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.

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 Description and evaluation of NorESM1-F: A fast version of the Norwegian Earth System Model (NorESM)

2018 ◽  
Author(s):  
Chuncheng Guo ◽  
Mats Bentsen ◽  
Ingo Bethke ◽  
Mehmet Ilicak ◽  
Jerry Tjiputra ◽  
...  
Keyword(s):  
Carbon Cycle ◽  
Sea Ice ◽  
Large Scale ◽  
Coupled Model ◽  
Coupled System ◽  
Internal Variability ◽  
Earth System Model ◽  
Meridional Overturning Circulation ◽  
System Model ◽  
Earth System

Abstract. A new computationally efficient version of the Norwegian Earth System Model (NorESM) is presented. This new version (here termed NorESM1-F) runs about 2.5 times faster (e.g. 90 model years per day on current hardware) than the version that contributed to the fifth phase of the Coupled Model Intercomparison project (CMIP5), i.e., NorESM1-M, and is therefore particularly suitable for multi-millennial paleoclimate and carbon cycle simulations or large ensemble simulations. The speedup is primarily a result of using a prescribed atmosphere aerosol chemistry and a tripolar ocean-sea ice horizontal grid configuration that allows an increase of the ocean-sea ice component time steps. Ocean biogeochemistry can be activated for fully coupled and semi-coupled carbon cycle applications. This paper describes the model and evaluates its performance using observations and NorESM1-M as benchmarks. The evaluation emphasises model stability, important large-scale features in the ocean and sea ice components, internal variability in the coupled system, and climate sensitivity. Simulation results from NorESM1-F in general agree well with observational estimates, and show evident improvements over NorESM1-M, for example, in the strength of the meridional overturning circulation and sea ice simulation, both important metrics in simulating past and future climates. Whereas NorESM1-M showed a slight global cool bias in the upper oceans, NorESM1-F exhibits a global warm bias. In general, however, NorESM1-F has more similarities than dissimilarities compared to NorESM1-M, and some biases and deficiencies known in NorESM1-M remain.

scholarly journals Description and evaluation of NorESM1-F: a fast version of the Norwegian Earth System Model (NorESM)

2019 ◽  
Vol 12 (1) ◽  
pp. 343-362 ◽  
Author(s):  
Chuncheng Guo ◽  
Mats Bentsen ◽  
Ingo Bethke ◽  
Mehmet Ilicak ◽  
Jerry Tjiputra ◽  
...  
Keyword(s):  
Carbon Cycle ◽  
Sea Ice ◽  
Large Scale ◽  
Coupled Model ◽  
Coupled System ◽  
Internal Variability ◽  
Earth System Model ◽  
Meridional Overturning Circulation ◽  
System Model ◽  
Earth System

Abstract. A new computationally efficient version of the Norwegian Earth System Model (NorESM) is presented. This new version (here termed NorESM1-F) runs about 2.5 times faster (e.g., 90 model years per day on current hardware) than the version that contributed to the fifth phase of the Coupled Model Intercomparison project (CMIP5), i.e., NorESM1-M, and is therefore particularly suitable for multimillennial paleoclimate and carbon cycle simulations or large ensemble simulations. The speed-up is primarily a result of using a prescribed atmosphere aerosol chemistry and a tripolar ocean–sea ice horizontal grid configuration that allows an increase of the ocean–sea ice component time steps. Ocean biogeochemistry can be activated for fully coupled and semi-coupled carbon cycle applications. This paper describes the model and evaluates its performance using observations and NorESM1-M as benchmarks. The evaluation emphasizes model stability, important large-scale features in the ocean and sea ice components, internal variability in the coupled system, and climate sensitivity. Simulation results from NorESM1-F in general agree well with observational estimates and show evident improvements over NorESM1-M, for example, in the strength of the meridional overturning circulation and sea ice simulation, both important metrics in simulating past and future climates. Whereas NorESM1-M showed a slight global cool bias in the upper oceans, NorESM1-F exhibits a global warm bias. In general, however, NorESM1-F has more similarities than dissimilarities compared to NorESM1-M, and some biases and deficiencies known in NorESM1-M remain.

scholarly journals Blow-Up of Solutions with High Energies of a Coupled System of Hyperbolic Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Jorge A. Esquivel-Avila
Keyword(s):  
Initial Data ◽  
Blow Up ◽  
Hyperbolic Equations ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Coupled System ◽  
Initial Energy ◽  
Evolution System ◽  
High Energies ◽  
Second Order In Time

We consider an abstract coupled evolution system of second order in time. For any positive value of the initial energy, in particular for high energies, we give sufficient conditions on the initial data to conclude nonexistence of global solutions. We compare our results with those in the literature and show how we improve them.

Analysis of the ENSO Cycle in the NCEP Coupled Forecast Model

2007 ◽  
Vol 20 (7) ◽  
pp. 1265-1284 ◽  
Author(s):  
Qin Zhang ◽  
Arun Kumar ◽  
Yan Xue ◽  
Wanqiu Wang ◽  
Fei-Fei Jin
Keyword(s):  
Model Simulation ◽  
Southern Oscillation ◽  
Coupled Model ◽  
Coupled System ◽  
Forecast Model ◽  
Enso Cycle ◽  
Positive Contribution ◽  
Test Bed ◽  
Model Simulations ◽  
Thermocline Feedback

Abstract Simulations from the National Centers for Environmental Prediction (NCEP) coupled model are analyzed to document and understand the behavior of the evolution of the El Niño–Southern Oscillation (ENSO) cycle. The analysis is of importance for two reasons: 1) the coupled model used in this study is also used operationally to provide model-based forecast guidance on a seasonal time scale, and therefore, an understanding of the ENSO mechanism in this particular coupled system could also lead to an understanding of possible biases in SST predictions; and 2) multiple theories for ENSO evolution have been proposed, and coupled model simulations are a useful test bed for understanding the relative importance of different ENSO mechanisms. The analyses of coupled model simulations show that during the ENSO evolution the net surface heat flux acts as a damping mechanism for the mixed-layer temperature anomalies, and positive contribution from the advection terms to the ENSO evolution is dominated by the linear advective processes. The subsurface temperature–SST feedback, referred to as thermocline feedback in some theoretical literature, is found to be the primary positive feedback, whereas the advective feedback by anomalous zonal currents and the thermocline feedback are the primary sources responsible for the ENSO phase transition in the model simulation. The basic mechanisms for the model-simulated ENSO cycle are thus, to a large extent, consistent with those highlighted in the recharge oscillator. The atmospheric anticyclone (cyclone) over the western equatorial northern Pacific accompanied by a warm (cold) phase of the ENSO, as well as the oceanic Rossby waves outside of 15°S–15°N and the equatorial higher-order baroclinic modes, all appear to play minor roles in the model ENSO cycles.

scholarly journals The periodic quasigeostrophic equations: existence and uniqueness of strong solutions

1982 ◽  
Vol 91 (3-4) ◽  
pp. 185-203 ◽  
Author(s):  
A. F. Bennett ◽  
P. E. Kloeden
Keyword(s):  
Existence And Uniqueness ◽  
Hyperbolic Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Coupled System ◽  
Classical Solutions ◽  
Schauder Estimates ◽  
Initial Vorticity ◽  
Relative Potential ◽  
Quasigeostrophic Equations

SynopsisThe periodic quasigeostrophic equations are a coupled system of a second order elliptic equation for a streamfunction and first order hyperbolic equations for the relative potential vorticity and surface potential temperatures, on a three-dimensional domain which is periodic in both horizontal spatial co-ordinates. Such equations are used in both numerical and theoretical studies in meteorology and oceanography. In this paper Schauder estimates and a Schauder fixed point theorem are used to prove the existence and uniqueness of strong, that is classical, solutions of the periodic quasigeostrophic equations for a finite interval of time, which is inversely proportional to the sum of the norms of the initial vorticity and surface temperatures.

scholarly journals Vibro-acoustic analysis of a trapezoidal cavity with a clamped flexible wall

2018 ◽  
Vol 37 (4) ◽  
pp. 801-815 ◽  
Author(s):  
Yuan Wang ◽  
Jianrun Zhang ◽  
Xinzhou Zhang ◽  
Bo Wu
Keyword(s):  
Acoustic Analysis ◽  
Coupled Model ◽  
Coupled System ◽  
Coupling Theory ◽  
Incident Plane ◽  
Resonance Frequencies ◽  
Modal Coupling ◽  
Cavity Coupling ◽  
Flexible Wall ◽  
Matching Degree

The coupled model between trapezoidal cavity and its clamped flexible wall is developed using classical modal coupling theory. Based on the coupled model, the resonance frequencies of coupled system are obtained and compared with the corresponding uncoupled one. Meanwhile, the reason for the variation of resonance frequencies of coupled system modes is analyzed in detail. Then, the response of coupled system is investigated using the acoustic potential energy in the cavity and panel vibration kinetic energy when it is excited by an incident plane wave outside of the cavity. Coupling coefficient between trapezoidal cavity and its clamped flexible wall is proposed to assess the modal matching degree between them. It is shown that the coupling selection is not satisfied except in the axis direction which is parallel to the inclined wall. In addition, a rectangular cavity with a clamped flexible wall is also considered and compared with that of the trapezoidal one.

Modelling a Structural-Acoustic Coupled System with an Equivalent Lumped Parameter Mechanical System

1999 ◽  
Vol 121 (4) ◽  
pp. 453-459 ◽  
Author(s):  
S. M. Kim ◽  
M. J. Brennan
Keyword(s):  
Coupled System ◽  
Acoustic Mode ◽  
Physical Parameters ◽  
Acoustic System ◽  
Acoustic Modes ◽  
Lumped Parameter ◽  
Resonance Frequencies ◽  
Mechanical Models ◽  
Equivalent Mass ◽  
Physical Insight

This paper describes the way in which a structural acoustic coupled system can be modelled using an equivalent lumped parameter mechanical model. The impedance-mobility approach is first used to model the system, and by relating the physical parameters to equivalent mass and stiffness, lumped parameter models can be derived provided that damping in the acoustic system is neglected in all modes, but the first (zero order) mode. A limitation of this approach, however, is that these simple mechanical models formulated in terms of the uncoupled structural and acoustic modes are only possible for either a single structural mode coupled to many acoustic modes, or a single acoustic mode coupled to many structural modes. These models facilitate physical insight into the dynamic behavior of a lightly-damped structural-acoustic system at frequencies close to the resonance frequencies of the coupled system.

Internal Model Variability of a Regional Coupled Wave-Atmosphere Model

2021 ◽  
Author(s):  
Anne Wiese ◽  
Joanna Staneva ◽  
Ha Thi Minh Ho-Hagemann ◽  
Sebastian Grayek ◽  
Wolfgang Koch ◽  
...  
Keyword(s):  
Internal Model ◽  
Coupled Model ◽  
Coupled System ◽  
Atmospheric Model ◽  
Model System ◽  
Ensemble Simulations ◽  
Atmosphere Interaction ◽  
Atmosphere Model ◽  
Model Variability ◽  
Coupled Wave

<p>In this study (Wiese et al., 2020) ensemble simulations are performed, in order to assess the significance of the impacts of wave-atmosphere coupling on simulations of both waves and atmospheric models on a regional scale as well as to quantify the internal model variability of both the regional atmospheric model and wave-atmosphere coupled model system. Comparing the magnitude of the internal model variability of the atmospheric model with the internal model variability of the coupled model system shows that the internal model variability can be reduced in the coupled system. While this effect is more pronounced during extreme events, it is still present in a general assessment of the mean internal model variability during the whole study period. Moreover, the impacts of this wave-atmosphere coupling can be distinguished from the internal model variability of the atmospheric model since the effects of the wave-atmosphere interaction are larger than the internal model variability. This study shows that in operational and climate research systems the internal model variability of the atmospheric model is reducible when the ocean waves are coupled to the atmosphere. Clear influences of the wave-atmosphere interaction on both the atmosphere and wave models can be detected and differentiated from the internal model variability. Furthermore, the results of the coupled system have a better agreement with observational data than the results of the reference set up.</p><p> </p><p>References:</p><p>Wiese A, Staneva J, Ho-Hagemann HTM, Grayek S, Koch W and Schrum C (2020) Internal Model Variability of Ensemble Simulations With a Regional Coupled Wave-Atmosphere Model GCOAST. Front. Mar. Sci. 7:596843. doi: 10.3389/fmars.2020.596843</p>

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