Tuned Mass Dampers: Controlling Wind-Induced Building Motion

Tall, slender buildings rarely have a strength problem in wind − the columns and core are sized for gravity and seismic loads with plenty of reserve against a design wind event. The problem is comfort. Occupants near the top of a building that sways or accelerates noticeably in a moderate wind will notice it long before any structural member is in danger, and habitability criteria based on peak acceleration, not stress, often end up governing the design of the lateral system on very tall or very slender towers. A tuned mass damper (TMD) is one of the more direct ways to solve that problem without simply adding more stiffness.

The Basic Mechanism

A TMD is a secondary mass connected to the building through a spring and a damping element, tuned so its natural frequency sits close to the frequency of the building mode causing the discomfort − almost always the first sway mode in the direction being controlled. When the building moves at that frequency, the secondary mass oscillates out of phase with it, and the connecting spring and damper transfer energy from the building into the damper mass, where it is dissipated as heat rather than continuing to build up structural motion. This is the same physical idea covered in any discussion of resonance and damping, applied deliberately as a design device rather than treated as a problem to avoid.

The classic tuning relationships, developed for an undamped primary structure, size the auxiliary mass ratio (secondary mass divided by generalized modal mass of the structure, commonly in the range of 0.5 to 2 percent for building applications), the optimal frequency ratio between damper and structure, and the optimal damper damping ratio, all as functions of that mass ratio. A smaller mass ratio requires more precise tuning and gives a narrower band of effective frequencies; a larger mass ratio is more forgiving of tuning error and wider-band in its effectiveness, but costs more in damper mass, travel, and mechanical hardware.

Pendulum and Active Variants

Many building TMDs are built as pendulums rather than mass-on-a-spring assemblies, because a pendulum's period depends only on its effective length (approximately proportional to the square root of length for small swings), which is mechanically simpler to tune and maintain than a discrete spring system carrying tons of steel or concrete mass. A bidirectional pendulum TMD can control sway in two orthogonal directions with a single mass by shaping the pendulum's suspension geometry so it has different effective lengths, and hence different tuned frequencies, along each axis.

Tuned liquid dampers achieve a similar effect using sloshing water in a shallow tank instead of a solid mass; the sloshing frequency is tuned by the tank's water depth and plan dimensions. These trade some efficiency per unit mass for lower cost, no mechanical bearings to maintain, and the practical benefit that the "mass" is just water, which can double as a fire-suppression reserve on some projects.

Active and semi-active variants add sensors and actuators that adjust damper force in real time rather than relying purely on passive tuning, which can control a wider frequency range and adapt to changing structural properties, at the cost of a power supply, control system, and ongoing maintenance a purely passive damper does not need. Most completed tall-building installations to date still use passive or semi-active hardware rather than fully active control, largely because a passive damper keeps working through a power outage.

Sizing Against Wind Criteria

The design target for a TMD on an occupied building is almost always a peak or RMS acceleration limit at the top occupied floor under a wind event with a defined return period, evaluated against habitability guidelines that distinguish residential from office occupancies (residential occupants are generally assumed less tolerant of motion than transient office occupants). The designer works backward from the acceleration target, the building's estimated modal mass and inherent structural damping (often only 1 to 2 percent of critical for a bare steel or concrete frame before any auxiliary device is added), and the site's wind climate, to determine how much added damping the TMD needs to supply and, from that, how large the auxiliary mass must be. Because the benefit is so sensitive to the ratio between auxiliary mass and building modal mass, a TMD tends to become a more attractive solution, relative to just adding structural stiffness or bracing, as building height and slenderness increase and modal mass at the governing frequency actually goes down.