Tuned mass dampers are one of the most common devices for the passive control of structures subjected to earthquakes. The structure of these dampers consists of three main parameters: mass, damping, and stiffness. Tuned mass dampers reduce the amplitude of the responses affecting on a mode. In most cases, only a single TMD (tuned mass damper) or a few dampers at several points above the building height are installed on the roof of the building, requiring considerable mass and space in some parts of the structure as overhead. It is also more important to predict the elements that will meet the required mass. In this research, the performance of multiple tuned mass dampers (MTMDs) is investigated in L- and U-shaped regular and irregular tall steel buildings with 10 and 20 floors, under the near- and far-field records. Nonlinear time history analysis is also applied to evaluate the multiple tuned mass dampers effects on the seismic responses of the structures. The SAP2000 API and MATLAB genetic algorithm are used to determine the optimal location of the MTMDs in the roof plans of the buildings. The results show the effects of multiple tuned mass dampers in reducing the seismic response of acceleration, displacement, and base shear up to 50, 40, and 40% in average, respectively. The results of determining the optimum location of MTMDs in the models indicate the importance of the symmetry of the dampers relative to the centre of mass of the building.
During an earthquake event, a significant amount of energy is applied to the structure. If this energy is not absorbed or dissipated, it causes destruction that will result in significant financial and life damage. In conventional methods, the building exhibits resistance by combining stiffness, ductility, and energy dissipation as well as inertia against dynamic forces (e.g., wind, earthquake, vibration of machines, sea waves, etc.). The damping value in these structures is very low and therefore the damped energy is negligible in the elastic behavior range of the structure. These structures experience a great deal of displacement under the influence of strong dynamic forces such as earthquakes crossing the elastic range. Inelastic displacements cause the plastic joints to be positioned locally in some parts of the structure, which in turn increases the ductility, and consequently a large amount of earthquake energy is dissipated by local degradation in the lateral resisting system. In recent years, many efforts have been made to apply modern control devices to the structures exposed to earthquakes. These devices prevent the degradation of the structural elements during earthquake by absorbing some of the energy input into the structures [
Tuned mass dampers (TMDs) are a type of passive damping systems that attaches to the main structure as a secondary mass and reduces the dynamic response of the structure through damping and stiffness, which is widely used in control engineering systems and other civil engineering structures [
In a TMD system, a specific mass is mounted at a specified location of the structure and the vibration amplitude of the structure in the first mode is controlled by a spring and a damper with specified damping and stiffness coefficients. However, when external stimulation is such that the higher modes’ contribution in the response of the structure is greater than the first mode, the TMD system may have the opposite effect and increase the amplitude of vibrations. The basic idea of TMD was first proposed by Frahm [
Structural model of MTMDs [
Li [
To determine the MTMDs parameters, Sadek et al.’s [
The mechanical properties of ST37 steel are as follows (Table
Mechanical properties of steel.
Expected ultimate ( | Expected yield ( | Poisson coefficient ( | Ultimate ( | Yield stress ( |
---|---|---|---|---|
4070 kg/cm2 | 2640 kg/cm2 | 0.3 | 3700 kg/cm2 | 2400 kg/cm2 |
All the structures have been modelled as 3D models and analyzed with nonlinear dynamic analysis. The sample structures are considered to be steel structures with special ductility. The dead and live loads of the floors are 500 kgf/m2 and 200 kgf/m2, respectively, floors’ height is 3.2 meters, and the structure is made from 5 bays with 6-meter length and regular plan. According to Soto and Adeli [
Seismic parameters of models.
Models | T | T. | K | B | C | ||
---|---|---|---|---|---|---|---|
Regular 10-story | 7.5 | 1.07 | 0.15 | 0.7 | 1.42 | 1.632 | 0.076 |
Regular 20-story | 7.5 | 2.26 | 0.15 | 0.7 | 1.88 | 1.134 | 0.053 |
After spectral analysis, the structural elements are designed in SAP2000.v.19.2 software. AISC360-10 regulation is used to design members and seismic criteria are applied to design members. The utilized sections are HEB for beams and BOX for columns.
To determine the impact of the control system, 7 records from 7 different near-field earthquakes and 7 far-field earthquakes have been selected. In order to investigate the effects of damper in different models, earthquake records have been applied in one direction to the structure of analytical models. The properties of the selected records are given in Tables
Near-field earthquake properties.
Record | Station | Year | Dis (km) | Mag | PGA | PGV (cm/s) | Duration (sec) | ||
---|---|---|---|---|---|---|---|---|---|
1 | Alaska-Denali | Pump | 2002 | 2.74 | 7.9 | 0.32 | 1689 | 3.48 | 86 |
2 | Bam | Bam | 2003 | 1.7 | 6.6 | 0.59 | 417 | 0.78 | 37.36 |
3 | Chi-Chi | Thy101 | 1999 | 9.94 | 7.62 | 0.44 | 261.38 | 0.9 | 26.48 |
4 | Chi-Chi | Tcu 68 | 1999 | 0.32 | 7.62 | 0.56 | 312 | 0.42 | 12.48 |
5 | Imperial-Valley | El Centro Array | 1979 | 1.35 | 6.53 | 0.43 | 250.12 | 0.24 | 8.49 |
6 | Kobe | Takatori | 1995 | 1.47 | 6.9 | 0.61 | 206 | 1.22 | 11.34 |
7 | Borujerd | Silakhor | 1909 | 12 | 7.3 | 0.44 | 321 | 1.52 | 56.34 |
Far-field earthquake properties.
Record | Station | Year | Dis (km) | Mag | PGA | PGV (cm/s) | Duration (sec) | ||
---|---|---|---|---|---|---|---|---|---|
1 | Chi- Chi | Chy 065 | 1999 | 83 | 7.62 | 0.6 | 130.79 | 0.62 | 28.515 |
2 | Chi-Chi | Tap95 | 1999 | 109 | 7.62 | 0.15 | 178.062 | 0.98 | 15.8 |
3 | Imperial-Valley | Oak-2 | 1979 | 18.87 | 5.01 | 0.24 | 148.23 | 0.32 | 12.515 |
4 | Imperial-Valley | Outers | 1979 | 24.23 | 6.53 | 0.26 | 38.78 | 0.16 | 1.75 |
5 | Kobe | Hik | 1995 | 95 | 6.9 | 0.14 | 110.64 | 0.6 | 17.04 |
6 | Loma Prieta | Halls Valley | 1989 | 30.25 | 6.93 | 0.23 | 107.85 | 0.3 | 10.78 |
7 | Manjil | Qazvin | 1990 | 49.97 | 7.37 | 0.13 | 83.79 | 0.16 | 25.71 |
According to Code 2800, the accelerometer data used for structural analysis must be normalized. To normalize them, after scaling them to their maximum value (PGA), the accelerometer data response spectrum is provided for a 5% damping. Then, the obtained spectra of the accelerometer data are averaged and compared over the time intervals of 0.2 T and 1.5 T, so that according to the 2800 code the average spectrum should be 1.4 times larger than the standard code 2800 spectrum [
Comparison of response spectrum average of earthquake records with 2800 standard spectrum.
In this paper, according to Soto and Adeli [
Design parameters of mass damper in regular and irregular 10-story models.
Model | |||||
---|---|---|---|---|---|
Regular 10-story | 0.03 | 22779 | 496.65 | 212.3 | 22.07 |
L-shaped 10-story | 0.03 | 16297 | 311.93 | 142.59 | 14.83 |
U-shaped 10-story | 0.03 | 17531 | 227.2 | 126.22 | 13.12 |
The plan used in the models is a regular and irregular square with 5 bays with 5-meter openings for regular models. Irregular plans according to the definition of geometrical irregularities mentioned in the irregular plans based on the definition of plan geometrical irregularity in 4th edition 2800 code [
Mass application in the TMD model.
In this research, dampers are used in three conditions: at first, at one point on the roof, second, at two points on the roof, and third, at four points on the roof. The placement of the dampers is given in Figures
Damper at one point (right), dampers at two points (middle), and dampers at four points (left).
Damper at one point (right), dampers at two points (middle), and dampers at four points (left).
Damper at one point (right), dampers at two points (middle), and dampers at four points (left).
In this study, for the purpose of verification, the effects of multiple mass dampers on the seismic behavior of 3-story structure have been investigated experimentally by Chen and Wu [
Studied structure on the shaking table [
This structure is designed to test the control of a structure with a hydraulic actuator placed on the first roof. The model is restrained with steel braces in three floors and stimulated with a hydraulic Jack. Structural restraint with steel braces has no role in the structural behavior and is solely applied to evaluate the performance of the mass dampers. Each mass damper consists of a mass block, a set of continuous springs, and a sliding shaft ball bearing. The mass block attaches to the base wall of the damper via extension springs and can only move along the dual shafts. The natural frequency of the damper can be adjusted using different types of springs. Since no damping element has been added to the damper system intentionally, friction between the bearings and the shafts forms the main damping part of the system [
The concentrated masses on the first, second, and roof are 445, 394, and 388 kg, respectively. Forced excitation experiments were performed to identify the structural parameters for all three modes. First, several sine sweep experiments were performed to identify approximately the natural frequencies of the structure. Then, a series of concurrent tests with different excitation frequencies were performed around the natural frequencies of the tested structure. The modal properties of the test are shown in Table
Modal properties of structure [
Mode no., | 1 | 2 | 3 |
---|---|---|---|
Frequency, | 2.743 | 9.45 | 18.84 |
Normalized mode shape, Φ | |||
Damping ratio, | 0.48 | 1.15 | 1.45 |
Participation factor, | 33.904 | 8.293 | −2.863 |
Orthogonality with respect to mass matrix, |
Six different types of continuous springs were used consistently throughout the shake table tests. Three specimens were selected randomly and with determination of resilience constant. The properties of the dampers are given in Table
Utilized damper properties in the model [
Mass, | Damping, | Stiffness, |
---|---|---|
The damper free vibration pattern for the first mode is shown in Figure
First mode stimulation pattern [
The following results are obtained and compared with the values of the paper by studying the floor accelerations in the dampers with masses of 60 and 80 kg. It should be noted that this issue has been analyzed simultaneously in the OPENSEES and MATLAB programs. The comparison diagram of the controlled structure acceleration results with damper in software with the experimental model results is shown in Figure
Comparison diagram of controlled structure acceleration results with damper in software analysis with obtained results of the experimental model.
Mass dampers reduce the applied force to the structures by structural mass increase approach and the change in the stiffness and mass matrices of the structures, which results in a change in the effective time period of the structure and getting the structure away from the acceleration sensitive boundary. When the dampers are in a position of the structures, the control of seismic response of the structures is not significant and has little effect on the response of the structures with higher predominant modes. Thus, when the damper is located at more than one point, it is possible to control the seismic response of the structures by controlling the impact of higher modes.
To evaluate the effect of tuned mass dampers on the seismic response of regular and irregular structures in different damper position conditions, the maximum lateral displacement of the roof is extracted for near- and far-field records. In this study, dampers are mounted on the roof floor in three conditions: one, two, and four dampers. The records used in this study are 7 near-field and 7 far-field records. In this section, the displacement value for each record with damper and without damper conditions is plotted. Figure
Maximum roof displacement under the near-field (right) and far-field (left) earthquakes in the regular 10-story model.
According to the results of the maximum displacement investigated for the 10-story structure without mass dampers and with different conditions with different mass dampers, it can be seen that utilizing tuned mass dampers in near-field and far-field records significantly reduces the displacement of the 10-story structure. It is observed that the change in the number of dampers leads to a change in the responses. The highest displacement reduction for near-field records in the case of using a damper is 43%. This amount of reduced displacement is investigated toward the case of without damper. The highest amount of displacement reduction for the cases of two and four dampers is 49% and 52%, respectively. The results of the far-field records also show that, in the case of one damper, the reduced mean displacement compared to the cases of without damper, two dampers, and four dampers is 45%, 55%, and 60%, respectively, but on average using four dampers reduces displacement more than using two dampers. In a number of earthquake records, especially in near-field ones, due to the frequency content and earthquake parameters, using two dampers has better results than the four dampers.
Tuned mass dampers have the greatest impact on the acceleration value of the structures and control the seismic response of the structures by getting the structures away from the acceleration sensitive region. The maximum acceleration of the roof in the ten-story model is shown in Figure
Maximum roof acceleration under the near-field (right) and far-field (left) earthquakes in the regular 10-story model.
Since the acceleration of the floors of a structure is influenced by the transmitted acceleration from the ground and the dynamic characteristics of the structure, therefore the mass of the structure increases with the use of mass dampers and the acceleration of the floors reduces with increasing the time period of the structure. This issue is investigated for the 10-story structure in the case of using mass dampers compared to without damper, which yields interesting results. The floor acceleration of the 10-story structure in a fixed mass is affected by the damper number and position. This issue is also investigated for near- and far-field records and the frequency content effects of near- and far-field earthquake records. It is observed that the maximum acceleration reduction for near-field records when using one, two, and four dampers is 28, 46, and 46%, respectively. The results also show 36%, 46%, and 44% reduction for far-field earthquakes, respectively. The results show the effect of the number of dampers on the acceleration reduction of the structure affected by the near- and far-field records. It is also observed that the change in the properties of the record causes a change in the seismic responses such that the near-field records increase the acceleration values in the cases of using 1, 2, and 4 dampers over the far-field records due to the pulse in the velocity frequency content.
The base shear value reduces at a constant mass by changing the applied acceleration to the structure. In this section, the maximum base shear obtained from the time history analysis is presented for the near- and far-field records. The effects of the tuned mass dampers on the reflection of the earthquake force to the structures are evaluated considering the base shear, and the force dissipation is determined in different conditions considered for the multiple mass dampers. The maximum base shear in the ten-story model is given in Figure
Base shear under the near-field (right) and far-field (left) earthquakes in the regular 10-story model.
The base shear of the structures is important because any changing in the applied acceleration to the structures changes the amount of base shear. The acceleration value of the 10-story structure is investigated under the near- and far-field records in the cases of with damper and without damper. The results show that, in the case of using tuned mass damper, the reduction value of applied acceleration to the structures is proportional to the reduction value of structural base shear. This reduction is different for different dampers. In the case of using one damper, the maximum reduction for near- and far-field records is 40% and 36%, respectively. The results for using two and four dampers in near- and far-field records are 46%, 42%, 46%, and 44%, respectively.
In this section, the maximum base shear obtained from the time history analysis for near- and far-field records is presented. The maximum base shear in the ninth floor of the ten-story model is shown in Figure
Base shear with damper in the ninth story under the near-field (right) and far-field (left) earthquakes in the regular 10-story model.
The numerical results of the seven near- and far-field records for the case that the damper is placed on the ninth floor of the 10-story structure show that using tuned mass dampers on the penultimate floor of the structure also has a significant effect on reducing the base shear value. On the other hand, it can be seen that changing the number of dampers changes the base shear value, and in some cases, having more dampers leads to noticeable reduction in base shear. The numerical analysis of base shear for near-field records shows that, in the cases of using one, two, and four dampers, the maximum reduction is 30, 53, and 48%, respectively. For far-field records, these values are 24, 39, and 33%, respectively.
In this section, the maximum acceleration obtained from the time history analysis for near- and far-field records is given. The maximum acceleration in the ninth floor of the ten-story model is given in Figure
Acceleration with damper in the ninth story under the near-field (right) and far-field (left) earthquakes in the regular 10-story model.
Studying the maximum acceleration of the roof for the case where the dampers are placed on the ninth floor of the 10-story structure indicates that utilizing tuned mass dampers on the penultimate floor can control the acceleration of the structure. It is observed that the change in damper position has a different effect on the acceleration values of the roof. The change in the number of dampers in the plan also causes a change in the maximum value of roof acceleration. Numerical analysis of the roof acceleration shows that the maximum acceleration reduction of the floor for the cases with one, two, and four dampers under the near-field records is 36, 44, and 45%, respectively. This value for far-field records is 39, 43, and 47%, respectively.
In this section, the displacement obtained from the time history analysis for near- and far-field records is given. The maximum displacement in the ninth floor of the ten-story model is given in Figure
Displacement with damper in the ninth story under the near-field (right) and far-field (left) earthquakes in the regular 10-story model.
By studying the maximum lateral displacement of the roof in the case the damper is located in the ninth-floor, it can be seen that the change in the number of the dampers in the ninth floor has a different effect on the lateral displacement reduction of the roof. The maximum reduction in the lateral displacement in the case of using TMDs with one, two, and four dampers for near-field records is 52, 55, and 59%, respectively, and these values for far-field records are 51, 74, and 58%, respectively. The placement of the dampers in the ninth floor rather than the tenth floor affects the dynamic properties of the structure and changing the frequency characteristics of the structure including the time period of the structures alters the effects of the dampers in the seismic response of the structure. In general, regarding the location of the mass dampers in the tenth and ninth floors of the regular ten-story model, it can be concluded that using the mass dampers has significant effects on the seismic responses of the structures up to 50% reduction in average in the roof acceleration, displacement, and the base shear. Using 2 or 4 dampers compared to one damper shows a significant reduction up to 25% in the seismic response of the structure. The response reduction variations in near-field records are more noticeable than those in the far-field, due to the frequency content and the details of earthquake parameters. The responses also show better adaptation of the mass dampers to analytical models with near-field records. The placement of the dampers in the tenth floor shows little difference in the seismic response compared to the ninth floor in the present analytical model. It is worth noting that the application of dampers is also investigated in the irregular structures and the maximum percentage reduction in the regular and irregular structures is shown in Tables
Maximum displacement reduction percentage of roof in the regular and irregular 10-story models.
Roof displacement reduction % | 1-damper | 2-damper | 4-damper | |||
---|---|---|---|---|---|---|
Record | Near-field | Far-field | Near-field | Far-field | Near-field | Far-field |
Regular 10-story | 43 | 45 | 49 | 70 | 52 | 52 |
L-shaped 10-story | 40.85 | 51.75 | 48.02 | 80.5 | 50.44 | 56.16 |
U-shaped 10-story | 49.45 | 51.75 | 56.35 | 80.5 | 50.44 | 59.8 |
Maximum acceleration reduction percentage in the regular and irregular 10-story models.
Roof acceleration reduction % | 1-damper | 2-damper | 4-damper | |||
---|---|---|---|---|---|---|
Record | Near-field | Far-field | Near-field | Near-field | Far-field | Near-field |
Regular 10-story | 28 | 36 | 46 | 46 | 46 | 44 |
L-shaped 10-story | 27.72 | 32.04 | 40.02 | 45.54 | 45.54 | 43.56 |
U-shaped 10-story | 29.96 | 38.52 | 49.22 | 49.22 | 49.22 | 47.08 |
Maximum base shear reduction percentage in the regular and irregular 10-story models.
Base shear reduction % | 1-damper | 2-damper | 4-damper | |||
---|---|---|---|---|---|---|
Record | Near-field | Far-field | Near-field | Far-field | Near-field | Far-field |
Regular 10-story | 40 | 36 | 46 | 42 | 46 | 44 |
L-shaped 10-story | 44.8 | 38.52 | 51.52 | 36.54 | 51.52 | 49.28 |
U-shaped 10-story | 41.6 | 32.04 | 40.94 | 43.68 | 47.84 | 45.76 |
The results of the tables show the significant impact of the mass dampers on the reduction of seismic parameters and responses. The percentage of reduction in the models with multiple mass dampers is more than single dampers. In the case of base shear response, increasing the number of dampers from one to four increases the percentage reduction in all models and the responses are mostly reduced in near-field records and the desirable capabilities of the dampers are noticeable in controlling the displacement and accelerations of the structures in near-field records. In the case of roof displacement, as the number of dampers increases, an increase in the percentage of response reduction is observed, and the response of roof displacement is further reduced in far-field records such that, in the special cases, using two dampers under far-field earthquake shows a reduction by approximately 80%. Increasing the number of dampers has also remarkable effect in the reduction of acceleration responses.
In the optimization section, the effect of 2 and 4 dampers on the last floor of the 10- and 20-story structures has been investigated. For this purpose, a genetic algorithm has been used to find the optimal position of these dampers, so that the position of the structural nodes in the roof level (with
Thus, at the beginning of the algorithm, the number of
In all models, after a maximum of 4 generations, the response to the constant value has been converged, but in order to ensure that the answer to the problem has continued for up to 8 generations, it means for each model about 240 different damper combinations have been examined and in 8 generations all cases have been checked. The stop limitation was not to change the function of the target and the roof movement.
Nonlinear time history analysis under the El Centro earthquake is used to analyze the structures. The analysis output used to compare and evaluate the number and position of dampers is the maximum displacements of the roof. Modelling, analysis, and comparison of the outputs for different models are performed using the SAP software API.
API programming interface is a valuable tool for CSI software such as SAP and ETABS that allow engineers to exploit them with coding language such as Visual Basic under Excel (VBA), C#, C++, MATLAB, Fortran, and Python. In other words, an engineer using API is capable of coding all ETABS and SAP software commands and tools and accomplishes tasks such as modelling, loading, analyzing, and extracting a variety of results. Engineers can build custom work tools using the API to control CSI software. These tools are able to repeatedly perform time-consuming tasks in a matter of seconds without human error.
In this section, the effects of 2 and 4 dampers on the roof level for 10- and 20-story structures are investigated. For this purpose, the genetic algorithm is used to find the optimal position of these dampers for each number of dampers, so that the position of the structural nodes in the roof level (
Genetic algorithm parameters.
Mutation rate (%) | Selection rate (%) | Generation | Population | Algorithm type |
---|---|---|---|---|
20 | 70 | 15 | 30 | Continuous |
All models converged to a constant value after a maximum of 4 generations, but it continued for up to 8 generations to ensure the problem is answered (approximately 240 different damper combinations are examined for each model). The locations of the dampers in the cases of using 4 and 2 dampers obtained from genetic algorithm are shown for different structures in Figures
Convergence diagram of the ten-story model with 4 dampers in genetic algorithm (right) and damper optimal positions (left).
Convergence diagram of the ten-story model with 2 dampers in genetic algorithm (right) and damper optimal positions (left).
Displacement of the ten-story regular model with 2 and 4 dampers.
Convergence diagram of the ten-story model with 4 dampers in genetic algorithm (right) and damper optimal positions (left).
Convergence diagram of the ten-story model with 4 dampers in genetic algorithm (right) and damper optimal position (left).
Displacement of the ten-story irregular L-shaped model with 2 and 4 dampers.
Convergence diagram of the ten-story U-shaped model with 4 dampers in genetic algorithm (right) and damper optimal positions (left).
Convergence diagram of the ten-story U-shaped model with 2 dampers in genetic algorithm (right) and damper optimal positions (left).
Displacement of the ten-story irregular U-shaped model with 2 and 4 dampers.
The results indicate the significant effects of the mass dampers on the structures. Multiple dampers’ symmetrical placement in the plan also plays an important role in the results and responses and the changes in the positions of dampers have insignificant effect in the response of the structure if their overall positional symmetry does not disagree with the plan axes. In other words, proper and symmetric mass distribution of the mass dampers in the plan plays an important role in reducing the seismic responses of the structures. It can also be noted that the mass dampers with their mass and stiffness change the dynamic characteristics of the structures and affect the seismic responses. Therefore, if the placement of the mass dampers can bring the centre of mass closer to the centre of rigidity, it can reduce the amount of irregularities and its effects and optimize the seismic behavior of the structure. What is considered in determining the optimum position of the mass dampers is their symmetrical positioning which improves the seismic response of the structures. In irregular U-shaped structures, the distribution of dampers is almost symmetric. As it can be seen, the damper optimal positioning approaches the centres of mass and rigidity to each other and reduces the eccentricity and, as a result, improves the responses in irregular L-shaped structures.
All models converged to a constant value after a maximum of 4 generations, but it continued for up to 8 generations to ensure the problem is answered (approximately 240 different damper combinations are examined for each model). The locations of the dampers in the cases of using 4 and 2 dampers obtained from genetic algorithm are shown for different structures in Figures
Convergence diagram of the twenty-story model with 2 dampers in genetic algorithm (right) and damper optimal positions (left).
Convergence diagram of the twenty-story model with 4 dampers in genetic algorithm (right) and damper optimal positions (left).
Displacement of the twenty-story regular model with 2 and 4 dampers.
Convergence diagram of the twenty-story irregular L-shaped model with 2 dampers in genetic algorithm (right) and damper optimal positions (left).
Convergence diagram of the twenty-story irregular L-shaped model with 4 dampers in genetic algorithm (right) and damper optimal positions (left).
Displacement of the twenty-story irregular L-shaped model with 2 and 4 dampers.
Convergence diagram of the twenty-story irregular U-shaped model with 2 dampers in genetic algorithm (right) and damper optimal positions (left).
Convergence diagram of the twenty-story irregular U-shaped model with 4 dampers in genetic algorithm (right) and damper optimal positions (left).
Displacement of the twenty-story irregular U-shaped model with 2 and 4 dampers.
In this research, the effects of optimal number and position of multiple mass dampers on 10 and 20 regular and irregular steel buildings are investigated. The increasing use of high-rise buildings for economic and technical reasons has led to increased research into the control of such structures against earthquake and wind forces and their technical efficiency. Plan irregularity is also one of the important issues that designers and earthquake specialists face. In this research, a wide range of near- and far-field records with different earthquake intensities and parameters are used, and the dampers are designed and installed with respect to the dynamical relationships and the models are analyzed by nonlinear time history analysis. The results show a more desirable effect of using more dampers in models than single mass dampers. Placing dampers at more than one point further reduces the seismic response of the structures and increases the reduction rate of each response such as base shear, displacement, and acceleration of floors. As the dampers are positioned at different points, the mass distribution at the floor level is increased; thereby the applied force by the accelerated mass and the responses are reduced, but when the concentrated mass is positioned at one point of the structure, the applied acceleration to the point is increased and thereby less control is achieved over the seismic response of the structure. The results show that, in most far- and near-field records, when the dampers are positioned at four symmetrical points in the plan, the internal effort of the resisting members in a story is simultaneously contributed against the increasing applied forces by mass and thereby the responses of the structure are reduced due to the reduction of applied acceleration to the floors and the increase of the time period by controlling the amount of torsion in the irregular structures and the appropriate mass distribution between the lateral elements. It is observed that the effect of mass dampers for different earthquake records has considerable differences, because the characteristics and frequency content of far- and near-field records have differences such as maximum ground acceleration (PGA), magnitude, distance from the fault, the amount of energy released, and the durability, so adding a mass damper changes the dynamic properties and affects the effective frequency of the structure. In the same number of dampers in the far-field records, there is a reduction in the acceleration changes and in the near-field records, the maximum acceleration is observed. In general, multiple dampers in the near-field domain have a better performance in reducing the acceleration of the models, which is also true for floor displacements. The story base shear reduction is observed in the near-field domain and increasing number of dampers. The 45% reduction on average for displacement, base shear, and acceleration of the model floors using multiple mass dampers clearly indicates the appropriate performance of this device in improving the performance of structures. The results show that there is no significant change in the results of the seismic parameters due to changing the dampers position from the tenth floor to the ninth floor. In the ninth floor, the increase in the number of dampers also indicates the distribution of the dampers mass and the contribution of the dampers in controlling the response and the optimal performance of the structure. In irregular L-shaped structures, the position of the dampers in optimal mode brings the mass centre closer to the centre of rigidity and reduces the rate of eccentricity, and the results are significantly improved. Therefore, if the placement of mass dampers can bring the centre of mass closer to the centre of rigidity, it can reduce the irregular value and its effects and optimally improve seismic behavior. What has been considered in determining the optimal position of mass dampers is their symmetrical placement, which has improved seismic response in structures. In irregular U-shaped structures, the distribution of dampers has been almost symmetrical. In the case of optimum positioning using genetic algorithm, the results show that the symmetry of the dampers position in the plan plays an important role in the results and responses, and the positioning of multiple dampers symmetrically in the irregular structures plan plays an important role in the results and responses and the position changes of each damper are neglectable in the seismic response of the structures if their overall position relative to the plan axis is preserved. In other words, the appropriate and symmetric mass distribution of the dampers in the plan has an important role in reducing the seismic response of the structures. In irregular L-shaped structures, the damper optimal position approaches the centre of mass to the centre of rigidity, reduces the eccentricity, and improves the results significantly.
No data were used to support this study.
The authors declare that they have no conflicts of interest.