Proposal of optimum tuning of semiactive TMDs used to
reduce harmonic vibrations based on phase control strategy
Fernando Ferreira | Carlos Moutinho | Álvaro Cunha | Elsa Caetano
CONSTRUCT/VIBEST, Faculty of
Engineering (FEUP), University of Porto,
R. Dr. Roberto Frias, 4200‐465 Porto,
Fernando Ferreira, CONSTRUCT/
VIBEST, Faculty of Engineering (FEUP),
University of Porto, R. Dr. Roberto Frias,
4200‐465 Porto, Portugal.
Fundação para a Ciência e a Tecnologia,
Grant/Award Number: SFRH / BD / 61944
Tuned mass dampers (TMDs) are a well‐established technology for passive
structural vibration control involving harmonic vibrations. Some design issues
are critical to guarantee the proper functioning of the device, in particular,
the adequate tuning and the adequate space to accommodate the TMD stroke.
With regard to the first aspect, semiactive TMDs were proposed as an alterna-
tive means of correcting the vibrating frequency of the device by adding a
semiactive element between the TMD and the structure. In this case, several
control strategies have been proposed, among which phase control has proven
to lead to excellent results. However, in the framework of this control approach,
the minimization of the structure displacements is often used as the main objec-
tive of the control, as the relative displacements of the TMDs mass are consid-
ered a secondary issue, which nevertheless may be a crucial aspect in some
applications. In this context, this paper proposes a strategy to optimally tune
the semiactive TMD, taking into account a balance between the level of the
reduction of the structural response and the amplitude of the TMD stroke.
The optimal tuning is found by minimizing the system stationary mechanical
energy. The problem is formulated as an optimization process, and the corre-
sponding results are presented and discussed.
harmonic vibrations, magneto‐rheological dampers, optimal tuning, phase control, semiactive control,
tuned mass dampers
1 | INTRODUCTION
Tuned mass dampers (TMDs) have proven to be an effective solution to reduce harmonic vibrations in structures sub-
jected to several types of loads, as is the case, for example, of footbridges subjected to pedestrian actions, road and railway
bridges excited by traffic loads, and tall buildings exposed to wind forces. A TMD consists of a secondary mass added to a
structure by means of a spring and damper with parallel mounting. The spring and mass are assigned in order to achieve
a vibrating frequency close to the natural frequency of the system to be controlled.
In this case, the TMD absorbs the
structure vibration energy and dissipates it in the viscous damper, guaranteeing lower resonant amplifications of the
primary system. Several design formulas are available in literature for TMD optimum tuning regarding the minimization
of structural displacement, velocity, acceleration, and other design criteria.
TMDs are known to be very sensitive to the design parameters, especially to frequency tuning, which may lead to
significant losses of effectiveness in reducing vibrations. In an attempt to increase the performance of TMDs under such
Received: 21 November 2016 Revised: 26 October 2017 Accepted: 17 November 2017
Struct Control Health Monit. 2018;25:e2131.
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