Nonlinear and parametric analysis on the influence of design parameters of a liquid dynamic absorber for multi-directional lateral vibration mitigation

Abstract This paper investigates a tuned toroidal multi-column liquid dynamic vibration absorber (TTLCD) for multi-directional lateral vibration control in engineering systems, in order to address the directional limitations of traditional unidirectional dynamic vibration absorbers. A nonlinear dynamic model of the TTLCD, incorporating hydrodynamic damping, is developed. Modified formulas for natural frequency, effective length, and area ratio are derived based on the TTLCD’s geometric characteristics. The TTLCD-controlled system’s response to free and harmonic excitations is analyzed numerically using an adaptive step-size method. A parametric study investigates the influence of the TTLCD’s design parameters, including barrier count, area ratio, length ratio, mass ratio, and tuning frequency, on vibration attenuation, exploring parameter interactions for optimal damping performance. Results demonstrate the TTLCD’s effectiveness in controlling vibrations under various lateral excitations. Specifically, the resonance response is reduced to 3.48%–12.3% of the uncontrolled response at tuning frequency ratios of 0.934–0.96 and dynamic vibration absorber mass ratios of 8%–6%. The area ratio primarily affects the TTLCD’s size with minimal impact on damping, allowing up to a 50% reduction in mean diameter. Design charts are provided for efficient initial design, facilitating enhanced damping performance and system stability.