credibility of the modeling approach, the numerical solution is contrasted against experimental data.     

Development of a single-layer finite element and a simplified finite element modeling approach for constrained layer damped structures

A new finite element (FE) is formulated based on an extension of previous FE models for studying constrained layer damping (CLD) in beams. Most existing CLD FE models are based on the assumption that the shear deformation in the core layer is the only source of damping in the structure. However, previous research has shown that other types of deformation in the core layer, such as deformations from longitudinal extension, and transverse compression, can also be important. In the finite element formulated here, shear, extension, and compression deformations are all included. As presented, there are 14 degrees of freedom in this element. However, this new element can be extended to cases in which the CLD structure has more than three layers. The numerical study shows that this finite element can be used to predict the dynamic characteristics accurately. However, there is a limitation when the core layer has a high stiffness, as the new element tends to predict loss factors and natural frequencies that are too high. As a result, this element can be accepted as a general computation model to study the CLD mechanism when the core layer is soft. Because the element includes all three types of damping, the computational cost can be very high for large scale models. Based on this consideration, a simplified finite modeling approach is presented. This approach is based on an existing experimental approach for extracting equivalent properties for a CLD structure. Numerical examples show that the use of these extracted properties with commercially available FE models can lead to sufficiently accurate results with a lower computational expense.     

How an added mass matrix estimation may dramatically improve FSI calculations for moving foils

This paper presents a corrected partitioned scheme for investigating fluid–structure interaction (FSI) that may be encountered by lifting devices immersed in heavy fluid such as liquids. The purpose of this model is to counteract the penalizing impact of the added mass effect on the classical partitioned FSI coupling scheme. This work is based on an added mass corrected version of the classical strongly coupled partitioned scheme presented in Song et al. (2013). Results show that this corrected version systematically allows convergence to the coupled solution. The fluid flow model considered here uses a non-stationary potential approach, commonly termed the Panel Method. The advantage of this kind of approach is twofold: first, in restricting itself to a boundary method and, second, in allowing an added mass matrix to be estimated as a post-processing phase. Whereas the classical scheme encounters an acceptable (no numerical oscillation) convergence limit for fluid densities higher than 8 kg/m³ for the considered case, our corrected scheme is not dependent on fluid density and converges with only 6 iterations. This makes it possible to investigate the dynamic behavior of a 2D foil immersed in heavy fluids such as water. For example, it recognizes that frequency shifting may occur as the consequence of a strong added mass effect.     

Modeling of viscoelastic contact-impact problems

An accurate finite element (FE) model for analyzing the response of viscoelastic structure under low-velocity impact is presented. Generalized standard linear solid (Wiechert) model is adopted to simulate the internal damping of the structure, because its capability of describing both creep and relaxation phenomena adequately. Newmark time integration scheme is proposed to transfer the problem into a static one for each time increment. The incremental convex programming method is modified to accommodate viscoelastic dynamic-contact problems. The Lagrange multiplier technique is selected to incorporate the contact condition. One, two and three-dimensional finite element model is presented to compare between the elastic and viscoelastic materials.     

Residual saturated porous media – from oscillating water blobs to waves in ground earth

A model for wave propagation in residual saturated porous media is presented distinguishing enclosed fluid clusters with respect to their eigenfrequency and damping properties. The additional micro-structure information of cluster specific damping is preserved during the formal upscaling process and allows a stronger coupling between micro- and macro-scale than characterisation via eigenfrequencies alone. A numerical example of sandstone filled with air and liquid clusters of different eigenfrequency and damping distributions is given. If energy dissipation due to viscous damping dominates energy storage due to cluster oscillations, the damping distribution is more influential than the eigenfrequency distribution and vice versa. Spreading the damping distribution around a constant mean value supported the effect of capillary forces and spreading the eigenfrequency distribution around a constant mean value supported the effect of viscous damping in the investigated samples. For a wide distribution of the liquid clusters' damping properties, two damping mechanisms of propagating waves occur at the same time: damping due to viscous effects (for highly damped clusters) and energy storage by cluster oscillations (for underdamped clusters). (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability calculation of travelling waves in a simplified brake model

We consider a system composed of an elastic tube, which is fixed at the outer boundary and in frictional contact with a rigid cylinder, rotating inside the tube about the common axis. Using a 1–mode Galerkin ansatz in radial direction, a non–smooth PDE for the tangential and radial deformations at the contact between the two bodies is obtained. It has been shown ([1]) that different types of travelling stick–slip–separation waves exist, but these waves are unstable for most parameter values. In this investigation we first enlarge the model by viscuous damping and second we introduce a larger number of nodes in radial direction for the numerical analysis. The influence of these two effects on the shape and stability of the travelling waves is studied. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structural health monitoring of hybrid composite structure with piezoelectric patches

Structural health monitoring is performed on a hybrid structure specially designed for simple assembly and disassembly or replacement of components. The net-like structure is composed of composite beams connected with aluminum pads and it is fixed to a frame in selected locations. Modal analysis is performed both experimentally and numerically. The experiment is carried out using impact hammer, accelerometer and spectrum analyzer and the frequency and damping characteristics are thus obtained. The numerical model using finite element method is validated by comparison of the calculated and measured eigenfrequencies and eigenshapes. Furthermore, piezoelectric patches are applied on selected beam. The modal analysis is carried out again using the piezoelectric patches and with some of the composite beams replaced by damaged beam. The variation in modal characteristics between original and damaged configurations is analyzed both experimentally and numerically. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Damping of Periodic Waves in Physically Significant Wave Systems

Damping of periodic waves in the classically important nonlinear wave systems—nonlinear Schrödinger, Korteweg–deVries (KdV), and modified KdV—is considered here. For small damping, asymptotic analysis is used to find an explicit equation that governs the temporal evolution of the solution. These results are then confirmed by direct numerical simulations. The undamped periodic solutions are given in terms of Jacobi elliptic functions. The damping structure is found as a function of the elliptic function modulus, m=m(t) . The damping rate of the maximum amplitude is ascertained and is found to vary smoothly from the linear solution when m= 0 to soliton waves when m= 1 .     

Numerical electroseismic modeling: A finite element approach

Electroseismics is a procedure that uses the conversion of electromagnetic to seismic waves in a fluid-saturated porous rock due to the electrokinetic phenomenon. This work presents a collection of continuous and discrete time finite element procedures for electroseismic modeling in poroelastic fluid-saturated media. The model involves the simultaneous solution of Biot’s equations of motion and Maxwell’s equations in a bounded domain, coupled via an electrokinetic coefficient, with appropriate initial conditions and employing absorbing boundary conditions at the artificial boundaries. The 3D case is formulated and analyzed in detail including results on the existence and uniqueness of the solution of the initial boundary value problem. Apriori error estimates for a continuous-time finite element procedure based on parallelepiped elements are derived, with Maxwell’s equations discretized in space using the lowest order mixed finite element spaces of Nédélec, while for Biot’s equations a nonconforming element for each component of the solid displacement vector and the vector part of the Raviart-Thomas-Nédélec of zero order for the fluid displacement vector are employed. A fully implicit discrete-time finite element method is also defined and its stability is demonstrated. The results are also extended to the case of tetrahedral elements. The 2D cases of compressional and vertically polarized shear waves coupled with the transverse magnetic polarization (PSVTM-mode) and horizontally polarized shear waves coupled with the transverse electric polarization (SHTE-mode) are also formulated and the corresponding finite element spaces are defined. The 1D SHTE initial boundary value problem is also formulated and approximately solved using a discrete-time finite element procedure, which was implemented to obtain the numerical examples presented.     

Simulation of Vortex-Induced Oscillations within a Shear Thinning Liquid

The present work discusses the impact of nonlinear shear thinning in a viscous fluid flow on the vibration behavior of an elastic bar. In the process numerical simulations have been performed concerning a well-known FSI benchmark geometry. In contrast to past investigations a non-Newtonian liquid of the Carreau-Yasuda type is used as fluid component. In order to accomplish the coupling between the liquid and the solid domain, an approach using quasi-Newton iterations is applied. In a parameter study material and geometrical parameters are changed. The solutions show distinct deviations compared to results obtained with a Newtonian liquid. These differences emphasize the nonlinearity of the shear thinning material model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

有限元模型修正问题的不精确最速下降迭代解

在结构动力分析中,往往需利用结构振动测试所得的实际测量数据(如振动频率和振型),对结构分析模型进行最优修正,使之更能合理反映结构的实际性能,其实质即为计算数学中的特征值反问题.本文考虑有阻尼结构振动中的-类反问题,用一组不完备的模态测量数据修正系统质量矩阵、刚度矩阵和阻尼矩阵,通过等价正交投影思想将原问题转化成-个闭凸锥上的正交投影问题,构造-个不精确最速下降迭代法求解,并讨论了收敛性.算例表明算法是有效的.