Stabilization beyond the distributions.
Stabilization of a coupled multidimensional system.
We introduce a model of a vibrating multidimensional structure made of a n-dimensional body and a one-dimensional rod. We actually consider the anisotropic elastodynamic system in the n-dimensional body and the Euler-Bernouilli beam in the one-dimensional rod. These equations are coupled via their boundaries. Using appropriate feedbacks on a part of the boundary we show the exponential decay of the energy of the system.
Stabilization of a hybrid system: An overhead crane with beam model.
Stabilization of a layered piezoelectric 3-D body by boundary dissipation
We consider a linear coupled system of quasi-electrostatic equations which govern the evolution of a 3-D layered piezoelectric body. Assuming that a dissipative effect is effective at the boundary, we study the uniform stabilization problem. We prove that this is indeed the case, provided some geometric conditions on the region and the interfaces hold. We also assume a monotonicity condition on the coefficients. As an application, we deduce exact controllability of the system with boundary control...
Stabilization of Berger–Timoshenko’s equation as limit of the uniform stabilization of the von Kármán system of beams and plates
We consider a dynamical one-dimensional nonlinear von Kármán model for beams depending on a parameter and study its asymptotic behavior for large, as . Introducing appropriate damping mechanisms we show that the energy of solutions of the corresponding damped models decay exponentially uniformly with respect to the parameter . In order for this to be true the damping mechanism has to have the appropriate scale with respect to . In the limit as we obtain damped Berger–Timoshenko beam models...
Stabilization of Berger–Timoshenko's equation as limit of the uniform stabilization of the von Kármán system of beams and plates
We consider a dynamical one-dimensional nonlinear von Kármán model for beams depending on a parameter ε > 0 and study its asymptotic behavior for t large, as ε → 0. Introducing appropriate damping mechanisms we show that the energy of solutions of the corresponding damped models decay exponentially uniformly with respect to the parameter ε. In order for this to be true the damping mechanism has to have the appropriate scale with respect to ε. In the limit as ε → 0 we obtain damped Berger–Timoshenko...
Stabilization of Timoshenko beam by means of pointwise controls
We intend to conduct a fairly complete study on Timoshenko beams with pointwise feedback controls and seek to obtain information about the eigenvalues, eigenfunctions, Riesz-Basis-Property, spectrum-determined-growth-condition, energy decay rate and various stabilities for the beams. One major difficulty of the present problem is the non-simplicity of the eigenvalues. In fact, we shall indicate in this paper situations where the multiplicity of the eigenvalues is at least two. We build all the above-mentioned...
Stabilization of Timoshenko Beam by Means of Pointwise Controls
We intend to conduct a fairly complete study on Timoshenko beams with pointwise feedback controls and seek to obtain information about the eigenvalues, eigenfunctions, Riesz-Basis-Property, spectrum-determined-growth-condition, energy decay rate and various stabilities for the beams. One major difficulty of the present problem is the non-simplicity of the eigenvalues. In fact, we shall indicate in this paper situations where the multiplicity of the eigenvalues is at least two. We build all the...
Stable and unstable bifurcation in the von Kármán problem for a circular plate.
Stacionární teplotní pole v nekonečném válci při součiniteli přestupu tepla periodicky proměnném podél obvodu
Statical moments of exact and approximate profiles of air springs
Statistically stored dislocations in rate-independent plasticity.
Stimuli-Responsive Polymers in Nanotechnology: Deposition and Possible Effect on Drug Release
Stimuli-responsive polymers result in on-demand regulation of properties and functioning of various nanoscale systems. In particular, they allow stimuli-responsive control of flow rates through membranes and nanofluidic devices with submicron channel sizes. They also allow regulation of drug release from nanoparticles and nanofibers in response to temperature or pH variation in the surrounding medium. In the present work two relevant mathematical models are introduced to address precipitation-driven...
Stochastic finite element for structural vibration.
Stochastic finite element technique for stochastic one-dimensional time-dependent differential equations with random coefficients.
Stoneley waves in a non-homogeneous orthotropic granular medium under the influence of gravity.
Stress equations of motion of Ignaczak type for the second axisymmetric problem of micropolar elastodynamics
A second axially-symmetric initial-boundary value problem of linear homogeneous isotropic micropolar elastodynamics in which the displacement and rotation take the forms , ((r,θ,z) are cylindrical coordinates; cf. [17]) is formulated in a pure stress language similar to that of [12]. In particular, it is shown how and can be recovered from a solution of the associated pure stress initial-boundary value problem, and how a singular solution corresponding to harmonic vibrations of a concentrated...
Stress waves in a microperiodic layered elastic solid revisited.
Stress-controlled hysteresis and long-time dynamics of implicit differential equations arising in hypoplasticity
A long-time dynamic for granular materials arising in the hypoplastic theory of Kolymbas type is investigated. It is assumed that the granular hardness allows exponential degradation, which leads to the densification of material states. The governing system for a rate-independent strain under stress control is described by implicit differential equations. Its analytical solution for arbitrary inhomogeneous coefficients is constructed in closed form. Under cyclic loading by periodic pressure, finite...
Strong asymptotic stability for n-dimensional thermoelasticity systems
We use a new approach to prove the strong asymptotic stability for n-dimensional thermoelasticity systems. Unlike the earlier works, our method can be applied in the case of feedbacks with no growth assumption at the origin, and when LaSalle's invariance principle cannot be applied due to the lack of compactness.