5TH International Congress on Technology - Engineering & Science - Kuala Lumpur - Malaysia (2018-02-01)

Determination Of Optimal Tuning Parameters For Tuned Mass Dampers Under Earthquake Excitation

Control systems are used to reduce the response of structures under dynamic lateral loads (wind or earthquake forces). Structural control devices can be passive, active, semi-active or hybrid systems. Passive systems which are economical to design and construct do not need external power [1]. Tuned mass damper (TMD) is one of the main passive control devices which has been widely applied in the recent years; however, its main idea dates back to 1909. Based on a well-known text book “Mechanical Vibrations” written by Den Hartog it was invented by Frahm as shown in Figure 1a [2]. He showed that by adding a comparatively small mass (md) and stiffness (kd) to the main mass (M) the response of the main mass to a harmonic excitation is negligible if the natural frequency of the auxiliary mass (ωd) is the same as excitation frequency (ω). The setting of TMD natural frequency is called tuning and if there is a small deviation from tuning frequency, the response will increase significantly which is called detuning. So for broadband excitation, the tuning frequency is selected to be the same as natural frequency of structure (ωs) to prevent resonance. As shown in Figure 1b, Den Hartog add a viscous damping (Cd) to TMD for preventing detuning. The tuning parameters for Den Hatorg model are frequency ratio (f) and damping ratio (ξd) which are defined as the ratio of TMD frequency to the natural frequency of structure (ωd/ωs) and damping of TMD to critical damping (Cd/(2ωdmd)) respectively. This model has been evaluated by Den Hartog and Warburton so explicit formula for calculating optimal tuning parameters has been proposed as a function of mass ratio (μ) which are depicted in Table 1 [2,3]. The mass ratio is defined as the ratio of TMD mass to main mass (md/M). In this study, ant colony optimization (ACO) which is a metaheuristic algorithm is used to find the optimum tuning frequency and damping ratio of the TMD under earthquake excitation [4]. A benchmark single degree of freedom system (SDOF) with parameters reported in Table 2, is analyzed under first Ahar-Varzaghan earthquake (11 August 2012) in the Azerbaijan province (northwest of Iran) and its optimal tuning parameters are determined by a Matlab code. The result of this optimization is shown in Figure 2. For comparing the response history of uncontrolled with controlled structures by different methods, the response history of SDOF for μ=0.2 is depicted in Figure 3. The results show that under earthquake excitation the pattern for traditional tuning parameters are the same as the proposed method. The frequency and damping ratio increase and decrease respectively as the mass ratio increases. The optimum damping ratio for the present approach is much below the traditional methods, so the proposed study gives economical results in compare to traditional methods. Additionally from the Figure 3, it can be seen that although this study has slightly mitigated the peak displacement in compare to traditional methods, it does not have the smallest response in each time step, so it shows the importance of frequency content of the earthquake excitation.
Maziar Fahimi-Farzam, babak Alinejad