Optimal absorption design for damped elastic systems

In this work we consider the optimal absorption design for damped elastic systems represented by second-order wave equations with variable damping coefficients. We consider different design criteria and offer a numerical study of damping designs with respect to these criteria for a ID wave equation with either viscous or Kelvin-Voigt damping. Several examples are given to illustrate the ideas

[1]  E. Zuazua.  Exponential decay for the semilinear wave equation with localized damping , 1990 .

[2]  Kangsheng Liu,et al.  Exponential Decay of Energy of the Euler--Bernoulli Beam with Locally Distributed Kelvin--Voigt Damping , 1998 .

[3]  Kangsheng Liu.  Locally Distributed Control and Damping for the Conservative Systems , 1997 .

[4]  F. J. Narcowich,et al.  Exponential decay of energy of evolution equations with locally distributed damping , 1991 .

[5]  E. Zuazua,et al.  The rate at which energy decays in a damped String , 1994 .

[6]  C. Canuto.  Spectral methods in fluid dynamics , 1991 .

[7]  H. Banks,et al.  Exponentially stable approximations of weakly damped wave equations , 1991 .

[8]  Kaïs Ammari,et al.  Stabilization of Bernoulli--Euler Beams by Means of a Pointwise Feedback Force , 2000, SIAM J. Control. Optim..

[9]  Enrique Zuazua,et al.  Exponential Decay for The Semilinear Wave Equation with Locally Distributed Damping , 1990 .

[10]  Kazufumi Ito,et al.  Material Surface Design to Counter Electromagnetic Interrogation of Targets , 2006, SIAM J. Appl. Math..

[11]  Zhuangyi Liu,et al.  Exponential decay of energy of vibrating strings with local viscoelasticity , 2002 .

[12]  J. Lagnese,et al.  Control of Wave Processes with Distributed Controls Supported on a Subregion , 1983 .

[13]  Harvey Thomas Banks,et al.  A Unified Framework for Approximation in Inverse Problems for Distributed Parameter Systems. , 1988 .

[14]  Kazufumi Ito,et al.  The Primal-Dual Active Set Strategy as a Semismooth Newton Method , 2002, SIAM J. Optim..