Application of tunable distributed mass dampers in beams subjected to random excitation with peaked PSD

The problem of vibrations of the Euler-Bernoulli beam of variable cross-section with the attached distributed mass dampers, subjected to random excitations with peaked Power Spectral Densities, is presented in the paper. The problem of the beam vibrations is solved using the Galerkin method, the Lagrange's equations of second kind and the Laplace time transformation. The Power Spectral Densities of the beam deflection are determined. Numerical example presents some optimization problem of distributed mass dampers position for global objective function adopted.