Added mass of a spheriod oscillating in a linearly stratified fluid

A spheriod oscillating vertically along its axis of symmetry in an otherwise-still, inviscid, incompressible, linearly stratified fluid of infinite extent is considered. Using linearized Boussinesq equation, the exact solution for the Stokes stream function is obtained for the case when the frequency of oscillation is greater than the Brunt-Väisälä frequency of the fluid. The fluid force acting on the oscillating spheriod is calculated and expressed in terms of the added mass for all range of frequency. It is found that the effect of density stratification is to reduce the added mass for high frequency when no internal gravity waves are generated. For frequency less than the Brunt-Väisälä frequency, the effect of stratification on the fluid force is to increase its magnitude and also cause a phase shift with respect to the acceleration of the spheriod.     

Finite element computation of sloshing modes in containers with elastic baffle plates

A finite element method to approximate the vibration modes of a plate in contact with an incompressible fluid is analysed in this paper. The effect of the fluid is taken into account by means of an added mass formulation, discretized by standard piecewise linear tetrahedral finite elements. Gravity waves on the free surface of the liquid are considered in the model. The plate is modelled by Reissner–Mindlin equations discretized by MITC3 locking‐free elements. Implementation issues are discussed and numerical experiments are presented. In particular, the method is compared with analytical approximations and with an experimental study which has been recently reported. Copyright © 2002 John Wiley & Sons, Ltd.     

Added mass computation by the boundary integral method

Computational techniques for the treatment of fluid-structure interaction effects by discrete boundary integral methods are examinde. Attention is focused on the computation of the added mass matrix by finite element methods for a structure submerged in an infinite, inviscid, incompressible fluid. A general computational procedure is presented that is based upon a variational approach involving the assumption of constant source strength over each surface element. This is followed by an analysis of the discretization error for a spherical body that is then used to develop a hierarchy of computational schemes. These schemes are than evaluated numerically in terms of ‘fluid boundary modes’ for a submerged spherical surface. One scheme has been found to be surprisingly accurate in relation to its computational demands.     

结构在静流场中振动时的附加质量分布

结构在静流场中振动时,附加质量的分布形式对其振动特性有非常大的影响,尤其是对较为轻薄的结构,但截至目前,对附加质量显式分布的研究甚少。基于三维问题的边界元法,在合适的Dirichlet及Neumann条件下,提出了一种较简单的方法,可求解结构以任意给定模式在不可压缩单相静流场中振动时的附加质量显式分布。数值计算表明,该方法的求解结果与理论解及实验结果吻合良好,可较好地应用于复杂形状结构在有界或无界静流场中振动时的附加质量分布计算。     

Vibration analysis of fluid–solid systems using a finite element displacement formulation

This report presents a finite element solution for the vibration interaction between an inviscid fluid and a solid. The equation of motion governing the inviscid fluid is expressed in terms of the displacements. This ensures that compatibility and equilibrium will be satisfied automatically along the interface of the coupled systems. To suppress circulation modes with non-zero energy, reduced integration is used when computing the element stiffness matrix contributed by the fluid. In addition, a projection is used on the element mass matrix in order to remove the spurious modes which result from the use of reduced integration. Numerical examples for both fluid and coupled fluid–solid systems are performed and the results are shown.     

障板上矩形薄板在浅水环境中的振动及声辐射解析分析

通过推导得到浅水环境中矩形板声辐射阻抗矩阵的解析表达,进一步结合振动假设模态方法及辐射表面单元辐射器思想求解浅水环境中矩形板的振动响应,分析水深对矩形板模态附加质量的影响,给出矩形板模态附加质量随水深的变化情况,得到波导模态的激发对附加质量的影响,并通过对辐射抗矩阵的特征分析得到附加质量在板上分布的主要模式;进一步结合声辐射模态辐射效率,分析水深变化对矩形板振动响应峰值及远场声辐射的影响,分析结果表明:水深度变化对振动响应峰值及声辐射功率的影响与第1阶声辐射模态的辐射效率随深度的变化具有一致性。     

The added-mass coefficients of a torus

Summary The generalised added-mass coefficients of a torus in translatory and rotational motion in an inviscid incompressible fluid are obtained via an exact solution of Laplace's equation in toroidal coordinates. Of the six possible independent coefficients three are found to have nonzero, finite and separate values, due to symmetry. These are translation in, and perpendicular to the ring plane and rotation around a diameter. For translation normal to the ring plane, the added mass is somewhat larger than the mass of the torus of equal density. This coefficient tends to the torus mass for slender tori (large ratio of ring to core diameters). For translation in the ring plane the added mass tends to one half the torus mass, and for rotation the added inertia is approximately the torus moment of inertia for such slender tori. Simple relations for the added-mass coefficients as a function of the diameter ratio for general tori are also presented.     

Theoretical and experimental study of mass sensitivity of PSAW-APMson ZX-LiNbO3

Acoustic plate mode (APM) devices have recently been used as sensing elements, both for the physical measurement of fluid properties and in biosensor applications. One of the primary interaction mechanisms in these devices is mass loading caused by the added mass bound to the layered crystal surface. However, the material properties of these thin composite layers are not well characterized or known as is required in order to accurately predict the sensor response. In the present work, perturbation theory is used to derive expressions for the sensitivity of the APM sensors to mass loading and viscoelastic stiffening. Mass sensitivity experiment was conducted on ZX-LiNbO₃ in a liquid environment to accurately reflect the sensitivity of an actual biosensor and the results are compared to theory. The measured data show a f² dependence for the mass sensitivity for APMs on ZX-LiNbO₃ in the measured frequency range, which indicates a SAW-like behavior. This behavior is due to the fact that the acoustic plate modes on ZX-LiNBO₃ are pseudo-SAW (PSAW) derived, and the acoustic energy is confined to the sensing surface. As a result, the APMs on ZX-LiNbO₃ are referred to as PSAW-APMs. Discussions are given in terms of the added mass which occurs in typical biosensor applications     

静水中反应堆吊篮结构的振动特性研究

将吊篮与压力容器视为包含粘性流体的有限长同心圆柱壳体结构。从圆柱壳的运动控制微分方程和流体的 N- S方程出发 ,在流体不可压缩粘性假设下 ,导出吊篮结构自由振动时 ,流体作用于壳体结构上的附加质量、附加阻尼矩阵。再结合固体有限元技术 ,建立吊篮结构的流固耦合振动的有限元模型。用此模型对吊篮结构在静水中的固有振动特性进行分析 ,计算结果与试验实测结果的比较表明 ,本文方法能较好地满足工程分析要求     

三维结构振动诱导流场附加质量的数值分析

在流体环境中,结构的振动会诱导周边的流体一起运动从而产生附加质量的影响,这也是结构工程中大跨度柔性结构耦合风振理论模型的重要组成部分。根据势流理论,采用奇点配置法利用空间点源(汇)及偶极子基本解推导了三维情形下结构振动诱导流场附加质量的计算式。数值分析结果表明:该方法能有效地计算复杂结构边界条件下流场的附加质量;其中索穹顶结构的数值算例也表明,在这类大跨度柔性结构的风振分析中附加质量的影响是很大的,必须引起足够的重视。     

Improved fractional step method for simulating fluid‐structure interaction using the PFEM

Numerical difficulties are present in the particle finite element method even though it has been shown to be a powerful and effective approach to simulating fluid‐structure interaction. To overcome problems of mass loss on the free surface and the added‐mass effect, an improved fractional step method (FSM) that handles added‐mass terms in a mathematically exact way is developed. A further benefit is that no assumptions regarding the structural response are made in handling added‐mass terms, thus it is straightforward to incorporate material nonlinearity in fluid‐structure interaction (FSI) under this approach. Patch tests and comparisons with experimental data are presented in order to verify and validate the improved FSM for FSI applications. The computational cost of this approach is shown to be negligible compared with the other aspects of the FSM, particularly when the size of the structure and the fluid‐structure interface is small relative to the volume of fluid. Copyright © 2014 John Wiley & Sons, Ltd.     

Evaluation of added mass by a cloning algorithm

In problems of structure interaction with infinite surrounding of incompressible, inviscid fluid media, added mass matrices on wet surfaces have been considered for modelling the effects of outgoing waves. For an arbitrary geometry of the wet surface, an expression for the added mass matrix is derived according to a finite element procedure which utilizes the force-displacement relations of representative elements on the boundary. In the element mass matrix a certain symmetry, which characterizes interactions between the interior and exterior surfaces, helps reduce the quadratic matrix equation of the cloning algorithm to a linear eigenvalue problem. A benchmark example is included to establish the numerical accuracy of the proposed formulation.     

Acceleration sensitivity of crystal resonators affected by the mass and location of electrodes

Predominant thickness-shear frequencies and modes of a crystal plate with electrodes of arbitrary shape and mass distribution are obtained by a finite-element method, based on Mindlin's first-order equations with platings. These frequencies and modes are used in a perturbation method for computing the acceleration sensitivity of crystal resonators with electrodes. Computations are made for a square AT-cut quartz plate that is supported by a four-point mount and coated with identical square and uniform electrodes on the upper and lower faces of the plate. To study the effect of uneven distribution of electrode mass, acceleration sensitivities are calculated when a small mass is added at various locations near the edges of the square electrodes. It is found that the percent increase of the acceleration sensitivity of the resonator with a small added mass to that of the resonator without added mass ranges from 3.8% to 541.7%, depending on the location of the small mass placed at the edges of the electrodes.     

An Arbitrary Lagrangian-Eulerian finite element method

This paper describes an Arbitrary Lagrangian- Eulerian (ALE) finite element method for the simulation of fluid domains with moving structures. The fluid is viscous, incompressible and unsteady and the fluid motion is solved by a fractional step discretization of the Navier-Stokes equations. The emphasis is on convection dominated flows, and a three-step method is used for the convection term. The moving structure causes the mesh of the fluid domain to move, and a new algorithm is proposed to solve the important and crucial problem of the calculation of the mesh velocities. Numerical calculations of the added mass and added damping of a vibrating two-dimensional circular cylinder in the frequency Reynolds number range Re _w =20−2000 are performed to evaluate the proposed ALE finite element method. The numerically calculated added mass and added damping are compared to both analytical and numerical results. To further demonstrate the generality of the method, a numerical simulation of flow past an oscillating schematic sports car is presented.     

Guided waves propagating in a bi-layer system consisting of a piezoelectric plate and a dielectric fluid layer

This study employs a theoretical modeling and an experimental measurement for investigating the dispersion behavior of guided waves propagating in a bi-layer system consisting of a piezoelectric plate and a dielectric fluid layer. The theoretical model is based on a recursive asymptotic stiffness matrix method (RASM) with the fluid layer modeled as an equivalent elastic body. A laser ultrasound technique is used to measure the dispersion relations of the bi-layer system. Behaviors of mode couplings between guided modes propagating in the piezoelectric plate and those in fluid layer are characterized in the modeling and measurements. Dispersion behaviors of guided modes propagating in the bi-layer system are discussed for varying fluid thicknesses. For all of the investigated cases, the theoretical modeled dispersion spectra agree well with the measurements.     

Coupled analysis on the thickness-shear vibrations of a quartz plate resonator covered with micro-beams immersed in inviscid liquid and computation of the induced frequency-shift by the surface loadings

The dynamic equations of a quartz crystal resonator (QCR) vibrating in the thickness-shear modes (TSM) with the upper surface covered by an array of micro-beams, while the micro-beams are immersed in inviscid liquid, is established. A frequency-dependent effective mass ratio is put forward to simulate the effect of surface loadings (micro-beams immersed in liquid) on the dynamic characteristics of QCR. The seeping depth of vibration energy into liquid is analyzed and the added mass of liquid to micro-beams is examined. The induced frequency-shift of the compound QCR system consisting of QCR and the surface loadings is calculated in detail.     

Nanobeam sensor for measuring a zeptogram mass

Single-walled carbon nanotubes (SWCNTs) have attracted intense interest in recent years due to their suitability for a wide range of applications, such as nano-sensors and nano-actuators. The primary objective of this paper is presenting a simplified nonlocal finite element model to investigate the potential application of CNTs as a nanomechanical mass sensor. Nonlocal differential elasticity of Eringen is exploited to reveal the long-range interactions between atoms. The CNT resonator is proposed as a bridge Euler–Bernoulli nanobeam with attached mass. An efficient finite element model is developed to discretize the nanobeam domain and solve the equation of motion numerically. The effect of nonlocal parameter on vibration characteristics is discussed and compared with published works. The effects of added mass on the nonlocal frequency shift percentage and higher vibrational modes are discussed in details. Numerical results show that the mass sensitivity of the nanotube sensor is in the zeptogram range.     

Viscoplastic response of a circular plate to an underwater explosion shock

Summary Viscoplastic response of a fully-clamped circular plate to an underwater explosion shock is studied in this paper. Strain-rate effect is included in the response. A fluid-structure interaction model is introduced, which is characterized by two stages: In the early stage, only the shock wave in water is considered, and the motion of structure is neglected. In the second stage, the wave propagation in structure and fluid is disregarded, and only long-term fluid force (added mass) and long-term structural force (membrane stress) are considered. Based on this model, the equation of motion of a fully-clamped circular plate is established, the solutions of which are compared with two experiments. The calculated maximum plastic deformations from present model are close to the observed values. The dependence of maximum plastic deformation on charge weight, plate radius and material property is also discussed.     

A projection semi‐implicit scheme for the coupling of an elastic structure with an incompressible fluid

We address the numerical simulation of fluid–structure systems involving an incompressible viscous fluid. This issue is particularly difficult to face when the fluid added‐mass acting on the structure is strong, as it happens in hemodynamics for example. Indeed, several works have shown that, in such situations, implicit coupling seems to be necessary in order to avoid numerical instabilities. Although significant improvements have been achieved during the last years, solving implicit coupling often exhibits a prohibitive computational cost. In this work, we introduce a semi‐implicit coupling scheme which remains stable for a reasonable range of the discretization parameters. The first idea consists in treating implicitly the added‐mass effect, whereas the other contributions (geometrical non‐linearities, viscous and convective effects) are treated explicitly. The second idea, relies on the fact that this kind of explicit–implicit splitting can be naturally performed using a Chorin–Temam projection scheme in the fluid. We prove (conditional) stability of the scheme for a fully discrete formulation. Several numerical experiments point out the efficiency of the present scheme compared to several implicit approaches. Copyright © 2006 John Wiley & Sons, Ltd.