“…Furthermore, the P-TMD is less sensitive to an increase in the tuning frequency ratio than the TMD and vice versa when the tuning frequency ratio decreases. Such an asymmetric response of the P-TMD to an increase or decrease in the tuning frequency ratio has already been observed in several nonlinear or nontraditional TMDs (Araz, 2020; Kim and Lee, 2020). Figure 12.Effect of frequency detuning on the peak response.…”
A special type of a tuned mass damper, which consists of a mass and an elasto-plastic spring without using any viscous damper, is used to reduce the steady-state response of structures to base excitation. Previous work of the authors showed that the elasto-plastic tuned mass damper (P-TMD) could help reduce the seismic responses, and a method based on energy equalization was proposed to design it. In this study, the effectiveness of the P-TMD is investigated under harmonic support motion, and a direct approach is developed to find its optimum parameters. To estimate the nonlinear steady-state response of P-TMD-controlled systems, an analytical framework is established using the Fourier series approximation, which is validated by direct numerical integration of the equations of motion. The obtained results for the optimum P-TMD are discussed and compared with those of the optimum elastic tuned mass damper.
“…Furthermore, the P-TMD is less sensitive to an increase in the tuning frequency ratio than the TMD and vice versa when the tuning frequency ratio decreases. Such an asymmetric response of the P-TMD to an increase or decrease in the tuning frequency ratio has already been observed in several nonlinear or nontraditional TMDs (Araz, 2020; Kim and Lee, 2020). Figure 12.Effect of frequency detuning on the peak response.…”
A special type of a tuned mass damper, which consists of a mass and an elasto-plastic spring without using any viscous damper, is used to reduce the steady-state response of structures to base excitation. Previous work of the authors showed that the elasto-plastic tuned mass damper (P-TMD) could help reduce the seismic responses, and a method based on energy equalization was proposed to design it. In this study, the effectiveness of the P-TMD is investigated under harmonic support motion, and a direct approach is developed to find its optimum parameters. To estimate the nonlinear steady-state response of P-TMD-controlled systems, an analytical framework is established using the Fourier series approximation, which is validated by direct numerical integration of the equations of motion. The obtained results for the optimum P-TMD are discussed and compared with those of the optimum elastic tuned mass damper.
“…Den Hartog [1] obtained analytical solution for the TMD with dashpot element called the traditional TMD. This study was followed by other works that suppressing the resonant vibrations of the main structure due to various excitations [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. These works indicate that a TMD device yields a higher level of control performance in suppressing the vibrations of the main structures.…”
Passive control devices have been used for a long time to reduce unwanted vibrations. The most commonly used of these devices are tuned mass dampers. The optimum parameters of the three-element tuned mass damper for damped main structures due to ground acceleration are investigated in this paper. Unlike the traditional tuned mass damper, the three-element tuned mass damper contains two spring elements and one of them is connected in series with the damping element. The optimum parameters are obtained by simulated annealing algorithm. Numerical results show that the three-element tuned mass damper is very effective in reducing dynamic vibrations of the damped structures.
“…Therefore, this paper presents a reliable optimization strategy used to obtain the optimal parameters of the TMDs. It can be used for systems excited at the resonance frequencies to obtain results very close to the analytical ones with absolute error comparable to existing numerical optimization procedures (Araz, 2020) and also for systems excited with the nonresonant frequencies, for which numerical calculation must be used (Gebai, 2020). The optimization is based on the reduction in the amplitude of the system in the frequency domain, considering the resolution of the response in the time domain.…”
Section: Objective Functionmentioning
confidence: 99%
“…Numerical and analytical results agree well, with an absolute error less than 0.75% for the frequency ratio and 0.60% for the modal damping ratio (Gebai, 2020). A numerical optimization performed by Araz (2020) using the fminimax algorithm shows an error of 1.53% in the frequency ratio and an error of 0.01% in the modal damping ratio of a TMD when compared to analytical equations of optimal parameters of a TMD attached to an undamped structure. Therefore, this paper presents a reliable optimization strategy used to obtain the optimal parameters of the TMDs.…”
Tuned mass dampers (TMDs) are proposed as a solution to reduce the involuntary tremor at the upper limb of a patient with postural tremor. The upper limb is modeled as a three-degrees-of-freedom rotating system in the vertical plane, with a flexion-extension motion at the joints. The measured extensor carpi radialis signal of a patient is used to excite the dynamic model. We propose a numerical methodology to optimize the parameters of the TMDs in the frequency domain combined with the response in the time domain. The objective function for the optimization of the dynamic problem is the maximum angular displacement of the wrist joint. The optimal stiffness and damping of the TMDs are obtained by satisfying the minimization of the selected objective function. The considered passive absorber is a cantilever beam–like TMD, whose length, beam cross-sectional diameter, and mass position reflect its stiffness for a chosen additional mass. A parametric study of the TMD is conducted to evaluate the effect of the TMD position along the hand segment, the number of TMDs, and the total mass of TMDs. The sensitivity of the TMD to a decrease of its modal damping ratio is studied to meet the range of stainless steel. TMDs are manufactured using stainless steel beams of the same length (9.1 cm) and cross-sectional diameter (0.79 mm), for which the mass (14.13 g) position is adjusted to match the optimal frequency. Three TMDs holding a mass of 14.13 g each cause 89% reduction in the wrist joint angular displacement.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
