On a structural acoustic model which incorporates shear and thermal effects in the structural component

In this paper we consider a structural acoustic model which takes account of thermal effects over and above displacement, rotational inertia and shear effects in the flat flexible structural component of the model. Thus the structural medium is a Reissner-Mindlin plate into which an additional degree of freedom, viz. temperature variation in the plate, has been introduced and the constitutive equations for the structural acoustic model couple parabolic dynamics with hyperbolic dynamics. We show unique solvability of the mathematical model and investigate the effect of the presence of thermal effects on the mechanical dissipation devices needed to attain uniform stabilization of the two-dimensional model in which the structural component is a Timoshenko beam. It turns out that, as in linear structural acoustic models which use the Euler-Bernoulli equation or the Kirchoff equation to describe the deflections of the thermo-elastic structural medium, uniform stabilization of the energy associated with the model can be attained without introducing mechanical dissipation at the free edge of the beam. Open problems with regard to the stabilization of the three-dimensional model are outlined.     

On the stabilizability of a structural acoustic model which incorporates shear effects in the structural component

In this paper we consider a linear three-dimensional structural acoustic model which takes account of displacement, rotational inertia and shear effects in the flat flexible structural component of the model. Thus the deflections of the structural component of the structure are governed by the Reissner–Mindlin plate equations. We show strong stabilization of the coupled model without incorporating viscous or boundary damping in the equations for the gas dynamics and without imposing geometric conditions. It turns out that damping is needed in the interior of the plate, to which end Kelvin–Voigt damping is introduced in the plate equations. As our main tool we use a resolvent criterion for strong stability due to Tomilov.     

Uniform stabilization of a nonlinear structural acoustic model with a Timoshenko beam interface

This paper is concerned with a nonlinear model which describes the interaction of sound and elastic waves in a two‐dimensional acoustic chamber in which one flat ‘wall’, the interface, is flexible. The composite dynamics of the structural acoustic model is described by the linearized equations for a gas defined on the interior of the chamber and the nonlinear Timoshenko beam equations on the interface. Uniform stability of the energy associated with the interactive system of partial differential equations is achieved by incorporating a nonlinear feedback boundary damping scheme in the equations for the gas and the beam. Copyright © 2006 John Wiley & Sons, Ltd.     

Strong stability for a fluid–structure interaction model

In this paper we consider the question of stabilization of a fluid–structure model that describes the interaction between a 3‐D incompressible fluid and a 2‐D plate, the interface, which coincides with a flat flexible part of the surface of the vessel containing the fluid. The mathematical model comprises the Stokes equations and the equations for the longitudinal deflections of the plate with inclusion of the shear stress, which the fluid exerts on the plate. We show that the energy associated with the model decays strongly when the interface is equipped with a locally supported dissipative mechanism. Our main tool is an abstract resolvent criterion due to Tomilov. Copyright © 2008 John Wiley & Sons, Ltd.     

On a structural acoustic model with interface a Reissner-Mindlin plate or a Timoshenko beam

This paper is concerned with a model which describes the interaction of sound and elastic waves in a structural acoustic chamber in which one “wall” is flexible and flat. The model is new in the sense that the composite dynamics of the three-dimensional structure is described by the linearized equations for a gas defined on the interior of the chamber and the Reissner-Mindlin plate equations on the two-dimensional flat wall of the chamber, while, if a two-dimensional acoustic chamber is considered, the Timoshenko beam equations describe the deflections of the one-dimensional “wall.” With a view to achieving uniform stabilization of the structure linear feedback boundary damping is incorporated in the model, viz. in the wave equation for the gas and in the system of equations for the vibrations of the elastic medium. We present the uniform stability result for the case of a two-dimensional chamber and outline the method for the three-dimensional model which shows strong resemblance with the system of dynamic plane elasticity.     

Strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions

We consider a wave equation with semilinear porous acoustic boundary conditions. This is a coupled system of second and first order in time partial differential equations, with possibly semilinear boundary conditions on the interface. The results obtained are (i) strong stability for the linear model, (ii) exponential decay rates for the energy of the linear model, and (iii) local exponential decay rates for the energy of the semilinear model. This work builds on a previous result showing generation of a well-posed dynamical system. The main tools used in the proofs are (i) the Stability Theorem of Arendt-Batty, (ii) energy methods used in the study of a wave equation with boundary damping, and (iii) an abstract result of I. Lasiecka applicable to hyperbolic-like systems with nonlinearly perturbed boundary conditions.     

On the structural stability of thermoelastic model of porous media

In the present paper we study the structural stability of the mathematical model of the linear thermoelastic materials with voids. We prove that the solutions of problems depend continuously on the constitutive quantities, which may be subjected to error or perturbations in the mathematical modelling process. Thus, we assume to have changes in the various coupling coefficients of the model and then we establish estimates of continuous dependence of solutions. We have to outline that such estimates play a central role in obtaining approximations to these kinds of problems. To derive a priori estimates for a solution we first establish appropriate bounds for the solutions of certain auxiliary problems. These are achieved by means of so‐called Rellich‐like identities. We also investigate how the solution in the coupled model behaves as some coupling coefficients tend to zero. Copyright © 2007 John Wiley & Sons, Ltd.     

Control-theoretic properties of structural acoustic models with thermal effects,I. Singular estimates

We consider a class of structural acoustics models with thermoelastic flexible wall. More precisely, the PDE system consists of a wave equation (within an acoustic chamber) which is coupled to a system of thermoelastic plate equations with rotational inertia; the coupling is strong as it is accomplished via boundary terms. Moreover, the system is subject to boundary thermal control. We show that—under three different sets of coupled (mechanical/thermal) boundary conditions—the overall coupled system inherits some specific regularity properties of its thermoelastic component, as it satisfies the same singular estimates recently established for the thermoelastic system alone. These regularity estimates are of central importance for (i) well-posedness of Differential and Algebraic Riccati equations arising in the associated optimal control problems, and (ii) existence of solutions to the semilinear initial/boundary value problem under nonlinear boundary conditions. The proof given uses as a critical ingredient a sharp trace theorem pertaining to second-order hyperbolic equations with Neumann boundary data.     

Strong competition model with non-uniform dispersal in a heterogeneous environment

In this study, a strong competition model was considered between two species in a heterogeneous environment. For a system with two different constant diffusion rates for each competitor, the fast diffuser can be selected evolutionally under suitable assumptions if the competing interaction between the species is strong. We also claim that a strongly interacting competition leads to a more evolutionary selection than that with the same population dynamics if a species moves with a certain non-uniform dispersal. Furthermore, species with a certain non-uniform dispersal have a competitive advantage over linear random diffusers. In addition, a species with highly sensitive dispersal response to the environment may survive. These strongly competitive advantages were demonstrated by investigating the stability of semi-trivial solutions of the system with non-uniform dispersal and comparing it to the conditions of the model with constant diffusion.     

有重复观测时二次EV模型参数的强相合性

给出了在一些实验点重复观测时二次EV模型参数的估计，在一般条件下证明了估计是强相合的。     

The role of magnetic fields in the strong stabilization of a hybrid magneto‐elastic structure

In this paper, we are concerned with a model for the magneto–elastic interactions of a three‐dimensional elastic body and a two‐dimensional flexible plate, which is attached to the flat flexible part of the surface of the body. Both the solid body and the plate are permeated by magnetic fields. The mathematical model is analyzed from the point of view of existence and uniqueness and stabilization.It turns out that, in the presence of the magnetic fields in the solid and the plate, strong stabilization can be achieved under viscous damping in the plate in one direction that is determined by the nature of the primary magnetic fields in the body and the plate. Copyright © 2011 John Wiley & Sons, Ltd.     

Moisture absorption and mechanical and acoustic responses in shear of a glass fiber fabric/epoxy resin composite

An analysis of the mechanical and acoustic responses of a laminate composed of 12 layers of glass fiber fabric/epoxy resin and conditioned in environments with relative humidities of 0, 60, and 96% RH at 60°C is presented. The first part of the study consists in following the weight gain according to the duration of hygrothermal conditioning, and the second part—in test ing 45°-oriented specimens in uniaxial tension up to failure at constant imposed displacement rates, with registrating the acoustic emission to track the damage process. The influence of moisture content in the material showed up as a significant decrease in its shear modulus, shear stress, and acoustic emission with growing quantity of absorbed water. An exponential function is proposed for describing the relationship between the varying shear modulus and the shear strain. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 595–602, September–October, 2007.     

Strong convergence of LAD estimates in a censored regression model

A regression model with a nonnegativity constraint on the dependent variable, known as censored median regression model, is considered. Under some mild conditions, the LAD estimate of the regression coefficient is shown to be strongly consistent. Furthermore, its convergence rate and Bahadur strong representation are also obtained.     

Thermal self-action effects of acoustic beam in a vibrationally relaxing gas

Thermal self-action of acoustic beam in a molecular gas with excited internal degrees of molecules’ freedom, is studied. This kind of thermal self-action differs from that in a Newtonian fluid. Heating or cooling of a medium takes place due to transfer of internal vibrational energy. Equilibrium and non-equilibrium gases, which may be acoustically active, are considered. A beam in an acoustically active gas is self-focusing unlike a beam in a standard viscous gas. The self-action effects relating to wave beams containing shock fronts, are discussed. Stationary and non-stationary kinds of self-action are considered.     

混合误差下半参数回归模型小波估计的强相合性

研究了一类半参数回归模型,利用最小二乘法和小波估计法给出了未知参数β和未知函数g(.)的估计.在误差序列为ψ-混合或φ-混合下得到了^β的强相合性,给出了^g(.)的一致强相合性和r阶矩相合性.     

Structural stability and stabilization of solutions of the reversible three‐component Gray‐Scott system

This paper is concerned with the structural stability and stabilization of solutions to the three‐component reversible Gray‐Scott system under the Dirichlet or Neumann boundary conditions defined in a bounded domain of for 1 ≤ n ≤ 3. We prove that each solution depends on changes in a coefficient of the ratio of the reverse and forward reaction rates for the autocatalytic reaction as well as proving the continuous dependence on the initial data. We also prove that under Dirichlet's boundary conditions, the system is stabilized to the stationary solution by finitely many Fourier modes.     

Stability,structural stability,and games: Toward a theory of differential hypergames

Differential games (DG's) are investigated from a stability point of view. Several resemblances between the theory of optimal control and that of structural stability suggest a differential game approach in which the operators have conflicting interests regarding the stability of the system only. This qualitative approach adds several interesting new features. The solution of a differential game is defined to be the equilibrium position of a dynamical system in the framework of a given stability theory: this is the differential hypergame (DHG). Three types of DHG are discussed: abstract structural DHG, Liapunov DHG, and Popov DHG. The first makes the connection between DG and the catastrophe theory of Thom; the second makes the connection between the value function approach and Liapunov theory; and the third provides invariant properties for DG's. To illustrate the fact that the theory sketched here may find interesting applications, the up-to-date problem of the world economy is outlined.This research was supported by the National Research Council of Canada.     

A Proof of the Necessity of Linear Independence Condition and Strong Second-Order Sufficient Optimality Condition for Lipschitzian Stability in Nonlinear Programming

For a nonlinear programming problem with a canonical perturbations, we give an elementary proof of the following result: If the Karush–Kuhn–Tucker map is locally single-valued and Lipschitz continuous, then the linear independence condition for the gradients of the active constraints and the strong second-order sufficient optimality condition hold.     

随机截尾下污染数据部分线性模型的强相合估计

考虑一类新的污染数据部分线性模型,当受污染后的因变量被随机右截断时,就截断分布已知的情形,利用所获得截断观测数据构造了模型中的参数分量,非参数分量及污染系数的估计量,并在适当的条件下,证明了这些估计量的强相合性.