# Effect of Tuned Spring on Vibration Control Performance of Modified Liquid Column Ball Damper
## 1 Introduction  
The trend of high-rise building construction has dramatically increased in recent decades [1]. The use of innovative and high-strength materials in high-rise construction makes the structures slender and susceptible to vibrations [2]. These vibrations cause damages in both the structural and non-structural elements in the building, depending on the amplitude of the vibrations [3, 4]. Apart from structural damages, extensive vibrations could lead to occupants' discomfort [5]. To control and limit the vibrations of the building within the acceptable limit range, various vibration control techniques are used [6; 7; 8; 9]. These techniques include active, passive, and semi-passive control systems [10; 11]. An active control system reduces the vibrations in the structures by modifying the damping or stiffness of the structures through hydraulic or electro-mechanical systems [5]. It consists of three components: (1) sensors, installed at the structure to gauge the structure responses due to external excitations; (2) controllers, to determine the action pathway of the actuators; and (3) actuators, to control the undesirable vibrations after getting the command signals from the controllers. An active control system includes an active tuned mass damper [12] and active tendons. Active control systems are very effective for controlling vibrations due to wind and earthquakes [13; 14]. However, the main disadvantages of such control devices are the high consumption of power, the possibility of destabilization dueto sudden changes in the input parameters [15], and the deactivation of the system under power loss. A semi-active control system requires a minimum external power supply for operation and develops control forces based on structural motion [16]. Control forces are developed based on a feedback signal from sensors that measure the excitations of the structure. Semi-active control system devices can be classified into four categories: (1) variable orifice dampers, (2) variable stiffness dampers, (3) variable friction devices, and (4) controllable fluid devices [5]. These devices have a wide range of applications to control medium- and large-amplitude vibrations. Many of them are designed to function in the post-yield region and are not suitable for small-amplitude vibrations [17]. Passive control systems do not require any external power supply, actuators, or sensors to dissipate unwanted vibration [18]. However, the limitation of such devices is their passive nature, which makes them unable to modify the control forces during an external excitation event. However, this limitation of passive control devices makes them a source of reliability, because passive controls are not affected by the loss of power during a seismic event. Passive control devices are also less sophisticated and have low maintenance costs [19]. Therefore, compared to other control systems, passive systems are intuited to be reliable, economical, and effective. During an external excitation event, passive devices attract the external forces from the main structure and dissipate them to minimize both structural and non-structural damages. These devices include tuned liquid column dampers (TLCDs) [20], tuned mass dampers (TMDs) [21], combined tuned dampers (CTDs) [22], etc. The TLCD was first introduced by [PERSON] et al. in 1989 [23]. It consists of a U-shaped tube filled with fluid, preferably water, with an orifice in the horizontal portion of the tube. Since 1989, various strategies have been proposed for optimum performance of TLCDs under wind and earthquake loadings, such as proposing optimum design parameters [24; 25; 26; 27], optimum tuning, and damping ratios [28; 29] for better performance of TLCDs. [PERSON] and [PERSON] studied a modified version of TLCDs attached to the main structure through a spring under seismic excitation [30].