scholarly journals Frequency domain approach to decay rates for a coupled hyperbolic-parabolic system

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Bopeng Rao ◽  
Xu Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Heat Equation ◽  
Frequency Domain ◽  
Parabolic System ◽  
Decay Rates ◽  
Fluid Structure Interactions ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Frequency Domain Approach

<p style='text-indent:20px;'>We consider the asymptotic behavior of a linear model arising in fluid-structure interactions. The system is formed by a heat equation and a wave equation in two distinct domains, which are coupled by atransmission condition along the interface of the domains. By means of the frequency domain approach, we establish some decay rates for the whole system. Our results also showthat the decay of the fluid-structure interaction depends not only on the transmission of the damping from the heat equation to the wave equation, but also on the location of the damping for the wave equation.</p>

Frequency Domain Analysis of Vibrations in Liquid-Filled Piping Systems

1999 ◽  
Author(s):  
Zongxia Jiao ◽  
Qing Hua ◽  
Kai Yu
Keyword(s):  
Frequency Domain ◽  
Transfer Matrix ◽  
Fluid Structure Interaction ◽  
Viscous Friction ◽  
Domain Analysis ◽  
Frequency Domain Analysis ◽  
Piping System ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Piping Systems

Abstract In the analysis of liquid-filled piping systems there are Poisson-coupled axial stress waves in the pipe and liquid column, which are caused by the dilation of the pipe. In some conditions the influence of viscous friction that is usually frequency-dependent should not be omitted, which in fact is another kind of coupled form. It directly influences the amplitude of vibration of piping systems to some degree. The larger the viscosity of the liquid is, the greater the influence will be. Budny (1991) included the viscous friction influence in time domain analysis of fluid-structure interaction, but did not give frequency domain analysis. Lesmez (1990) gave the model analysis liquid-filled piping systems without considering friction. If the friction is not included in frequency domain analysis, the vibration amplitude will be greater than that when friction is included, especially at harmony points, cause large errors in the simulation of fluid pipe network analysis, although it may have little influence on the frequency of harmony points. The present paper will give detail solutions to the transfer matrix that represents the motion of single pipe section, which is the basis of complex fluid-structure interaction analysis. Combined with point matrices that describe specified boundary conditions, overall transfer matrix for a piping system can be assembled. Corresponding state vectors can then be evaluated to predict the piping and liquid motion. At last, a twice-coordinate transformation method is adopted in joint coupling. Consequently, the vibration analysis of spatial liquid-filled piping systems can be carried out. It is proved to be succinct, valid and versatile. This method can be extended to the simulation of the curved spatial pipeline systems.

Supporting New Insight in Pipeline Hydrodynamics Using Stochastic Approaches on External Corrosion Damage

2010 ◽  
Author(s):  
Zahiraniza Mustaffa ◽  
Pieter van Gelder
Keyword(s):  
Field Data ◽  
Corrosion Damage ◽  
Circular Cylinders ◽  
Fluid Structure Interactions ◽  
Fluid Structure ◽  
Subsea Pipeline ◽  
Structure Interaction ◽  
Actual Field ◽  
External Flows ◽  
External Corrosion

Several recent discoveries in the fluid-structure interactions between the external flows and circular cylinders placed close to the wall have added new values to the hydrodynamics of unburied marine pipelines on a seabed. The hydrodynamics of waves and/or currents introduced vortex flows surrounding the pipeline. External corrosions formed in marine pipelines were assumed to be partly contributed by such fluid-structure interactions. The spatial consequences of such interactions were of interest of this study. This paper summarized some experimental and numerical works carried out by previous researchers on these new discoveries. Actual field data were utilized in this study to support this hypothesis. The characteristics of corrosion orientations in the pipelines were studied comprehensively using stochastic approaches and results were discussed. Results adopted from the field data acknowledged well to the hypothesis from the reported literature. The updated knowledge from this fluid-structure interaction is hoped to be given more attention by the industry and perhaps to be incorporated into the current subsea pipeline designs.

Fluid-structure Interactions

1998 ◽  
Vol 120 (04) ◽  
pp. 66-68 ◽  
Author(s):  
Klaus-Ju¨rgen Bathe
Keyword(s):  
Finite Element ◽  
Fluid Structure Interactions ◽  
Physical Processes ◽  
Fluid Structure ◽  
Modeling And Analysis ◽  
Structure Interaction ◽  
Design And Manufacturing ◽  
Physical Phenomena ◽  
Acoustic Fluid ◽  
Made In

This article reviews finite element methods that are widely used in the analysis of solids and structures, and they provide great benefits in product design. In fact, with today’s highly competitive design and manufacturing markets, it is nearly impossible to ignore the advances that have been made in the computer analysis of structures without losing an edge in innovation and productivity. Various commercial finite-element programs are widely used and have proven to be indispensable in designing safer, more economical products. Applications of acoustic-fluid/structure interactions are found whenever the fluid can be modeled to be inviscid and to undergo only relatively small particle motions. The interplay between finite-element modeling and analysis with the recognition and understanding of new physical phenomena will advance the understanding of physical processes. This will lead to increasingly better simulations. Based on current technology and realistic expectations of further hardware and software developments, a tremendous future for fluid–structure interaction applications lies ahead.

Analysis of Fluid-Structure Interaction of an Elastic Blade in Cascade

2002 ◽  
Author(s):  
R. C. K. Leung ◽  
Y. L. Lau ◽  
R. M. C. Si
Keyword(s):  
Numerical Technique ◽  
Fluid Structure Interaction ◽  
Uniform Flow ◽  
Frequency Parameter ◽  
Generation Process ◽  
Noise Generation ◽  
Fluid Structure Interactions ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Normalized Frequency

A time-marching numerical model for the analysis of fluid-structure interaction caused by oncoming alternating vortices has been developed by Jadic et al. (1998). Its applicability to analyzing realistic fluid–structure interaction problems has successfully been established in a recent experimental work of a flat plate in a circular cylinder wake (Lau et al. 2002). Using the model, So et al. (1999) have predicted that, under the excitation of oncoming Karman vortex street (KVS) vortices, an elastic airfoil/blade in inviscid uniform flow exhibits two types of fluid–structure resonance, namely aerodynamic and structural resonance. Aerodynamic resonance is of pure aerodynamic origin and occurs with rigid airfoil/blade excited at normalized frequency parameter c/d = 0.5, 1.5, 2.5 etc., where c is the blade chord and d is the streamwise separation between two neighboring vortices. For an elastic airfoil/blade, as a result of coupled fluid–structure interaction, structural resonance occurs at a normalized frequency close to the natural frequency in vacuo of the airfoil/blade. The occurrence of fluid-structure resonance has also been shown critical in noise generation process (Leung & So 2001). The present study extends the scope of the analysis to fluid–structure interactions occurring in axial–flow turbomachine cascade. When the flow is passing through the rotor, it generates wakes containing KVS vortices behind the rotor blades. The convecting wake will induce perturbations on the downstream stator blades at a wake passing frequency (Rao 1991). Such wake–blade interaction is important in determining the fatigue life of the blades and noise generation of the cascade. The cascade analysis starts with modeling the two-dimensional turbine stator by five high–loading blades evenly separated by s in inviscid uniform flow. Oncoming KVS vortices are released upstream to represent the passing wake originating from the rotor, and are allowed to pass through the stator blades. The blade pitch to blade chord ratio s/c and normalized frequency parameter c/d are important parameters of the problems. Fluid–structure interactions are fully resolved by the same numerical technique (Jadic et al. 1998, So et al. 1999). The combined effects of s/c and c/d on the aerodynamic and structural responses of the central blade are studied and discussed.

Fluid Structure Interactions for Blast Wave Mitigation

2011 ◽  
Vol 78 (3) ◽  
Author(s):  
Wen Peng ◽  
Zhaoyan Zhang ◽  
George Gogos ◽  
George Gazonas
Keyword(s):  
Shock Wave ◽  
Blast Wave ◽  
Fluid Structure Interaction ◽  
Wave Formation ◽  
Plate Motion ◽  
Fluid Structure Interactions ◽  
Free Standing ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Shock Wave Formation

The dynamic response of a free-standing plate subjected to a blast wave is studied numerically to investigate the effects of fluid-structure interaction (FSI) in blast wave mitigation. Previous work on the FSI between a blast wave and a free-standing plate (Kambouchev, N., et al., 2006, “Nonlinear Compressibility Effects in Fluid-Structure Interaction and Their Implications on the Air-Blast Loading of Structures,” J. Appl. Phys., 100(6), p. 063519) has assumed a constant atmospheric pressure at the back of the plate and neglected the resistance caused by the shock wave formation due to the receding motion of the plate. This paper develops an FSI model that includes the resistance caused by the shock wave formation at the back of the plate. The numerical results show that the resistance to the plate motion is especially pronounced for a light plate, and as a result, the previous work overpredicts the mitigation effects of FSI. Therefore, the effects of the interaction between the plate and the shock wave formation at the back of the plate should be considered in blast wave mitigation.

A Perturbation Method for Low-Frequency Fluid-Structure Interaction Problems

1973 ◽  
Vol 40 (2) ◽  
pp. 388-394 ◽  
Author(s):  
Y. K. Lou
Keyword(s):  
Wave Equation ◽  
Perturbation Method ◽  
Electromagnetic Scattering ◽  
Perturbation Methods ◽  
Separation Of Variables ◽  
Fluid Structure Interaction ◽  
Low Frequency ◽  
Approximate Solutions ◽  
Fluid Structure ◽  
Structure Interaction

Perturbation methods have been used for electromagnetic scattering and diffraction problems in recent years. A similar method suitable for low-frequency fluid-structure interaction problems is presented. The essence of the method lies in the fact that approximate solutions for fluid-structure interaction problems can be obtained from a set of Poisson’s equations, rather than from the reduced wave equation. The method is particularly useful for those problems where the Poisson’s equation may be solved by the method of separation of variables while the reduced wave equation cannot. As an illustrative example, the vibrations of a submerged spherical shell is studied using the perturbation method and the accuracy of the method is demonstrated.

scholarly journals The exponential stability of a coupled hyperbolic/parabolic system arising in structural acoustics

1996 ◽  
Vol 1 (2) ◽  
pp. 203-217 ◽  
Author(s):  
George Avalos
Keyword(s):  
Wave Equation ◽  
Feedback Control ◽  
Exponential Stability ◽  
Parabolic System ◽  
Hyperbolic Equations ◽  
Coupled System ◽  
Beam Equation ◽  
Structural Acoustics ◽  
Uniform Stabilization ◽  
Structure Interaction

We show here the uniform stabilization of a coupled system of hyperbolic and parabolic PDE's which describes a particular fluid/structure interaction system. This system has the wave equation, which is satisfied on the interior of a bounded domainΩ, coupled to a “parabolic–like” beam equation holding on∂Ω, and wherein the coupling is accomplished through velocity terms on the boundary. Our result is an analog of a recent result by Lasiecka and Triggiani which shows the exponential stability of the wave equation via Neumann feedback control, and like that work, depends upon a trace regularity estimate for solutions of hyperbolic equations.

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