Rocking of a rigid block freestanding on a flat pedestal

The seismic protection of objects contained within Museums is a topic of great interest, especially with reference to how they are displayed or stored. This problem is the same as that of a large class of non-structural components, such as mechanical and electrical hospital and laboratory equipment that could lose their functionality because of earthquakes. Statues and ceramics simply supported on the floor represent a significant set of case. In some cases, like the Bronzes of Riace, isolation systems have been developed. However, in general museum exhibits are not equipped with devices capable of mitigating the oscillations induced by possible earthquakes. The case study of a marble statue placed on a freestanding squat rigid pedestal is examined. The system of algebraic differential equations governing the problem has been derived and included in an ad-hoc numerical procedure. It is shown that the insertion of a squat rigid body with low frictional resistance at the lower interface with the floor, and high frictional resistance at the upper interface with the artifact significantly reduces the amplitude of the rocking response. As a result the artifact rocks without sliding on the rigid base that slides without rocking with respect to the floor. The numerical analysis performed can be a tool to help in the choice of the optimal friction values in the surfaces of the flat block, designed as a simple isolation system

Non-smooth dynamics of buckling based metainterfaces: rocking-like motion and bifurcations

The non-smooth dynamics is investigated for an elastic planar metainterface composed by two layers of buckling elements, each one allowing motion on one side only. Through the analogy between buckling and unilateral contact and by assuming no-bouncing at impact, the motion of the relevant two degrees of freedom system is reduced to that of a single degree governed by a piecewise-smooth differential equation. The metainterface dynamics has strong similarities with the rocking motion of rigid blocks and displays several types of dynamic bifurcations in the presence of oscillatory forces, including period doubling, branch point cycle, grazing, as well as quasi-periodic and chaotic responses. Moreover, the multistable response is found to be broaden to conditions representative of monostable states within a quasi-static setting, disclosing a multistability anticipation by dynamics. The wide landscape of the dynamic response for the buckling based metainterface provides a novel theoretical framework to be exploited in the design of mechanical devices for vibration attenuation and for energy harvesting.Comment: 34 pages, 15 figure

Dynamic shear behaviour of truss towers for wind turbines

The global interest in renewable energy sources has increased the attention to the manufacturing of wind turbine towers, since they are largely diffused in seismic areas too. Different types of towers have been produced in recent years. Among them, the truss structures assure a reduced mass and the modular characteristics necessary for easy transportation. Reduced costs of production, installation and maintenance are typical of these structures. Nonlinear dynamics is an efficient framework to analyze structures subjected to variable actions, i.e. to assess the seismic safety of wind turbine towers in case of earthquake actions. This study outlines a procedure to evaluate the post-elastic behavior of truss towers for wind turbines. Rigid-plastic behaviour is taken into account to develop approximate solutions for the problem of a tower modeled as a vertical cantilever beam and subjected to harmonic base motion. A comparison with the results of a finite element model is proposed

INVESTIGATION OF THE TOPPLING OF RECTANGULAR RIGID BLOCKS USING A SHAKE TABLE AND DISTINCT ELEMENT MODELS

Understanding the engineering principles of failure modes in rock formations from seismic activity continues to be a challenging problem for engineers and geologists. The complexity of the geology, geometry, discontinuities, and earthquake ground motions contribute to the difficulty in estimating the stability of rock slopes. In this study, one classic rock slope failure mode is examined: the toppling behavior of a single rigid rectangular block under dynamic loading. An investigation employing experimental and numerical modeling techniques was performed to observe the response of wooden blocks with different aspect (width/height) ratios subjected to loading at the base and compared to established theoretical methods that use pseudostatic loads applied at the centroid. The physical experiments were conducted using a shake table with a data acquisition system consisting of accelerometers and a high-speed video camera. Because the shake table is a newly acquired research tool, a large component of the experimental program involved developing multiple calibration tests validated with mechanical engineering theory to verify the performance of the testing equipment and the experimental data. The link between the two loading scenarios (base and centroid) applied to the toppling block was accomplished using numerical modeling, with the simulations performed using Itasca’s two-dimensional distinct element software UDEC. Results from the shake table and centroid loading scenario using UDEC matched theory. This study demonstrates the significance of understanding the fundamental rocking behavior of rigid blocks to better assess complicated toppling failures due to dynamic forces

Rad ne sadrži naslov na drugom jeziku.

In this work, dynamic characterisation of blocky structures is investigated. First, rocking of blocks is investigated. By this model, the behaviour of historical monuments, dry-stones, blocks in nuclear power plants, and masonry structures after the failure of the mortar may be described. Non-linear equations of motion are derived and solved numerically. The exact time of impact is detected and the kinematic contact conditions after the impact are derived. Experimentally obtained energy loss is introduced. The algorithm is validated using a specially designed set of experiments, which also represent benchmark cases for validation of rocking. Conditions for complete or partial overturning of a dual-block stack are investigated experimentally and numerically. Second, organisation of an ordered multiple-block assembly inside a basin due to harmonic excitation is investigated. The parameters for detection of diverse modes of organisation and characterisation of undesirable events are defined from experimental observation.U ovom radu se istražuje dinamička karakterizacija blokovskih sustava. Ponašanje blokovskih sustava može opisati ponašanje povijesnih spomenika, suhozidanih konstrukcija, blokova u nuklearnim elektranama i zidanih konstrukcija nakon popuštanja veziva. Najprije se istražuje ljuljanje samo jednog bloka pod utjecajem pobude baze na kojoj se blok nalazi. Nelinearne jednadžbe kretanja koje opisuju ljuljanje jednog bloka su izvedene i riješene numerički koristeći Newmarkovu metodu za numeričku integraciju i Newton-Raphsonovu metodu za iterativno rješavanje nelinearnih jednadžbi. Detektirano je točno vrijeme sudara između tijela, što omogućuje određivanje brzine i ubrzanja sustava neposredno prije sudara. Izvedene su i brzine neposredno nakon sudara iz uvjeta da je moment količine kretanja sustava tijekom sudara održan obzirom na točku koja predstavlja novi centar rotacije. Odnos između brzine neposredno prije i neposredno nakon sudara je definiran koeficijentom restitucije. Posebno osmišljenom i provedenom serijom eksperimentalnih ispitivanja slobodnog ljuljanja, uz pomoć sustava za beskontaktno optičko mjerenje pomaka i deformacija GOM Aramis i Pontos, dobivene su stvarne vrijednosti koeficijenta restitucije. Pokazano je da tako dobivene vrijednosti potvrđuju potrebu za korištenjem modificirane formule za izračun koeficijenta restitucije. Eksperimentalno dobivene vrijednosti su uvedene u numerički model. Algoritam je eksperimentalno potvrđen pomoć posebno osmišljenog skupa pokusa, koji također predstavljaju benchmark primjere za validaciju simulacija ljuljanja: ljuljanje (i prevrtanje) bloka prilikom konstantnog ubrzanja podloge određenog trajanja (provedeno na air-track uređaju), te ljuljanje (i prevrtanje) prilikom jednog vala sinusoidalnog ubrzanja podloge (provedeno na preciznoj potresnoj platformi Quanser ST-III). Stupac koji se sastoji od dva bloka jednakih širina koji stoje jedan na drugome se prilikom ljuljanja može naći u osam različitih konfiguracija. Nelinearne jednadžbe kretanja za ljuljanje u svih osam konfiguracija su izvedene iz Lagrangevih jednadžbi. Definirani su prelasci između konfiguracija, koji se događaju ukoliko su kinematički uvjeti za aktivaciju ’više’ konfiguracije zadovoljeni, ili ukoliko je došlo do sudara između tijela u sustavu (ili između gornjeg i donjeg bloka ili između donjeg bloka i podloge). Na temelju navedenog je napisan numerički algoritam pomoću Newmarkove metode za integraciju i Newton-Raphsonove iterativne metode, te procedure za detektiranje točnog vremena svakog sudara između tijela. Brzine u sustavu nakon sudara su izvedene iz uvjeta da moment količine kretanja gornjeg bloka te moment količine kretanja cijelog stupca obzirom na točke koje predstavljaju centre rotacije nakon sudara moraju biti održani pri sudaru. Algoritam je eksperimentalno potvrđen serijom ispitivanja ljuljanja stupca od dva bloka prilikom jednog vala sinusoidalnog ubrzanja podloge. Uvjeti za potpuno (oba bloka) ili djelomično (samo gornji blok) prevrtanje stupca su istraženi numerički i eksperimentalno. Stupac koji se sastoji od tri bloka je eksperimentalno ispitan na posebno osmišljenoj platformi za dvostruki impuls ROORI1 na Sveučilištu u Oxfordu. Ispitani su uvjeti (posebice vrijeme između dva impulsa pobude baze) pod kojima dolazi do prevrtanja samo najgornjeg bloka, dva gornja bloka i cijelog stupca. Na kraju, istražena je organizacija uređene skupine od više blokova unutar posude prilikom horizontalne harmonijske pobude. Parametri za detekciju različitih oblika organizacije, periodično ponašanje te karakterizaciju nepoželjnih događaja, poput položaja težišta sustava te momenta inercije sustava s obzirom na težište, su definirani na temelju eksperimentalnih promatranja

Seismic assessment strategies for masonry structures

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 181-189).Masonry structures are vulnerable to earthquakes, but their seismic assessment remains a challenge. This dissertation develops and improves several strategies to better understand the behavior of masonry structures under seismic loading, and to determine their safety. The primary focus is on historic arched or vaulted structures, but more modern unreinforced masonry structures are also considered. Assessment strategies which employ simplified quasi-static loading to simulate seismic effects are initially addressed. New analysis methods which focus on stability or strength are presented, and the merits of these strategies are clarified. First, a new parametric graphical equilibrium method is developed which allows real-time analysis and illuminates the complex stability of vaulted masonry structures. Second, a finite element strategy for predicting brittle fracture of masonry structures is extended to incorporate non-proportional loading and shell elements. These extensions enable prediction of damage and collapse mechanisms in general, but are specifically used to predict the response of a full-scale masonry structure to quasi-static cyclic loading. Subsequently, assessment methods based on the dynamic response of masonry structures under earthquake loading are presented. First, rigid body dynamics and an experimental testing program are used to characterize the rocking response of the masonry arch for the first time.(cont.) An assessment criterion is developed which successfully predicts experimentally observed arch collapse under a variety of earthquake time histories. Second, the behavior of rocking structures is addressed in general, and clearly distinguished from typical dynamic oscillators. The rocking response is time dependent, evoking the development of a statistical method for predicting collapse. Finally, the ability of discrete element methods to predict the dynamics of masonry structures is evaluated through comparison with analytical and experimental results, and a rational method for assigning modeling parameters is proposed.by Matthew J. DeJong.Ph.D

Soil-Structure Interaction for low damage Seismic Rocking Systems

In earthquake prone areas, stakeholders now ask for low damage systems that can be easily repaired, following even earthquakes of catastrophic potential. Seismic protection of structures by means of rocking isolation is becoming increasingly popular, since allowing uplift is an inexpensive way to reduce the damage demand placed in structures. However, understanding the role of soil–structure interaction in the response of rocking systems remains a challenge. The goal of this thesis is to offer new knowledge on this field by assessing experimentally and computationally the response of rocking structures and the soil they are founded in. For the first time, structural and foundation rocking are unified under a common experimental campaign. Two building models, designed to rock above or below their foundation level so that they can reproduce structural and foundation rocking respectively, were tested side by side in a centrifuge. The models were placed on a dry sand bed and subjected to a sequence of earthquake motions. Dense and then medium dense (loose) sand were used. The range of rocking amplitude that is required for base isolation was quantified. Overall, it is shown that the relative density of sand does not influence structural rocking, while for foundation rocking, the change from dense to loose sand can affect the time‐frequency response significantly and lead to more predictable load demands. Results also demonstrate that the rocking motion of the buildings is evident in the soil response beneath the structures, and foundation rocking causes larger dynamic differential settlements than structural rocking for a given rocking amplitude. Within OpenSees, foundation and structural rocking were modelled using a Beam-on-a-Nonlinear-Winkler-Foundation model (BNWF). The modelling incorporated flat-slider elements for footing-soil and superstructure-footing interactions, respectively. A modified BNWF model (mBNWF) was presented that involved an uplift-dependent stiffness and viscosity transmission for both vertical and horizontal directions, and a friction-vertical force coupling. In general, the proposed modelling approach, without calibration, adequately captured the experimental response observed in centrifuge experiments. Due to its inherent dependency on initial conditions, foundation rocking was found more sensitive than structural rocking to the type of soil model and the soil properties. Finally, selecting appropriate modal damping ratios can further improve the response profile and based on these parameters a calibration scheme was proposed.EPSRC FIBE CDT, UK (College and Tuition Fees) EPSRC FIBE CDT, UK (Secondment expenses) University of California at Berkeley, USA (Secondment expenses) Cambridge Commonwealth, European & International Trust, UK (hardship funding) A. G. Leventis Foundation, Greece (Funding for living costs

In situ free ‐ vibration tests on unrestrained and restrained rocking masonry walls

In the out‐of‐plane assessment of rocking walls, a relevant and yet uncertain aspect is the influence of energy dissipated during motion due to impacts and restraints, such as a floor or tie rods. Therefore, in situ rocking tests on unrestrained and restrained unreinforced masonry walls, made of composite (rubble + blockwork) masonry, were performed and analyzed. The restraint is given by steel springs of assigned stiffness, simulating a floor connected to full‐scale (4 × 1 × 0.6 m3) specimens from a dismantling building. The specimens are displaced from a static equilibrium position and released, allowing to evaluate energy dissipation. The coefficient of restitution is estimated as the square root of consecutive peak velocities of the same sign, to take into account nonhomogeneities in walls. For unrestrained walls, experimental coefficients of restitution vary between 81 and 88% of analytical ones, confirming the latter as conservative. For restrained configurations, experimental coefficients of restitution are between 74% and 83% of analytical values of unrestrained walls. Hence, an additional energy damping can be ascribed to the springs. Equivalent viscous damping ratios of a nonlinear rocking system are calculated by considering a velocity logarithmic decrement, resulting between 6% and 8% (unrestrained condition) and between 8% and 10% (restrained condition). An analytical formula is proposed for estimating the coefficient of restitution for restrained walls if the dynamic properties of the unrestrained wall and the horizontal restraint are known. Finally, the relevance of a refined estimation of energy dissipation is discussed by means of numerical time history analyses

Development of a sensitive superconducting gravity gradiometer for geological and navigational applications

A sensitive and stable gravity gradiometer would provide high resolution gravity measurements from space. The instrument could also provide precision tests of fundamental laws of physics and be applied to inertial guidance systems of the future. This report describes research on the superconducting gravity gradiometer program at the University of Maryland from July 1980 to July 1985. The report describes the theoretical and experimental work on a prototype superconducting gravity gradiometer. The design of an advanced three-axis superconducting gravity gradiometer is also discussed