Confinement of Vibrations in Flexible Structures Using Supplementary Absorbers: Dynamic Optimization

We propose a novel strategy for the optimal design of supplementary absorbers that warrant confinement with and without suppression of vibrations in flexible structures. We assume that the uncontrolled structure is sensitive to vibrations and that the absorbers are the elements where the vibrational energy is to be transferred. The design of these absorbers is formulated as a dynamic optimization problem in which the objective function is the total energy of the uncontrolled structure. The locations, masses, stiffnesses, and damping coefficients of these absorbers are optimized to minimize the total energy of the structure. We use the Galerkin method to discretize the equations of motion that describe the coupled dynamics of the flexible structure and the added absorbers. We develop a numerical code that computes the unknown parameters for a prespecified set of absorbers. We input a set of initial values for these parameters, and the code updates them while minimizing the total energy in the uncontrolled structure. To show the viability of the proposed design, we consider a simply supported beam with and without external excitations. In the absence of structural damping, we demonstrate that the beam, subjected to either an initial distributed energy or a harmonic excitation, periodically exchanges the vibration energy with the added absorbers. For damped beams, we show that the vibrational energy can be confined to the absorbers for suppression or harnessing purposes.