Optimization of Parameters for Tuned Mass Damper

Abstract

Currently, structures are being evaluated for a greater number of actions when compared to a few decades ago. This improvement in designing stage is happening because projects providing lightweight and slender structures, with lower implantation costs, are being more requested. As a result, evaluating structures not only subjected to static loads, but also to dynamic loads has become necessary. Dynamic loads acting on a structure are more damaging than static loads, if they are not well considered and dimensioned. Dynamic loads could occur from earthquakes, wind, equipment, movement of people or vehicles, among other sources, which cause vibrations in structures and may lead to a collapse. The tuned mass damper (TMD), a passive control device, emerges as a possibility to control and reduce vibration amplitudes. The TMD has several advantages, such as large capacity to reduce amplitude of vibration, easy installation, low maintenance, low cost, among others. This study aims at evaluating, through numerical simulation, the dynamic behavior of a ten-storey building subjected to seismic excitation, before and after the installation of TMD, which is optimized to get the best structural response towards the dynamic excitation. For this purpose, a computational routine is developed in Matlab using the Newmark method to determine the dynamic structural response in terms of displacement, velocity and acceleration. The seismic excitation accelerogram used regards to ground acceleration record occurred in 1940, under the Imperial Valley in southeastern California, called El Centro. First, structure is analyzed only with its own damping for comparison and reference. Second, TMD optimization is carried out, in which the objective function is to minimize the maximum displacement at the top of the building, and the design variable is the modal mass ratio (Structure-TMD). Firefly algorithm is used for optimization. The TMD is installed on top of the building and, after optimizing its parameters, new dynamic structural responses are determined. Finally, responses obtained after the optimized TMD installation are considerably reduced, minimizing the risk of damage and building collapse.