Problème de Riemann généralisé pour une sorte de systémes des cables
Reachability of nonnegative equilibrium states for the semilinear vibrating string by varying its axial load and the gain of damping
We show that the set of nonnegative equilibrium-like states, namely, like of the semilinear vibrating string that can be reached from any non-zero initial state , by varying its axial load and the gain of damping, is dense in the “nonnegative” part of the subspace of . Our main results deal with nonlinear terms which admit at most the linear growth at infinity in and satisfy certain restriction on their total impact on (0,∞) with respect to the time-variable.
Simultaneous controllability in sharp time for two elastic strings
We study the simultaneously reachable subspace for two strings controlled from a common endpoint. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability. Moreover we prove the lack of simultaneous exact controllability and we study the space of simultaneously reachable states as a function of the position of the joint. For each type of controllability result we give the sharp controllability time.
Simultaneous controllability in sharp time for two elastic strings
We study the simultaneously reachable subspace for two strings controlled from a common endpoint. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability. Moreover we prove the lack of simultaneous exact controllability and we study the space of simultaneously reachable states as a function of the position of the joint. For each type of controllability result we give the sharp controllability time.
Small vertical vibrations of strings with moving ends.
In this work we investigate a mathematical model for small vertical vibrations of a stretched string when the ends vary with the time t and the cross sections of the string is variable and the density of the material is also variable, that is, p=p(x). It contains Kirchhoff model for fixed ends. We obtain solutions by Galerkin method and estimates in Sobolev spaces.
The Rotating String.
Time domain simulation of a piano. Part 1: model description
The purpose of this study is the time domain modeling of a piano. We aim at explaining the vibratory and acoustical behavior of the piano, by taking into account the main elements that contribute to sound production. The soundboard is modeled as a bidimensional thick, orthotropic, heterogeneous, frequency dependent damped plate, using Reissner Mindlin equations. The vibroacoustics equations allow the soundboard to radiate into the surrounding air, in which we wish to compute the complete acoustical...
Tracking control of a vibrating string with an interior mass viewed as delay system
Tracking control of a vibrating string with an interior mass viewed as delay system
A vibrating string, modelled by the wave equation, with an interior mass is considered. It is viewed as a linear delay system. A trajectory tracking problem is solved using a new type of controllability.
Un modèle relaxé pour les câbles inextensibles
Un problème issu de l'étude numérique d'un fil sans raideur soumis au frottement sec
Unstable simple modes for a class of Kirchhoff equations
Verification of functional a posteriori error estimates for obstacle problem in 1D
We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above by a majorant error estimate. The sharpness of the majorant error estimate is discussed.
Verification of functional a posteriori error estimates for obstacle problem in 2D
We verify functional a posteriori error estimates proposed by S. Repin for a class of obstacle problems in two space dimensions. New benchmarks with known analytical solution are constructed based on one dimensional benchmark introduced by P. Harasim and J. Valdman. Numerical approximation of the solution of the obstacle problem is obtained by the finite element method using bilinear elements on a rectangular mesh. Error of the approximation is measured by a functional majorant. The majorant value...
Weyl formula with optimal remainder estimate of some elastic networks and applications
We consider a network of vibrating elastic strings and Euler-Bernoulli beams. Using a generalized Poisson formula and some Tauberian theorem, we give a Weyl formula with optimal remainder estimate. As a consequence we prove some observability and stabilization results.
Методы теории граничного управления в нестационарной обратной задаче для неоднородной струны
Методы теории граничного управления в обратной спектральной задаче для неоднородной струны