Liquid Sloshing Damping in an Elastic Container

2011 ◽  
Vol 79 (1) ◽  
Author(s):  
Thomas Miras ◽  
Jean-Sébastien Schotté ◽  
Roger Ohayon
Keyword(s):  
Incompressible Liquid ◽  
Coupled System ◽  
Liquid Sloshing ◽  
Test Case ◽  
Numerical Application ◽  
Damping Matrix ◽  
Reduced Equations ◽  
Complex Modes ◽  
Elastic Container ◽  
Sloshing Damping

It is proposed to investigate in this paper the damped vibrations of an incompressible liquid contained in a deformable tank. A linearized formulation describing the small movements of the system is presented. At first, a diagonal damping is introduced in the reduced equations of the hydroelastic sloshing problem. We obtain a nonclassically damped coupled system with a damping matrix that is not symmetric. Then, by projecting the system onto its complex modes, the frequency and time responses for different type of loads are built. A numerical application is illustrated on a test case.

Approximate Solution of Nonclassically Damped Systems

1991 ◽  
Author(s):  
F. Ma ◽  
J. H. Hwang
Keyword(s):  
Approximate Solution ◽  
Large Scale ◽  
Computational Effort ◽  
Frequency Separation ◽  
Common Procedure ◽  
Damping Matrix ◽  
Complex Modes ◽  
Modal Coupling ◽  
Order Of Magnitude ◽  
Damped Systems

Abstract In analyzing a nonclassically damped linear system, one common procedure is to neglect those damping terms which are nonclassical, and retain the classical ones. This approach is termed the method of approximate decoupling. For large-scale systems, the computational effort at adopting approximate decoupling is at least an order of magnitude smaller than the method of complex modes. In this paper, the error introduced by approximate decoupling is evaluated. A tight error bound, which can be computed with relative ease, is given for this method of approximate solution. The role that modal coupling plays in the control of error is clarified. If the normalized damping matrix is strongly diagonally dominant, it is shown that adequate frequency separation is not necessary to ensure small errors.

Non-Linear Dynamic Analysis of a Cable-Stayed Beam

2005 ◽  
Author(s):  
Carlos E. N. Mazzilli ◽  
Franz Rena´n Villarroel Rojas
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Multiple Scale ◽  
Local Mode ◽  
Numerical Application ◽  
Global Mode ◽  
Lower Mode ◽  
Reduced Equations ◽  
External Resonance ◽  
Non Linear

The dynamic behaviour of a simple clamped beam suspended at the other end by an inclined cable stay is surveyed in this paper. The sag due to the cable weight, as well as the non-linear coupling between the cable and the beam motions are taken into account. The formulation for in-plane vibration follows closely that of Gattulli et al. [1] and confirms their findings for the overall features of the equations of motion and the system modal properties. A reduced non-linear mathematical model, with two degrees of freedom, is also developed, following again the steps of Gattulli and co-authors [2,3]. Hamilton’s Principle is evoked to allow for the projection of the displacement field of both the beam and the cable onto the space defined by the first two modes, namely a “global” mode (beam and cable) and a “local” mode (cable). The method of multiple scales is then applied to the analysis of the reduced equations of motion, when the system is subjected to the action of a harmonic loading. The steady-state solutions are characterised in the case of internal resonance between the local and the global modes, plus external resonance with respect to either one of the modes considered. A numerical application is presented, for which multiple-scale results are compared with those of numerical integration. A reasonable qualitative and quantitative agreement is seen to happen particularly in the case of external resonance with the higher mode. Discrepancies should obviously be expected due to strong non-linearities present in the reduced equations of motion. That is specially the case for external resonance with the lower mode.

Transforming Complex Eigenmodes into Real Ones Based on an Appropriation Technique

2000 ◽  
Vol 123 (1) ◽  
pp. 92-97 ◽  
Author(s):  
E. Foltete ◽  
J. Piranda
Keyword(s):  
Normal Modes ◽  
Quality Criterion ◽  
Experimental Tests ◽  
New Method ◽  
Damping Matrix ◽  
Complex Modes ◽  
Applied Forces ◽  
Forced Responses

A new method allowing the determination of normal modes corresponding to the complex ones identified on a structure is proposed. It is based on an appropriation technique applied to forced responses computed from the identified eigensolutions. The set of applied forces is optimized with respect to an appropriation quality criterion. The knowledge of both complex and normal modes allows the full generalized damping matrix to be determined. The complex modes can then be recalculated using the normal modes and the full generalized damping matrix which provides a test of validity by comparison with the original complex modes. Simulated and experimental tests demonstrate the efficiency of this new method.

Coupled Mode Flutter Analysis of Turbomachinery Blades Using an Adaptation of the P-K Method

2020 ◽  
Author(s):  
Matthias Schuff ◽  
Virginie Anne Chenaux
Keyword(s):  
Coupled System ◽  
Mode Shapes ◽  
Test Case ◽  
Mass Ratio ◽  
Coupled Mode ◽  
Turbomachinery Blades ◽  
Time Marching ◽  
Low Mass ◽  
Low Mass Ratio ◽  
Turbomachinery Design

Abstract Current trends in turbomachinery design significantly reduce the mass ratio of structure to air, making them prone to flutter by aerodynamic coupling between mode shapes, also called coupled-mode flutter. The p-k method, which solves an aeroelastic eigenvalue problem for frequency and damping respectively excitation of the aerodynamically coupled system, was adapted for turbomachinery application using aerodynamic responses computed in the frequency domain. A two-dimensional test case is validated against time-marching fluid-structure coupled simulations for subsonic and transonic conditions. A span of mass ratios is investigated showing that the adapted p-k method is able to predict the transition between aeroelastically stable and unstable cascades depending on the mass ratio. Finally, the p-k method is applied to a low mass ratio fan showing that the flutter-free operating range is significantly reduced when aerodynamic coupling effects are taken into account.

Calculation of Intake-Fan-Bypass Interaction With a Fan Similarity Model

2018 ◽  
Author(s):  
Mauro Carnevale ◽  
Feng Wang ◽  
Luca di Mare
Keyword(s):  
Boundary Conditions ◽  
Three Dimensional ◽  
Coupled System ◽  
Design Stage ◽  
Modern Trend ◽  
Test Case ◽  
Operation Condition ◽  
Present Contribution ◽  
Aero Engines ◽  
Very High

Modern trend in installation design is moving towards very high-bypass ratio turbofans. Very high-bypass turbofans represent an effective way of improving the propulsive efficiency of civil aero-engines. Such engines require larger and heavier nacelles, which partially offset the gains in specific fuel consumption. The penalty associated with a larger installation can be mitigated by adopting thinner walls for the nacelle and by shortening the intake section. Such inlet sections are characterized by more restrictive operation condition because they are more prone to separation at high incidence flight conditions. Moreover, in short nacelle installations the by-pass guide vanes and pylon are closer to the fan blades and consequently the distortion due to potential effects induced by the presence of the pylon and non-axisymmetric OGV stage play a significant role in terms of unsteady interaction in the entire system. It is mandatory to consider the inlet, fan, bypass and pylon as a unique coupled system also at the design stage, for assessment of fan force. This kind of assessment is usually carried on by expensive URANS calculation. The factors leading to high computational demands are the spatial resolution required in the fan domain and the time resolution required to sample the fan blade passing frequency. Large savings are therefore possible if simplifications are introduced which relax the resolution requirements in the fan passages and change the nature of the computation into a steady-state computation for the ducts. The present contribution documents a simplified fan model for fan-intake computations based on the solution of the double linearization problem for unsteady, transonic flow past a cascade of thin aerofoils with finite mean load. The coupling with the intake flow and the bypass is performed by using the flow patterns at fan face and fan exit as boundary conditions for the fan model and computing circumferentially non-uniform boundary conditions for the intake and the bypass from the fan model. The computation of the flow in the intake, bypass and pylon is therefore reduced to a steady problem, whereas the computation of the flow in the fan is reduced to one steady problem and a set of linearised models in the frequency domain. The model is applied to a well-documented test case and compares favourably with experimental data and much more expensive three-dimensional, time domain computations.

Coupled Mode Flutter Analysis of Turbomachinery Blades Using an Adaptation of the P-k Method

2020 ◽  
Author(s):  
Matthias Schuff ◽  
Virginie Anne Chenaux
Keyword(s):  
Coupled System ◽  
Mode Shapes ◽  
Test Case ◽  
Mass Ratio ◽  
Coupled Mode ◽  
Turbomachinery Blades ◽  
Time Marching ◽  
Low Mass ◽  
Low Mass Ratio ◽  
Turbomachinery Design

Abstract Current trends in turbomachinery design significantly reduce the mass ratio of structure to air, making them prone to flutter by aerodynamic coupling between mode shapes, also called coupled-mode flutter. The p-k method, which solves an aeroelastic eigenvalue problem for frequency and damping respectively excitation of the aerodynamically coupled system, was adapted for turbomachinery application using aerodynamic responses computed in the frequency domain. A two-dimensional test case is validated against time-marching fluid-structure coupled simulations for subsonic and transonic conditions. A span of mass ratios is investigated showing that the adapted p-k method is able to predict the transition between aeroelastically stable and unstable cascades depending on the mass ratio. Finally, the p-k method is applied to a low mass ratio fan showing that the flutter-free operating range is significantly reduced when aerodynamic coupling effects are taken into account.

Liquid Sloshing Damping Computation in Cylindrical Tank Based on VOF Method

2013 ◽  
Vol 390 ◽  
pp. 116-120 ◽  
Author(s):  
Fei Tang ◽  
Yong Li ◽  
Yong Bin Geng
Keyword(s):  
Free Surface ◽  
Empirical Equation ◽  
Liquid Sloshing ◽  
Finite Volume Scheme ◽  
Cylindrical Tank ◽  
Construction Scheme ◽  
Cylindrical Tanks ◽  
Semi Empirical ◽  
Theoretical Results ◽  
Sloshing Damping

For liquid sloshing in partially filled cylindrical tank, the influence of the free surface on the sloshing damping is very important, especially in the application of spacecraft. In order to calculate the damping characteristic of partially filled cylindrical tanks more accurately, the finite volume scheme base on Volume-of-Fluid (VOF) is used to simulate the interface flow in the tank. Second order accurate piecewise line interface construction scheme is used to reconstruct the free surface. Through the numerical simulation, the influence on the sloshing damping with different liquid fill ratios in the cylindrical tanks is obtained.At the end, by use of semi-empirical equation, found that it agrees with theoretical results reasonably well.

Liquid Sloshing in a Rigid Cylindrical Tank Equipped with a Rigid Annular Baffle and on Soil Foundation

2020 ◽  
Vol 20 (03) ◽  
pp. 2050030 ◽  
Author(s):  
Ying Sun ◽  
Ding Zhou ◽  
Marco Amabili ◽  
Jiadong Wang ◽  
Huixuan Han
Keyword(s):  
Computational Cost ◽  
Coupled System ◽  
Least Square ◽  
Liquid Sloshing ◽  
Lumped Parameter Model ◽  
Equivalent Model ◽  
Complex Polynomial ◽  
Soil Parameters ◽  
Cylindrical Tank ◽  
Soil Foundation

Fluid sloshing in a rigid circular cylindrical tank is investigated; the tank is resting on soil foundation and is excited by horizontal seismic accelerations. A rigid annular baffle is connected to the inner wall of the storage tank to reduce liquid sloshing. By using the fluid subdomain method, the convective velocity potential is derived. An equivalent model with mass-spring oscillators is proposed to describe the sloshing motions of the contained liquid. Then, by means of the least square method, a complex polynomial fraction is employed to fit the dynamic impedance of the soil. A nested lumped parameter model is established to model the effect of the soil foundation. The substructure method allows to obtain the soil–tank–liquid coupled model. The equation of motion of the coupled system is solved by the Newmark-[Formula: see text] method. A comparison between the present sloshing results and those published in the literature shows an excellent agreement. The effects of the soil parameters, the baffle position and its size on the dynamic behavior of the soil–tank–liquid system are discussed in detail. The results demonstrate that the soil properties and the baffle parameters can have a remarkable influence on liquid sloshing. The novelty of this research is that an analytical model for the soil–tank–liquid–baffle coupled system is derived for the first time and it allows to study the dynamics and sloshing response of the system with accuracy and low computational cost.

AN Identification Method of Damping Matrix for Frame Structures

2011 ◽  
Vol 243-249 ◽  
pp. 967-970
Author(s):  
Sha Sha Dong ◽  
Wei Ying Wang ◽  
Fu Shun Liu ◽  
Zhi Qiang Gao
Keyword(s):  
Modal Analysis ◽  
Dynamic Characteristic ◽  
Experimental Modal Analysis ◽  
Frame Structure ◽  
Frame Structures ◽  
Order Complex ◽  
Identification Method ◽  
Damping Matrix ◽  
Complex Modes ◽  
Different Parts

Nowadays, damping is still the important dynamic characteristic that is the least understood and the most difficult to quantify. The advantage of the proposed damping matrix identification method is that several low order complex modes achieved by Experimental Modal Analysis (EMA) are capable of calculation precision. In order to identify the damping matrix, this paper also proposes a general damping matrix decompositon technique, which can be used in the situation that different parts of the structure have different damping. Then a five-story frame structure is applied to demonstrate the proposed method ,and the results obtained show the suitability of this approach for damping matrix identification in frame structures.

A Knowledge Management Approach to the Loosely Coupled Systems

2016 ◽  
Vol 29 (1) ◽  
pp. 75-90 ◽  
Author(s):  
Jernej Agrez ◽  
Nadja Damij
Keyword(s):  
Knowledge Management ◽  
Coupled System ◽  
Coupled Systems ◽  
Knowledge Network ◽  
Management Approach ◽  
Test Case ◽  
Loosely Coupled Systems ◽  
Loosely Coupled ◽  
Ontology Language ◽  
Process Architecture

The purpose of the research is to explore characteristics and design the concept of the knowledge management system that would be able to operate in a loosely coupled system. We used a literature review to determine characteristics of the conceptual design that would fit into the unstable organizational environment. Based on the theoretical insights, we designed the open framework that is capable of adjustments, multilevel designing, it allows integration of statistical methods and supports conversion into the web ontology language. We applied developed concept to a loosely coupled system test case, to achieve better understanding of its capabilities. The solution is appropriate for implementation to analyze knowledge network and process architecture relations in different informal organizational networks, as well as during events where spontaneous cooperation among different types of organizations and individuals is necessary, such as massive natural disasters and other simila events.

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