Optimal Absorption Design and Sensitivity of Eigenvalues

In this work, we consider a sensitivity approach for the optimal absorption design for damped elastic systems. These systems are generally represented by abstract wave equations with variable damping coefficients. Using the sensitivity equation of eigenvalues of the corresponding system generator, a solution method is developed and analyzed for determining the optimal design with respect to the design parameter. Based on such a solution method, approximation methods are also developed for construction of the optimal design. Numerical examples are presented to demonstrate the feasibility of our proposed method