Mathematical modeling and optimization scheme for omnidirectional tuned liquid column dampers. (13th October 2020) - Mehrkian, Behnam; Altay, Okyay
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 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 the 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 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. Graphical abstract: Image 1 Highlights: Mathematical representation of omnidirectional TLCDs (O-TLCD). Formal solution to determine the degree of freedom of O-TLCDs. Design criteria and optimization scheme with simulation under arbitrary excitation. Numerical demonstration of control efficiency and role of parameters such as head loss. Experimental study showing the validity of the proposed mathematical representation.