Abstract
Tuned Mass Dampers (TMDs) are widely used for the control and mitigation of vibrations in engineering structures, including buildings, towers, bridges and wind turbines. The traditional representation of a TMD is a point mass connected to the structure by a spring and a dashpot. However, many TMDs differ from this model by having multiple mass components with motions of different magnitudes and directions. We say that such TMDs have added mass. Added mass is rarely introduced intentionally, but often arises as a by-product of the TMD suspension system or the damping mechanism. Examples include tuned pendulum dampers, tuned liquid dampers and other composite mechanical systems. In this paper, we show how a TMD with added mass can be analyzed using traditional methods for simple TMDs by introducing equivalent simple TMD parameters, including the effective TMD mass, the mass of the equivalent simple TMD. The presence of added mass always reduces the effective TMD mass. This effect is explained as a consequence of smaller internal motions of the TMD due to the increased inertia associated with the added mass. The effective TMD mass must be correctly calculated in order to predict the TMD efficiency and in order to properly tune the TMD. The developed framework is easy to apply to any given general linear TMD system with a known motion. Here, we demonstrate the approach for a number of well-known examples, including tuned liquid dampers, which are shown to use only a small fraction of the total liquid mass effectively.
Highlights
Vibrations give rise to a great deal of problems to man-made structures and devices
The Tuned Mass Dampers (TMDs) is tuned relative to the natural frequency of the main structure, such that energy is rapidly transferred from the main structure vibrations to the TMD mass, which in turn dissipates the energy by internal damping
The effect of a TMD depends on the mass ratio μ, the TMD mass divided by the main structure mass, giving an added damping with a damping ratio of p order ζ ∼ μ/8; a relatively light TMD can introduce significant damping, and the added damping increases with the mass of the TMD
Summary
Vibrations give rise to a great deal of problems to man-made structures and devices. Vibrations can be annoying to people in a building or vehicle, or they may even lead to metal fatigue or structural collapse. The mass of a general TMD can be described in several ways, including the inertial mass M I associated with the momentum of the damper in the direction of the structure motion, the kinetic energy mass MK (sometimes referred to as the modal mass) associated with the kinetic energy internal to the damper and the total mass MT equal to the sum of the masses of each damper component (see Section 3.3). A simple TMD denotes a Tuned Mass Damper (TMD), where all mass moves in the same direction of the main structure. A general TMD denotes a general linear one degree-of-freedom system attached to a moving structure and consisting of N mass elements, whose motion relative to the structure is governed by a single coordinate x1.
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