Min-max Game Theory for Elastic and Visco-Elastic Fluid Structure Interactions
نویسندگان
چکیده
We present the salient features of a min-max game theory developed in the context of coupled PDE's with an interface. Canonical applications include linear fluid-structure interaction problem modeled by Oseen's equations coupled with elastic waves. We shall consider two models for the structures: elastic and visco-elastic. Control and disturbance are allowed to act at the interface between the two media. The sought-after saddle solutions are expressed in a pointwise feedback form, which involves a Riccati operator; that is, an operator satisfying a suitable non-standard Riccati differential equation. Motivations, applications as well as a brief historical account are also provided.
منابع مشابه
Wave Propagation Analysis of CNT Reinforced Composite Micro-Tube Conveying Viscose Fluid in Visco-Pasternak Foundation Under 2D Multi-Physical Fields
In this research, wave propagation analysis in polymeric smart nanocomposite micro-tubes reinforced by single-walled carbon nanotubes (SWCNT) conveying fluid is studied. The surrounded elastic medium is simulated by visco-Pasternak model while the composite micro-tube undergoes electro-magneto-mechanical fields. By means of micromechanics method, the constitutive structural coefficients of nano...
متن کاملA NOTE ON THE UNSTEADY FLOW OF A VISCO-ELASTIC MAXWELL FLUID THROUGH A RECTILINEAR PIPE
The unsteady flow of a visco-elastic Maxwell fluid through a rectilinear pipe having its cross-section as a parallelogram under the influence of a axial pressure gradient (I) varying linearly with time , and (II) decreasing exponentially with time has been discussed in the present paper. Variables separable and Laplace transform methods have been used to solve the problem.
متن کاملDynamic Instability of Visco-SWCNTs Conveying Pulsating Fluid Based on Sinusoidal Surface Couple Stress Theory
In this study, a realistic model for dynamic instability of embedded single-walled nanotubes (SWCNTs) conveying pulsating fluid is presented considering the viscoelastic property of the nanotubes using Kelvin–Voigt model. SWCNTs are placed in longitudinal magnetic fields and modeled by sinusoidal shear deformation beam theory (SSDBT) as well as modified couple stress theory. The effect of slip ...
متن کاملWave Propagation Approach to Fluid Filled Submerged Visco-Elastic Finite Cylindrical Shells
Multi-layer orthotropic finite cylindrical shells with a viscoelastic core in contact with fluids are gaining increasing importance in engineering. Vibrational control of these structures is essential at higher modes. In this study, an extended version of the wave propagation approach using first-order shear deformation theory of shell motion is employed to examine the free vibration of damped ...
متن کاملNonlinear Flow-Induced Flutter Instability of Double CNTs Using Reddy Beam Theory
In this study, nonlocal nonlinear instability and the vibration of a double carbon nanotube (CNT) system have been investigated. The Visco-Pasternak model is used to simulate the elastic medium between nanotubes, on which the effect of the spring, shear and damping of the elastic medium is considered. Both of the CNTs convey a viscose fluid and a uniform longitudinal magnetic field is applied t...
متن کامل