Damping vibrations of a hyperbolic cooling tower using a reactive damper

. Experience in the construction of buildings and structures in areas where there is a threat of earthquakes shows that it is necessary to take seismic protection measures to prevent damage. Vibration dampers are widely used as means of protection. When choosing a vibration damping method, it is necessary to take into account the design features of the building. In this study, the possibility of using a reactive damper to dampen the vibrations of a hyperbolic cooling tower was studied. A numerical experiment was carried out to evaluate the absorber efficiency and select its parameters. An analysis of the results showed that the faster the response time of each charge, the more effective the damping of oscillations. An increase in the reactive force of each charge increases the efficiency up to a certain limit, after which the structure begins to swing in the opposite direction. It was found that the two-sided actuation of charges increases the efficiency of vibration damping.


Introduction
Experience in the construction of buildings and structures in seismically hazardous areas shows that seismic protection measures must be applied to protect them from damage caused by earthquakes.Vibration dampers are widely used as protective devices.Vibration damping of mechanical systems can be achieved in various ways: using composite polymer materials [1], friction vibration dampers [2], roller systems [3], new technological solutions [4], etc.At present, various types of dampers have been developed and optimized.oscillations, of which the most common are Tuned Mass-Damper [5][6][7], Tuned Mass Column Damper [8,9], used mainly for high-rise buildings.However, some of these absorbers are effective only in a narrow range of operating oscillation frequencies.Therefore, it is necessary to develop more versatile, efficient and relatively inexpensive methods of semi-active or passive vibration damping.In [10][11][12], new original methods of vibration damping of various designs and calculation methods were considered, in particular, a belt-cable system with a single-acting hydraulic cylinder.When choosing a vibration damping method, it is important to take into account the design features of the building.In this paper, the possibility of damping oscillations of a hyperbolic cooling tower using a reactive damper is investigated.

Materials and methods
A numerical experiment was performed to evaluate the absorber performance, select and adjust its parameters.The structure under study was a three-dimensional hyperbolic cooling tower with a hexagonal shape in plan (Fig. 1).

Fig. 1. Spatial cooling tower diagram
The maximum diameter of the cooling tower is 20 m, the minimum diameter is 10 m.The cooling tower consists of seven tiers 3 m high.The total height of the structure is 21 m.2012.
The seismic load was modeled using the volumetric accelerogram of the earthquake in the city of Gazli (Uzbekistan) in 1976.The dynamics problem was solved in the form of a finite element method using the Newmark method.

Results
Let us consider vibrations that would be typical for the cooling tower under study under the conditions of an earthquake in the city of Gazli (Uzbekistan) in 1976.The movements of one of the upper nodes of the cooling tower are shown in Figure 2. The maximum movement along the x-axis is 0.33 m, along the y-axis -0.164 m, along the z-axis -0.241 m.Design Rules", the limiting horizontal displacements of the top of highrise buildings, taking into account the roll of the foundations when calculating according to the undeformed scheme, depending on the height of the building, should not exceed h/500 (h is the construction height of the building).For the considered cooling tower, the limit displacement is 21/500=0.042m.
Consider the harmonic load acting on the nodes of the structure in the horizontal direction.The load value changes according to the law: P=50·sin(0,9w1) (1) where w1 -the lowest frequency of natural oscillations.With such a load, a beating effect appears on the graph of displacements of the upper node of the cooling tower.The maximum horizontal movement is 0.083 m.Thus, the cooling tower in question does not comply with current regulations.
An active damper installed in the central node of the upper tier of the cooling tower was used to combat structural vibrations.The damper is set to operate under the following conditions: the amount of horizontal displacement along the X axis of one of the upper nodes exceeds 0.02 m and the direction of the velocity vector in this node coincides with the direction of movement.The reactive force created by the absorber was directed in the direction opposite to the displacement.As variable parameters, the response time of each charge and the force that occurs when the charge is triggered are taken.
At the beginning of the research, let us compare the efficiency of vibration damping with the help of a reactive damper with its one-sided and two-sided operation.The research results are shown in Figure 3.With one-sided actuation of charges, the efficiency of vibration damping is reduced compared to two-sided actuation.With a charge actuation time of 0.025 s and a reactive force of each charge of 900 N, the maximum horizontal displacement of the upper unit of the cooling tower decreased: with two-sided actuation -up to 0.037 m (by 55.4%), with one-  With a charge response time of 0.025 s and a reactive force of each charge of 800 N, the maximum horizontal displacement of the upper cooling tower assembly decreased to 0.041 m, i.e. by 50.6%, with a charge response time of 0.05 to 0.044 m, i.e. by 47.0%, with a charge response time of 0.075 to 0.049 m, i.e. by 41.0%.It has been established that the shorter the response time of each charge, the more effective the damping of oscillations.
A number of numerical experiments were carried out to study the influence of the reactive force of each active absorber charge on the extinguishing efficiency.The data obtained is shown in Figure 5.It has been established that with an increase in the reactive force of the charge to 900 N, the efficiency of the absorber increases.With the given charge strength and the charge response time of 0.025 s, the maximum horizontal displacement of the upper cooling tower assembly decreased to 0.037 m, i.e. by 55.4%, with a charge response time of 0.05 to 0.04 m, i.e. by 51.8%, with a charge response time of 0.075 to 0.047 m, i.e. by 43.4%.With a further increase in the charge strength, the efficiency of the reactive absorber decreases.With a charge strength of 1000 N and a charge response time of 0.025 s, the maximum horizontal displacement of the upper unit of the cooling tower decreased to 0.04 m, i.e. by 51.8%, with a charge response time of 0.05 to 0.042 m, i.e. by 49.4%, with a charge response time of 0.075 to 0.056 m, i.e. by 32.5%.This is due to the fact that due to the high force of the charge, the absorber "rocks" the structure in the opposite direction.

Conclusions
In the course of the numerical experiment, it was found that with one-sided actuation of charges, the oscillation damping efficiency decreases compared to two-sided actuation.Analysis of the results showed that the shorter the actuation time of each charge, the more effective the damping of oscillations.An increase in the reactive force of each charge increases the efficiency up to a certain limit, after which the absorber "rocks" the structure in the opposite direction.In general, the studies carried out prove the high efficiency of reactive

Fig. 2 .
Fig. 2. Movements of the top node of the cooling tower along the x, y and z axes

Fig. 3 .
Fig. 3. Movements of the upper node of the cooling tower without a damper and with a damper in case of two-sided and one-sided actuation of charges (charge actuation time 0.025 s,), graph of change in the reactive force of the damper: a -reactive force 100 N; b -reactive force 600 N; c -reactive force 900 N

Fig. 4 .
Fig. 4. Movements of the upper unit of the cooling tower without and with a damper (reactive force 800 N), graph of the change in the reactive force of the damper: a -charge response time 0.025 s: bcharge response time 0.025 s; c -charge response time 0.025 s.

Fig. 5 .
Fig. 5. Graphs of the dependence of the maximum displacement of the upper node on the value of the reactive force of the absorber at different charge response times (0.025, 0.05 and 0.075 s) Conferences 458, 08014 (2023) EMMFT-2023 https://doi.org/10.1051/e3sconf/202345808014absorbers with double-acting actuation, their use allows to reduce oscillations by more than 2 times.