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.

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>

scholarly journals Uniform stabilization of a coupled structural acoustic system by boundary dissipation

1998 ◽  
Vol 3 (3-4) ◽  
pp. 377-400 ◽  
Author(s):  
Mehmet Camurdan
Keyword(s):  
Smart Materials ◽  
Acoustic Pressure ◽  
Hyperbolic Equations ◽  
Coupled Model ◽  
Coupled System ◽  
Acoustic System ◽  
Structural Damping ◽  
Uniform Stabilization ◽  
Boundary Dissipation ◽  
Chamber Floor

We consider a coupled PDE system arising in noise reduction problems. In a two dimensional chamber, the acoustic pressure (unwanted noise) is represented by a hyperbolic wave equation. The floor of the chamber is subject to the action of piezo-ceramic patches (smart materials). The goal is to reduce the acoustic pressure by means of the vibrations of the floor which is modelled by a hyperbolic Kirchoff equation. These two hyperbolic equations are coupled by appropriate trace operators. This overall model differs from those previously studied in the literature in that the elastic chamber floor is here more realistically modeled by a hyperbolic Kirchoff equation, rather than by a parabolic Euler-Bernoulli equation with Kelvin-Voight structural damping, as in past literature. Thus, the hyperbolic/parabolic coupled system of past literature is replaced here by a hyperbolic/hyperbolic coupled model. The main result of this paper is a uniform stabilization of the coupled PDE system by a (physically appealing) boundary dissipation.

A numerical study on the influences of underlying soil and backfill characteristics on the dynamic behaviour of typical integral bridges

Bauingenieur ◽  
2020 ◽  
Vol 95 (11) ◽  
pp. S 2-S 11
Author(s):  
H. D. B. Aji ◽  
M. B. Basnet ◽  
Frank Wuttke
Keyword(s):  
Soil Structure ◽  
Dynamic Behaviour ◽  
Numerical Study ◽  
Coupled System ◽  
Soil Structure Interaction ◽  
Dynamic Resistance ◽  
Soil Characteristic ◽  
Structure Interaction ◽  
Integral Bridges ◽  
Underlying Soil

Abstract The identification of the dynamic behaviour of a structure is one of the crucial steps in the design of the dynamic resistance of the structure. The dynamic behaviour is represented by the natural frequencies and damping which are subsequently used along with the considered dynamic actions in the design process. In regard of integral bridge concept, one of the consequences of the omission of joints and bearings is the substantial soil-structure interaction which in turn increases the sensitivity of the dynamic behaviour of the bridges to the surrounding soil characteristic. In this article, we extended our hybrid BEM-FEM steady-state dynamic numerical tool to the 3D regime, developed by utilizing an in-house BEM and the commercial FEM software ABAQUS and use it to analyse the dynamic interaction between the bridge and the underlying soil as well as the backfill. The numerical results from four typical integral bridges show that underlying soil characteristic has great effect on the resonant frequencies and the damping. The backfill material properties tend to have less significant role due to the abutment wingwalls dominating the force transfer between the soil and the superstructure. The results also show that the degree of influence of the soil-structure interaction on the coupled system is affected by the type of load pattern in addition to the flexural stiffness of the superstructure.

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