Mathematical modeling and optimization scheme for omnidirectional tuned liquid column dampers

Abstract

As a well-known and reliable control device, tuned liquid column dampers (TLCDs) have been investigated numerically and experimentally and implemented in a number of structures over the last three decades. However, TLCDs basically suffer from the lack of multidirectionality, which is the critical need for real structures, in particular under random vibrations such as wind and earthquake excitations. This aspect has garnered the attention of the structural control community to modify this promising damper to achieve more efficiency and to extend its application range to multidirectional vibrations. This paper proposes a mathematical modeling and optimization approach for omnidirectional tuned liquid column dampers (O-TLCDs). As an improved and reformed TLCD, O-TLCDs are formed by circularly distributed of n (integer n ≥ 3) L-arms about a common joint point at the center, through which all L-arms are connected to each other. Thanks to this layout, O-TLCDs can control structures with full counteracting force capacity in all transversal directions regardless of the excitation angle of incidence. This paper, in the first step, proposes the governing equation of motion of O-TLCDs, for which Lagrange's principle is employed, and the equation of motion of the coupled O-TLCD-structure system. In doing so, a formal solution to determine the degree of freedom (DoF) of the O-TLCD is introduced, which proves independence of the O-TLCD response from the number of L-arms as well as from the angle of excitations. Second, for designing O-TLCDs, a set of design criteria and a general optimization scheme, which accommodate the online simulation of coupled O-TLCD-structure system under arbitrary excitations, are proposed. Consequently, without adding extra complication coming from extra DoFs to the motion equation of the damper, the O-TLCD functions as an enhanced liquid damper for multidirectional vibration attenuation. Next, using the O-TLCDs designed with different mass ratios, numerical simulations of O-TLCD-structure systems are conducted under seismic loads, free vibration, harmonic excitation and white noise and the controlled and uncontrolled responses of the systems are assessed in the time and the frequency domain. Here, the role of important parameters such as the mass ratio, the head loss coefficient, the liquid deflection and the excitation amplitude are evaluated and the influence of varying conditions on the efficiency of the O-TLCD are discussed. Results demonstrate that the proposed O-TLCD can be well tuned to the structure and markedly control the peak and the RMS of responses of the structure. In the end, an experimental study on a prototype O-TLCD is performed using a shaking table, which verifies the proposed mathematical modeling approach.

A review on various configurations of the passive tuned liquid damper

“…The horizontal portions of all the L-shaped limbs are provided with orifices. As shown by Mehrkian and Altay (2020), the effective head loss coefficient of an O-TLCD is equal to half of the total head loss coefficient in all the L-shaped limbs, determined from equation ( 16). Thus, the equivalent linear damping coefficient of an O-TLCD is also equal to half of the total equivalent linear damping coefficient calculated for all the L-shaped limbs using equation ( 17).…”

“…A similar approach would lead to the equations of motion of the structure-damper system involving other types of TLCDs except for the O-TLCD and the TLMCD. Lagrange's principle along with other compatibility criteria are used to derive the governing equations of motion for O-TLCD and TLMCD, which are described in detail in the works of Mehrkian and Altay (2020) and Cao et al (2020), respectively.…”

Adaptive control of damaged structures by using smart tunable liquid column gas damper considering dynamic soil–structure interaction

“…There are numerous numerical and experimental studies on the shape and orientation of liquid dampers to achieve optimal TLCD performance by designing two-way liquid dampers (Min et al, 2014), mathematical modeling and optimizing omnidirectional TLCDs (Mehrkian and Altay, 2020), and developing a model for tuned liquid multiple column dampers (Cao et al, 2020). A modified TLCD model called tuned liquid column ball damper (TLCBD) was also developed in 2015.…”

A tuned liquid mass damper implemented in a deep liquid storage tank for seismic vibration control of short period structures

“…[34] Performance of a TLD under vertical excitations was studied by Constantin et al [35] An annular TLD was proposed by McNamara et al [36] Tuned liquid column damper (TLCD) with fixed orifice at the center of the U-shaped container was proposed and implemented to control the vibration of the long period structures under earthquakes and wind excitations. [37][38][39][40][41][42][43][44] The fixed orifice inside the container was replaced by a moving orifice. [45][46][47] In order to improve the performance and robustness of, inerter devices are also attached recently.…”