Added Mass Models Research Articles

A 2D non-water substructure model in time domain for breakwater-water-bedrock (layered) system excited by inclined seismic waves

The coastal structures, such as breakwaters and reefs, are usually vulnerable to the strong earthquake waves propagating through their bedrock foundation. This study proposes a 2D non-water substructure model in time domain for breakwater-water-bedrock (layered) (BWB) system, where the fluid-solid dynamic interaction is embodied by added mass and the equivalent seismic loading calculated from ocean free-field (without structure) accomplishes the inclined incidence of P or SV wave with any angle. Besides, the cutoff boundaries of the fluid are applied exact absorbing boundary conditions (ABCs) to simulate the far-field of water while the viscous-spring ABCs are employed to simulate the far-field of bedrock. Then, the accuracy of substructure method is verified by some numerical examples. However, the exact added mass matrix is fully populated and not easy to use for general software. Therefore, the simplified added mass models for water-bedrock system, water-structure system and BWB system are furtherly developed, including the relevant simplified formulas fitted by curve fitting method. Additionally, the numerical results indicate the good effectiveness of proposed model.

Power-Law Scaling of Early-Stage Forces during Granular Impact.

We experimentally and computationally study the early-stage forces during intruder impacts with granular beds in the regime where the impact velocity approaches the granular force propagation speed. Experiments use 2D assemblies of photoelastic disks of varying stiffness, and complimentary discrete-element simulations are performed in 2D and 3D. The peak force during the initial stages of impact and the time at which it occurs depend only on the impact speed, the intruder diameter, the stiffness of the grains, and the mass density of the grains according to power-law scaling forms that are not consistent with Poncelet models, granular shock theory, or added-mass models. The insensitivity of our results to many system details suggests that they may also apply to impacts into similar materials like foams and emulsions.

Study on added mass of a circular curved membrane vibrating in still air

It is widely known that added mass has a significant influence on the natural frequency of membrane structures. Previously, some experimental studies on the added mass of flat membranes have been performed. However, the added mass of curved membrane vibrating in still air is unclear. In this study, first, vibration tests of a circular curved membrane in still air with various air pressures are conducted, and the natural frequencies of the circular curved membrane are identified with the Hilbert–Huang transform (HHT). An approximate estimation of the added mass coefficient of the circular curved membrane is given as 0.65 by fitting results of tests. Then, the efficiencies of two added mass models, one as simplified added mass method and the other as numerically analysis method established by using the Boundary Element Method (BEM), are verified by the circular curved membrane tests. At last, the Modal Assurance Criterion (MAC) values indicate that for uniform mass distribution of the circular curved membrane, there is little difference between the mode shapes of the membrane vibrating in vacuum and in air.

Void fraction influence on added mass in a bubbly flow

This paper proposes a relation for the added mass coefficient of spherical bubbles depending on void fraction based on results obtained by a semi-analytical method.This information is essential to completely characterize finely dispersed bubbly flows, where small spherical gas bubbles are present in a continuous liquid phase. Most of the closure relations for Euler–Euler or Euler–Lagrange models are obtained from experiments involving single bubbles. Their applicability to systems with high void fraction is therefore questionable.This paper uses solid harmonics to solve 3D potential flow around bubbles. Several configurations were calculated for different numbers of particles and spatial configurations. Our results are compared with previous studies. Depending on the model proposed by previous authors, added mass forces could increase or decrease with void fraction. This paper solves these discrepancies by underlining the effect of induced added mass.The main purpose of this work is to develop simple formulas fitting our semi-analytical results. These simple formulas are suitable for further use, particularly as added mass models for multiphase flow averaged equations.

Numerical analysis of added mass for open flat membrane vibrating in still air using the boundary element method

Added mass has significant effect on the vibration of membrane structures, which cannot be ignored during vibration analysis. Actually, the added mass of typical objects, such as cylinders and spheres, moving in fluid with acceleration have been widely investigated. However, research on the added mass of flexible structures is still limited. Although several numerical methods had been developed to investigate the added mass of flexible structures, the efficiency of the numerical methods is not verified by experiment tests. In this study, a framework to numerically analysis the added mass of open flat membranes has been established by using the Boundary Element Method (BEM). In order to evaluate hypersingular integral, the Stokes formula converting the surface integral to the curvilinear integral is used. Two added mass models are discussed, one only considering the effect of the membrane geometric shape, and another considering the effect of the geometric shape and the mode shape of membranes. Based on comparative analysis between numerical results and experimental results, it is shown that the added mass only considering the effect of geometric shape can agree well with the test results in low-order modes, however, the error will be increased as the order of vibration modes increasing. The added mass considering the effect of the geometric shape and the mode shape can have much better conformity with the test results both in low-order modes and high-order modes. The Modal Assurance Criterion (MAC) is used to compare the mode shapes of membranes vibrating in vacuum and in air. MAC values indicate that for uniform mass distribution of the membrane, there is little difference between the mode shapes of the membrane vibrating in vacuum and in air, while for nonuniform mass distribution of the membrane, the difference between the mode shapes of the membrane vibrating in vacuum and in air is little in low modes and is large in high modes.

Seismic response of intake towers including dam–tower interaction

AbstractThe seismic response of the intake–outlet towers has been widely analyzed in recent years. The usual models consider the hydrodynamic effects produced by the surrounding water and the interior water, characterizing the dynamic response of the tower–water–foundation–soil system. As a result of these works, simplified added mass models have been developed. However, in all previous models, the surrounding water is assumed to be of uniform depth and to have infinite extension. Consequently, the considered added mass is associated with only the pressures created by the displacements of the tower itself. For a real system, the intake tower is usually located in proximity to the dam and the dam pressures may influence the equivalent added mass. The objective of this paper is to investigate how the response of the tower is affected by the presence of the dam. A coupled three‐dimensional boundary element‐finite element model in the frequency domain is employed to analyze the tower–dam–reservoir interaction problem. In all cases, the system response is assumed to be linear, and the effect of the internal fluid and the soil–structure interaction effects are not considered. The results suggest that unexpected resonance amplifications can occur due to changes in the added mass for the tower as a result of the tower–dam–reservoir interaction. Copyright © 2008 John Wiley & Sons, Ltd.

Effect of Pre-stress States on the Impulsive Modes of Vibration of Cylindrical Tank-liquid Systems under Horizontal Motions

In this paper we investigate the influence of hydrostatic pressure and self-weight loads (pre-stress state) on the natural periods and mode shapes of steel cylindrical tanks and on the response under horizontal motions. The tank structure is modeled with finite elements and added mass models are used to represent the liquid. Only the impulsive component of the hydrodynamic response is considered. The natural periods and mode shapes for tank-liquid systems including and neglecting the effect of the pre-stress state are computed and compared. Three tank-liquid systems with different cylinder height to diameter ratios and slenderness ratios are considered. The numerical results show that the pre-stress state has a significant influence in the natural periods and mode shapes of tank-liquid systems with thinner walls; however, for thicker shells this effect is reduced. When the pre-stress state is neglected and included, the smaller differences in natural periods occur, for modes characterized by small circumferential wavenumbers. The steady-state response of a tank-liquid system to horizontal harmonic base accelerations was also computed. Large differences were found when the pre-stress state was neglected. A comparison of the frequency response functions shows that the peak responses occur at quite different load periods and they have significantly different amplitudes.

Impact Vibration Analysis of Group of Hexagonal Bars Immersed in Liquid

A simulation method was developed to calculate the vibrational response of a group of hexagonal bars installed in a restraint immersed in liquid during seismic excitation. The influence of fluid force on structural motion was modeled using an added-mass matrix. This matrix was then transformed into the space composed of the eigenmodes of the hexagonal bars without added mass and used for eigenvalue analysis of the entire bar-group structure. This method reduced the computational time needed for practical added-mass matrix calculation and the eigenvalue analysis. It was shown that the proposed method yielded almost the same eigenvalues as the conventional method conducted in standard physical space. Added-mass models for use in impact-vibration analysis were investigated using the proposed method. Comparing the results calculated using the proposed method with those calculated using concentrated added mass, which is a simplified model, showed that the latter can be used for a rough response calculation, while the precise calculation requires the added-mass matrix method.

Impact Vibration Analysis of Group of Hexagonal Bars Immersed in Liquid.

A simulation method was studied to calculate the vibration response during seismic excitation of a group of hexagonal bars installed in a restraint immersed in liquid. In this study, the influence of fluid force on structural motion was modeled using an added mass matrix. The added mass matrix was then transferred into the space composed of the eigen modes of hexagonal bars without the added mass and introduced into eigenvalue analysis of the whole bar group structure. By means of this method, the computational time of the added mass matrix calculation and the eigenvalue analysis can be reduced. It was shown that the proposed method yielded almost the same eigenvalues as the conventional method in the physical space. Using the proposed method, added mass models to be used in the impact vibration analysis were investigated. Comparing the calculated results by the proposed method with those using a concentrated added mass, which is a simplified model, showed that the concentrated added mass can be used for a rough response calculation, although the precise calculation requires the added mass matrix.