A new passive rolling‐pendulum vibration absorber using a non‐axial‐symmetrical guide to achieve bidirectional tuning

Abstract

SUMMARYA new, passive, vibroprotective device of the rolling-pendulum tuned mass damper type is presented that, relying on a proper three-dimensional guiding surface, can simultaneously control the response of the supporting structure in two mutually orthogonal horizontal directions. Unlike existing examples of ball vibration absorbers, mounted on spherical recesses and effective for axial-symmetrical structures, the new device is bidirectionally tuneable, by virtue of the optimum shape of the rolling cavity, to both fundamental structural modes, even when the corresponding natural frequencies are different, in such a case recurring to an innovative non-axial-symmetrical rolling guide.Based on Appell's non-holonomic mechanics, a non-linear dynamic model is first derived for the bidirectional absorber mounted on a 1-storey 3-degrees-of-freedom linear structure translating under the effect of both imparted base motion and applied dynamic forces. A laboratory-scaled prototype of the device is then tested to experimentally demonstrate the bidirectional tuning capability and to validate the mathematical model. The design procedure and the seismic performance of the absorber are finally exemplified through numerical simulation.

Life-cycle cost assessment of inelastic buildings with tuned mass dampers in seismic areas

“…More precisely, denoting by ω s and ζ s respectively the circular frequency and the damping ratio of the target mode, by m s,eff its effective modal mass, defined (Warburton, 1982) as the target modal mass divided by the squared amplitude of the mass-normalised target mode shape at the TMD position, and finally denoting by μ eff = m t /m s,eff and r = ω t /ω s respectively the effective mass ratio and the frequency ratio of the TMD, then the typical design procedure consists in: 1 arbitrarily fixing μ eff 2 accordingly finding r and ζ t which make the control optimal with respect to some desired objective. In most applications, optimality is identified with the minimisation of the H 2 -norm (Hoang et al, 2008) or the H ∞ -norm (Sladek and Klingner, 1983;Pinkaew et al, 2003;Matta et al, 2009) of some input-output transfer functions (TF) of the controlled system. In the present study, the TF from the ground acceleration to the maximum inter-storey drift ratio, denoted as T θu , is adopted, and the H ∞ f approach proposed in Matta (2011) is applied, which consists in the numerical minimisation of the H ∞ -norm of T θu multiplied by a Kanai-Tajimi filter whose circular frequency ω g equals the structural frequency ω s and whose damping ratio ζ g is set to 0.3.…”

Model calibration in the presence of resonant non-structural elements

“…Similar approaches (b) (c) (a) Fig. 1 NSEs on a single-DOF structure: a MS; b MS with a P-NSE; c MS with an S-NSE are used, in the same years, for dealing with resonant structural appendages of the ''tuned mass damper'' type, where the same interaction mechanism is exploited for the purposes of structural vibration absorption [30][31][32][33].…”

A novel bidirectional pendulum tuned mass damper using variable homogeneous friction to achieve amplitude‐independent control

“…This BTMD paradigm has been implemented in two variants, respectively belonging to the supported and to the hanging pendulum types. The first variant is the rolling‐pendulum BTMD proposed in Matta et al (Figure A). In this case, the 3D pendulum surface is ensured by special 3D rolling‐pendulum bearings, made of two identical cavities symmetrical facing each other and sandwiching a rolling ball.…”