This paper proposes a passive vibration control device, series rolling-pendulum tuned mass damper (SRPTMD), with a “ball-in-ball” configuration. A conventional pendulum TMD (PTMD) generally requires a long cable length that usually exceeds one-story height for high-rise buildings. A rolling-pendulum TMD (RPTMD) is a mass that can roll on a base with a curvature instead of swaying with a cable, significantly reducing the requirement of vertical rooms. In addition, a ball-in-ball SRPTMD is equivalent to a system with two degrees of freedom in series. This study aimed to derive equations of motion of the primary building-SRPTMD system, conduct a parametric study for SRPTMD, and investigate the structural control performance of an SRPTMD. Results showed that an SRPTMD performed similarly to an RPTMD. One advantage of an SRPTMD is that the fundamental natural frequency of an SRPTMD can be altered to a certain extent by changing the radius ratio of the inner ball to the outer ball, whereas the natural frequency of an RPTMD can only be altered by changing the curvature of its base, which is far more difficult. Another advantage is that the two modal frequencies of an SRPTMD can be manipulated by selecting a specific set of radius ratios between the base, the outer ball, and the inner ball, which means that an SRPTMD has higher potential on multiple modes control.

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