Non-linear hydrodynamics of thin laminae undergoing large harmonic oscillations in a viscous fluid

Smoothed Particle Hydrodynamics is implemented to study the motion of a thin rigid lamina undergoing large harmonic oscillations in a viscous fluid. Particularly, the flow physics in the proximity of the lamina is resolved and contours of non-dimensional velocity, vorticity and pressure are presented for selected oscillation regimes. The computation of the hydrodynamic load due to the fluid–structure interaction is carried out using Fourier decomposition to express the total fluid force in terms of a non-dimensional complex-valued hydrodynamic function, whose real and imaginary parts identify added mass and damping coefficients, respectively. For small oscillations, the hydrodynamic force reflects the harmonic nature of the displacement, whereas multiple harmonics are observed as both the amplitude and frequency of oscillation increase. We propose a novel formulation of hydrodynamic function that incorporates added mass and damping coefficients for a thin rigid lamina spanning large amplitudes in viscous fluids in a broad range of the oscillation frequencies. Results of the simulations are validated against numerical and experimental works available in the literature in addition to theoretical predictions for the limit case of zero-amplitude oscillations.     

Finite amplitude oscillations of flanged laminas in viscous flows: Vortex–structure interactions for hydrodynamic damping control

In this paper, we study the problem of harmonic oscillations of a flanged lamina in a quiescent Newtonian incompressible viscous fluid. We conduct a comprehensive fluid–structure interaction investigation with the goal of assessing the effect of the presence of the flanges on the added mass and hydrodynamic damping experienced by the oscillating solid. We determine the complex nonlinear hydrodynamic function incorporating these effects via its real and imaginary parts, respectively, and its dependence on three nondimensional parameters that govern the flow evolution. We further investigate in detail the flow physics and the effects of nonlinearities on vortex shedding, convection, and diffusion in the vicinity of the oscillating structure. We find that the added mass effect is relatively independent of the oscillation amplitude and increases with the flange size. On the other hand, the hydrodynamic damping effect is remarkably affected by the interplay of geometry and dynamic parameters resulting into a peculiar non-monotonic behavior. We show the existence of a minimum in the hydrodynamic damping which can be attained via specific control of vortex–structure interaction dynamics and discuss its properties and significance from a physical perspective through analysis of the relevant flow fields. This novel finding has potential application for damping reduction in elastic systems where reduction of energy losses and increase of oscillation quality factor are desired.     

Fluid–structure interaction analysis of flexible composite marine propellers

There is an increasing interest in the marine industry to use composites to improve the hydrodynamic and structural performance of naval structures. Composite materials have high strength-to-weight and stiffness-to-weight ratios, and the fiber orientations can be exploited to tailor the structural deformation to reduce the load and stress variations by automatically adjusting the shape of the structure. For marine propellers, the bending–twisting coupling characteristics of anisotropic composites can be exploited to passively tailor the blade rake, skew, and pitch distributions to improve propeller performance. To fully explore the advantages of composite marine propellers, a coupled boundary element (BEM) and finite element (FEM) approach is presented to study the fluid–structure interaction of flexible composite propellers in subcavitating and cavitating flows. An overview of the formulation for both the fluid and structural models is presented. Experimental validation studies are shown for two composite propellers tested at the Naval Surface Warfare Center (NSWCCD). The feasibility of passive hydroelastic tailoring of composite marine propellers is discussed.     

A comparison of boundary element and finite element methods for modeling axisymmetric polymeric drop deformation

A modified boundary element method (BEM) and the DEVSS‐G finite element method (FEM) are applied to model the deformation of a polymeric drop suspended in another fluid subjected to start‐up uniaxial extensional flow. The effects of viscoelasticity, via the Oldroyd‐B differential model, are considered for the drop phase using both FEM and BEM and for both the drop and matrix phases using FEM. Where possible, results are compared with the linear deformation theory. Consistent predictions are obtained among the BEM, FEM, and linear theory for purely Newtonian systems and between FEM and linear theory for fully viscoelastic systems. FEM and BEM predictions for viscoelastic drops in a Newtonian matrix agree very well at short times but differ at longer times, with worst agreement occurring as critical flow strength is approached. This suggests that the dominant computational advantages held by the BEM over the FEM for this and similar problems may diminish or even disappear when the issue of accuracy is appropriately considered. Fully viscoelastic problems, which are only feasible using the FEM formulation, shed new insight on the role of viscoelasticity of the matrix fluid in drop deformation. Copyright © 2001 John Wiley & Sons, Ltd.     

A boundary element method and spectral analysis model for small‐amplitude viscous fluid sloshing in couple with structural vibrations

A boundary element method (BEM) is presented for the coupled motion analysis of structural vibrations with small‐amplitude fluid sloshing in two‐dimensional space. The linearized Navier–Stokes equations are considered in the frequency domain and transformed into a Laplace equation and a Helmholtz equation with pure imaginary constant. An appropriate fundamental solution for the Helmholtz equation is provided. The conditions of zero stress are imposed on the free surface, and non‐slip conditions of fluid particles are imposed on the walls of the container. For rigid motion models, the expressions for added mass and added damping to the structural motion equations are obtained. Numerical examples are presented. Copyright © 2000 John Wiley & Sons, Ltd.     

A coupled FEM/BEM approach and its accuracy for solving crack problems in fracture mechanics

The finite element (FEM) and the boundary element methods (BEM) are well known powerful numerical techniques for solving a wide range of problems in applied science and engineering. Each method has its own advantages and disadvantages, so that it is desirable to develop a combined finite element/boundary element method approach, which makes use of their advantages and reduces their disadvantages. Several coupling techniques are proposed in the literature, but until now the incompatibility of the basic variables remains a problem to be solved. To overcome this problem, a special super-element using boundary elements based on the usual finite element technique of total potential energy minimization has been developed in this paper. The application of the most commonly used approaches in finite element method namely quarter-point elements and J-integrals techniques were examined using the proposed coupling FEM–BEM. The accuracy and efficiency of the proposed approach have been assessed for the evaluation of stress intensity factors (SIF). It was found that the FEM–BEM coupling technique gives more accurate values of the stress intensity factors with fewer degrees of freedom.     

Numerical investigation of ice breaking by a high-pressure bubble based on a coupled BEM-PD model

In this paper, by combining the boundary element method (BEM) and peridynamics (PD), a bubble-ice interaction model is established, which can investigate the dynamic interactions between a high-pressure bubble and an ice plate with particular focus on the mechanical behaviors of ice breaking. The bubble dynamics are solved by BEM based on the potential flow theory. Ice cracks initiation and propagation are simulated by the bond-based peridynamics which is validated by a three-point bending test. The fluid–structure interaction (FSI) is achieved by matching the normal velocity and hydrodynamic loads at the fluid–structure interface. To validate the proposed FSI model, an experiment is carried out in which an oscillating bubble is generated under an ice plate by underwater discharge system. The whole interaction process is captured by a Phantom V711 high-speed camera. Qualitative agreements are achieved between the numerical and experimental results. The underlying mechanism of cracks initiation, propagation, branching, and coalescence of the ice plate is found to highly depend on three parameters, i.e., bubble–ice distance, ice thickness and bubble size. The present study is expected to provide further assists in the understanding of ice breaking problems.     

大型复杂圆柱壳中高频振动噪声仿真计算方法研究

建立大型复杂圆柱壳中高频振动噪声仿真计算方法,对于解决船舶和飞机等大型复杂结构的辐射噪声预报问题具有重要意义。介绍了完美匹配层流固耦合计算方法,并成功应用于大型复杂双层圆柱壳的水下辐射噪声预报,相对于传统的声学流固耦合有限元和边界元计算方法,使外部流场域模型至少缩小了11/15。探讨了环频率和阻尼对圆柱壳结构振动传递的影响,提出了求解中高频声学问题时大型圆柱壳复杂结构仿真建模处理方法。数值算例表明,发展的PML方法和模型简化方法是合理的,可应用工程问题研究。     

圆形空心截面约束层阻尼梁整体单元建模与振动分析

增加阻尼对结构振动抑制具有很重要的意义,为克服三维有限元建模单元数量较大的问题,采用整体单元方法求解圆形空心截面约束阻尼梁的拉伸、弯曲和扭转振动。分析结果同三维有限元分析结果作了比较,证明了该方法的可行性,为圆形截面构件组成的刚架和桁架结构约束阻尼层振动抑制分析提供了简单的计算方法。     

INITIALLY TENSIONED ORTHOTROPIC CYLINDRICAL SHELLS CONVEYING FLUID: A VIBRATION ANALYSIS

A linear analysis of the vibratory behaviour of initially tensioned orthotropic circular cylindrical shells conveying a compressible inviscid fluid is presented. The model is based on the three-dimensional nonlinear theory of elasticity and the Eulerian equations. A nonlinear strain–displacement relationship is employed to derive the geometric stiffness matrix due to initial stresses and hydrostatic pressures. Frequency-dependent fluid mass, damping and stiffness matrices associated with inertia, Coriolis and centrifugal forces, respectively, are derived through the fluid–structure coupling condition. The resulting equation governing the vibration of fluid-conveying shells is solved by the finite element method. The free vibration of initially tensioned orthotropic cylindrical shells conveying fluid is investigated; numerical examples are given and discussed.     

Time-harmonic BEM for 2-D piezoelectricity applied to eigenvalue problems

We will derive the fundamental generalized displacement solution, using the Radon transform, and present the direct formulation of the time-harmonic boundary element method (BEM) for the two-dimensional general piezoelectric solids. The fundamental solution consists of the static singular and the dynamics regular parts; the former, evaluated analytically, is the fundamental solution for the static problem and the latter is given by a line integral along the unit circle. The static BEM is a component of the time-harmonic BEM, which is formulated following the physical interpretation of Somigliana’s identity in terms of the fundamental generalized line force and dislocation solutions obtained through the Stroh–Lekhnitskii (SL) formalism. The time-harmonic BEM is obtained by adding the boundary integrals for the dynamic regular part which, from the original double integral representation over the boundary element and the unit circle, are reduced to simple line integrals along the unit circle.The BEM will be applied to the determination of the eigen frequencies of piezoelectric resonators. The eigenvalue problem deals with full non-symmetric complex-valued matrices whose components depend non-linearly on the frequency. A comparative study will be made of non-linear eigenvalue solvers: QZ algorithm and the implicitly restarted Arnoldi method (IRAM). The FEM results whose accuracy is well established serve as the basis of the comparison. It is found that the IRAM is faster and has more control over the solution procedure than the QZ algorithm. The use of the time-harmonic fundamental solution provides a clean boundary only formulation of the BEM and, when applied to the eigenvalue problems with IRAM, provides eigen frequencies accurate enough to be used for industrial applications. It supersedes the dual reciprocity BEM and challenges to replace the FEM designed for the eigenvalue problems for piezoelectricity.     

考虑水弹性影响的水下航行体结构动响应研究

考虑水弹性的影响,计及惯性力、水动力和弹性力之间的相互耦合作用,将水动力学方程和结构动力学方程联合求解,采用三维势流理论和边界元法推导并计算了水下航行体结构的附加质量矩阵,对带空泡水下航行体出水过程中的结构动响应问题进行了分析.      

BEM–FEM coupling for the analysis of flexible propellers in non-uniform flows and validation with full-scale measurements

The first part of the paper presents a partitioned fluid–structure interaction (FSI) coupling for the non-uniform flow hydro-elastic analysis of highly flexible propellers in cavitating and non-cavitating conditions. The chosen fluid model is a potential flow solved with a boundary element method (BEM). The structural sub-problem has been modelled with a finite element method (FEM). In the present method, the fully partitioned framework allows one to use another flow or structural solver. An important feature of the present method is the time periodic way of solving the FSI problem. In a time periodic coupling, the coupling iterations are not performed per time step but on a periodic level, which is necessary for the present BEM–FEM coupling, but can also offer an improved convergence rate compared to a time step coupled method. Thus, it allows to solve the structural problem in the frequency domain, meaning that any transients, which slow down the convergence process, are not computed. As proposed in the method, the structural equations of motion can be solved in modal space, which allows for a model reduction by involving only a limited number of mode shapes.The second part of the paper includes a validation study on full-scale. For the full-scale validation study a purposely designed composite propeller with a diameter of 1 m has been manufactured. Also an underwater measurement set-up including a stereo camera system, remote control of the optics and illumination system has been developed. The propeller design and the underwater measurement set-up are described in the paper. During sea trials blade deflections have been measured in three different positions. A comparison between measured and calculated torque shows that the measured torque is much larger than computed. This is attributed to the differences between effective and nominal wakefields, where the latter one has been used for the calculations. To correct for the differences between measured and computed torque the calculated pressures have been amplified accordingly. In that way the deformations which have been computed with the BEM–FEM coupling for non-uniform flows became very similar to the measured results.     

非连续边界元——有限元耦合方法分析

对边界元－有限元耦合方法进行了分析，采用非连续元离散边界积分方程，解决了耦合分析中自由度约束问题，给出了非连续边界元同有限元耦合的具体实施步骤，通过对二维弹性力学和流＝固耦合问题分析，表明了该文方法的有效性。     

Wave propagation in a fluid wedge over a solid half-space – Mesh-free analysis with experimental verification

Interaction between a bounded ultrasonic beam and a liquid wedge over a solid half-space is studied. A semi-analytical technique called distributed point source method (DPSM) is adopted for modeling the ultrasonic field in a wedge shaped fluid structure over a solid half space. This study is important for analyzing the ultrasonic waves used for the non-destructive inspections of partially immersed structures. It is also useful for studying the effect of underwater ultrasonic or acoustic wave experiments on marine lives near the shore. The problem geometry considers a bounded acoustic beam striking a fluid–solid interface between a fluid wedge and a solid half-space at steady-state. Solution of this problem is beyond the scope of the currently available analytical methods when the beam is bounded. Only numerical method (boundary element method (BEM) or finite element method (FEM)) based packages (e.g. PZFlex) are in principle capable of modeling ultrasonic fields in such structures. At high frequencies FEM and BEM based packages require huge amount of computation memory and time for their executions that DPSM technique can avoid. Effect of the angle of strike and the fluid wedge angle variation on the wave propagation characteristics is studied. Theoretical predictions are compared with some experimental results.     

具有中心圆孔的[0°/90°]_s复合材料层合板的边界元法分析

本文在文[1]的基础上,采用子结构法建立了多层复合板的边界元方法,对具有中心园孔[0°/90°]_s的层合板的层间应力作了计算,同有限元法的结果进行了比较,结果表明,应用边界元法处理这类问题,单元划分少,节约了计算机时,而且有较高的计算精度。     

二维弹性结构入水冲击过程中的流固耦合效应

描述了一个研究弹性结构入水冲击过程中水弹性效应的数值方法,在弹性结构入水冲击过程中,流体域作用在结构上的水动力载荷由边界元法获得,而结构的弹性动力响应则由有限元方法求解,通过线性给离散Ｂｅｒｎｏｕｌｌｉ方程将有限元方程和边界元方程耦合到一起,从而获得了求解流场和结构动力响应的相互耦合的运动方程。在数值考虑了自由表面的非线性边界条件,通过引入射流单元以及最大射流厚度,较好地处理了冲击引起的射流问题。     

航天器噪声试验中结构振动响应预示方法研究

航天器在随运载火箭发射过程中要承受严酷的噪声环境,需通过噪声试验来检验航天器承受噪声环境并能正常工作的能力.航天器噪声试验中结构振动的响应特性是结构强度设计应该考虑的因素之一,更是制定器上组件随机振动试验条件的重要依据,因此有必要在航天器研制初期对噪声载荷作用下的结构振动进行响应预示.文章应用商用有限元分析软件MSC.Patran和MSC.Nastran建立了某型号航天器结构舱板的有限元模型,将噪声载荷声压谱转换为脉动压力功率谱密度,进而采用模态法分析结构在噪声载荷作用下的随机振动响应,并将仿真预示结果与试验结果进行对比研究,在仿真分析中考虑阻尼参数模型和流场附加质量效应等因素的影响;通过研究表明:采用阻尼比随频率提高而减小的经验阻尼参数模型可以较好地反映中高频响应特性、得到较为准确的总均方根响应分析结果,进一步采用虚拟质量法考虑流场附加质量效应可以得到较为准确的功率谱密度响应分析结果.文章提出的仿真分析方法建模简便、计算成本低,适用于在航天器研制初期对航天器噪声试验中的结构振动进行响应预示.      

Numerical and experimental studies on the hydrodynamic damping of a zero-thrust propeller

Fluid added mass and damping are significant parameters when predicting the dynamic response of a submerged structure. The hydrodynamic damping of underwater rotating machinery is numerically and experimentally investigated by a zero-thrust propeller in this paper. The lifting surface method(LSM) combined with forced vibration was introduced as the numerical method to compute the corresponding unsteady thrust, while the experimental method of measuring added damping was accomplished by a propeller undergoing rotation combined heave motion. Results of the theoretical method are in good agreement with the experimental results before cavitation occurs, as cavitation is regarded to weaken the unsteady response of the propeller partly. The calculation results also show that both the frequency ratio(vibration frequency divided by rotation frequency) and the blade angle have a significant influence on the hydrodynamic damping. Therefore, the effect of blade angle on hydrodynamic damping should be considered during the design phase.