Effectiveness of oscillating mass damper system in the protection of rigid blocks under impulsive excitation

Self Cite

Summary In this paper, the effects of a mass damper on the rocking motion of a non‐symmetric rigid block‐like structure, subject to different seismic excitation, are investigated. The damper is modelled as a single degree of freedom oscillating mass, running at the top of the block and connected to it by a linear visco‐elastic device. The equations of rocking motion, the uplift and the impact conditions are derived. A nondimensionalisation of the governing equations is performed with the aim to obtain an extensive parametric analysis. The results are achieved by numerical integration of these equations. The slenderness and the base of the rigid block, and the eccentricity of the centre of mass are taken as variable parameters in the analyses. The main objective of the study is to check the performance of the damper versus the spectral characteristics of the seismic input. Three earthquake registrations with different frequency contents are used in the analyses. The results show that the presence of the mass damper leads to different levels of improvement of the response of the system, depending on the spectral characteristics of the seismic input. Curves providing the overturning slenderness of blocks of specific sizes versus the characteristics of the TMD are obtained. Copyright © 2017 John Wiley & Sons, Ltd.

Section: Introductionsupporting

confidence: 90%

Section: Mechanical Systemmentioning

confidence: 99%

\begin{matrix} right x_{M A} (t) & left = x_{g} (t) + R_{A G} \cos (α_{A G} + ϑ (t)) & right \\ right y_{M A} (t) & left = R_{A G} \sin (α_{A G} + ϑ (t)) \end{matrix}

while the position of the oscillating mass reads

\begin{matrix} right x_{m A} (t) & left = x_{g} (t) + R_{A C} \cos (α_{A C} + ϑ (t)) + x (t) \cos (ϑ (t)) - h \sin (ϑ (t)) & right \\ right y_{m A} (t) & left = R_{A C} \sin (α_{A C} + ϑ (t)) + x (t) \sin (ϑ (t)) + h \cos (ϑ (t)) \end{matrix}

By evaluating the kinetic and the potential energy and following a Lagrangian approach, the rocking equations of motion around the base point A can be obtained (see for more details):

\begin{matrix} right & left g m R_{A C} \cos (α_{A C} + ϑ (t)) + g M R_{A G} \cos (α_{A G} + ϑ (t)) - g h m \sin (ϑ ()) \end{matrix}

…”

Section: Mechanical Systemmentioning

confidence: 99%

“…The uplift of the block around point A takes place when the resisting moment M R due to the vertical accelerations of the system (

M_{R} = M g x_{M_{1}} + m g x_{m_{1}} (t)

) is smaller than the overturning moment M O due to the inertial forces (

M_{O} = M {\overset{x}{true}}_{g} y_{M_{1}} + m (\overset{x}{true} (t) + {\overset{x}{true}}_{g} (t)) {y_{m}}_{1}

), both evaluated with respect to point A (Figure ). So, the uplift condition around the left corner A reads (see for more details)

M g x_{M_{1}} + m g x_{m_{1}} (t) ⩽ M {\overset{x}{true}}_{g} (t) y_{M_{1}} + m (\overset{x}{true} (t) + {\overset{x}{true}}_{g} (t)) y_{m_{1}}

where

\begin{matrix} right x_{M_{1}} & left = b_{1} & right \\ right y_{M_{1}} & left = \frac{H}{2} \end{matrix}

and

\begin{matrix} right x_{m_{1}} (t) & left = \frac{B}{2} \end{matrix}

…”

Section: Mechanical Systemmentioning

confidence: 99%

See 2 more Smart Citations

On the seismic performances of rigid block‐like structures coupled with an oscillating mass working as a TMD

Simoneschi

Geniola

Leo

et al. 2017

Self Cite

“…The equations present a similarity with several other problems of rocking-elasticity interaction [24,28,30,53,54].…”

Section: Equations Of Motion After Upliftmentioning

confidence: 60%

Dynamics of rocking podium structures

Bachmann

Vassiliou

Stojadinović

2017

Summary A rocking podium structure is a class of structures consisting of a superstructure placed on top of a rigid slab supported by free‐standing columns. The free‐standing columns respond to sufficiently strong ground motion excitation by uplifting and rocking. Uplift works as a mechanical fuse that limits the forces transmitted to the superstructure, while rocking enables large lateral displacements. Such ‘soft‐story’ system runs counter to the modern seismic design philosophy but has been used to construct several hundred buildings in countries of the former USSR following Polyakov's rule‐of‐thumb guidelines: (i) that the superstructure behave as a rigid body and (ii) that the maximum lateral displacement of the rocking podium frame be estimated using elastic earthquake displacement response spectra. The objectives of this paper are to present a dynamic model for analysis of the in‐plane seismic response of rocking podium structures and to investigate if Polyakov's rule‐of‐thumb guidelines are adequate for the design of such structures. Examination of the rocking podium structure response to analytical pulse and recorded ground motion excitations shows that the rocking podium structures are stable and that Polyakov's rule‐of‐thumb guidelines produce generally conservative designs. Copyright © 2017 John Wiley & Sons, Ltd.

Seismic control of rocking structures via external resonators

Pan

Mariotti

2020

Summary Tall rigid blocks are prevalent in ancient historical constructions. Such structures are prone to rocking behaviour under strong ground motion, which is recognizably challenging to predict and mitigate. Our study is motivated by the need to provide innovative nonintrusive solutions to attenuate the rocking response of historical buildings and monuments. In this paper, we examine a novel scheme that employs external resonators buried next to the rocking structure as a means to control its seismic response. The strategy capitalizes on the vibration absorbing potential of the structure‐soil‐resonator interaction. Furthermore, the benefits of combining the resonators with inerters in order to reduce their gravitational mass without hampering their motion‐control capabilities are also explored. Advanced numerical analyses of discrete models under coherent acceleration pulses with rocking bodies of different slenderness ratios under various ground motion intensities highlight the significant vibration absorbing qualities of the external resonating system. The influence of key system parameters such as the mass, stiffness, and damping of the resonator and those of the soil‐structure‐resonator arrangement are studied. Finally, a case study on the evaluation of the response of rocking structures with external resonators under real pulse‐like ground‐motion records confirms the important reductions in peak seismic rotational demands obtained with the proposed arrangement.