M. N. Chatzis

Robust Modeling of the Rocking Problem

The rocking motion of a solid block on a moving deformable base is a dynamic problem that, despite its apparent simplicity, involves a number of complex dynamic phenomena such as impacts, sliding, geometric and material nonlinearities and, under some circumstances, chaotic behavior. For this reason, since the first model proposed by G.W. Housner in 1963, a number of alternative models have been proposed for its mathematical simulation. In this work, two new models are developed for the simulation of a rigid body experiencing a 2D rocking motion on a moving deformable base. The first model, the concentrated springs model, simulates the ground as tensionless vertical springs with vertical dampers placed at each of the two bottom corners of the body, whereas the second, the Winkler model, simulates the ground as a continuous medium of tensionless vertical springs with vertical dampers. Both models take into consideration sliding (with the use of both a penalty method and an analytical formulation for frictio...

Examining the Energy Loss in the Inverted Pendulum Model for Rocking Bodies

AbstractUnderstanding the mechanisms that may lead to failure of rocking bodies is significantly important in quantifying and minimizing the associated risk. The most common model to describe the r...

Monocular Computer Vision Method for the Experimental Study of Three-Dimensional Rocking Motion

AbstractThe rocking problem is applicable to a wide variety of structural and nonstructural elements. The current applications range from bridge pier and shallow footing design to hospital and data center equipment, even art preservation. Despite the increasing number of theoretical and simulation studies of rocking motion, few experimental studies exist. Of those that have been published, most are focused on a reduced version of the problem introducing modifications to the physical problem with the purpose of eliminating either sliding, uplift, or the three-dimensional (3D) response of the body. However, all of these phenomena may affect the response of an unrestrained rocking body. The intent of this work is to present a computer vision method that allows for the experimental measurement of the rigid body translation and rotation time histories in three dimensions. Experimental results obtained with this method will be presented to demonstrate that it obtains greater than 97% accuracy when compared agai...

Vibration Mitigation and Monitoring: A Case Study of Construction in a Museum

Vibration from demolition and construction activities poses a serious risk to museum objects. This case study presents preventive conservation and vibration monitoring strategies developed in response to a large-scale renovation project on the floor directly below the Egyptian Art galleries of the Metropolitan Museum of Art in order to safeguard this fragile, ancient art collection. The paper discusses the methods and procedures that were developed not only to protect the art but also to allow visitors continued access to as much of the collection as possible during the work period. In advance of the construction, pilot testing was performed to determine the levels of vibrations caused by different tools, as well as to gain a better understanding of vibration propagation within the museum and to specific objects through their mounts, pedestals, and display shelves. Vibration prone installations were modified with isolation and/or dampening approaches to mitigate vibration, or when possible, selected objects were deinstalled. A variety of mitigation solutions were shown to be effective through testing. During the demolition and construction phase, continuous wireless vibration monitoring was provided from within the galleries, and sometimes from sensors directly on objects or their shelves to provide near real-time alerts to museum staff and construction personnel. Alert levels were based on frequency independent velocity levels.

Three-Dimensional Dynamics of a Rigid Body with Wheels on a Moving Base

AbstractFor reasons more related to functionality than safety, it is not uncommon for heavy mechanical and electrical equipment to be placed on wheels. Examples of such devices are medical carts, mechanical equipment in hospitals, electrical transformers, and recently, even supercomputers. Although wheels facilitate the operation of these devices, they also affect the response of these objects during earthquakes, but not necessarily in a beneficial way. While a wheel rolling favors the translational displacement of the body in the horizontal direction parallel to its plane over rocking, rocking is still possible along the plane perpendicular to the plane of the wheel. Moreover, because the plane of the wheel is in most cases free to rotate with respect to the body, it is not easy to identify the directions that favor rocking or displacement at any time. The problem becomes even more complicated, if one considers that one of the wheels, which can swivel, may be locked. Thus, in the most general case, a bod...

A Discontinuous Unscented Kalman Filter for Non-Smooth Dynamic Problems

For a number of applications, including real/time damage diagnostics as well as control, online methods, i.e., methods which may be implemented on-the-fly, are necessary. Within a system identification context, this implies adoption of filtering algorithms, typically of the Kalman or Bayesian class. For engineered structures damage or deterioration may often manifest in relation to phenomena such as fracture, plasticity, impact or friction. Despite the different nature of the previous phenomena, they are described by a common denominator: switching behavior upon occurrence of discrete events. Such events include for example, crack initiation, transitions between elastic and plastic response, or between stick and slide modes. Typically, the state-space equations of such models are non-differentiable at such events, rendering the corresponding systems non-smooth. Identification of non-smooth systems poses greater difficulties than smooth problems of similar computational complexity. Up to a certain extent, this may be attributed to the varying identifiability of such systems, which violates a basic requirement of online Bayesian Identification algorithms, thus affecting their convergence for non-smooth problems. Herein, a treatment to this problem is proposed by the authors, termed the Discontinuous D- modification, where unidentifiable parameters are acknowledged and temporarily excluded from the problem formulation. In this work the D- modification is illustrated for the case of the Unscented Kalman Filter UKF, resulting in a method termed DUKF, proving superior performance to the conventional, and widely adopted, alternative.

Observability and Identifiability Methods for Structural Dynamic Systems

An important consideration for experimental setups throughout various fields of science and engineering is whether the quantities measured suffice in determining the desired states of the underlying dynamic system (i.e., whether the measurements render these states observable). More often than not, there is uncertainty with regard to the real parameters of the dynamic system. The purpose of system identification methods is to obtain the most likely values for the parameters and the states given a set of measurements. This uncertainty with regard to the parameters of the system results in them being treated as new states in an augmented dynamic system. Consequently, even in the simplest case of a linear underlying dynamic system, the corresponding augmented system becomes nonlinear. Thus, the question of whether a system identification method could succeed for given measurements in defining the parameters and states of a system (i.e., the augmented states) becomes a problem of nonlinear observability. If only the parameters of the system are of interest, identifiability methods may, in certain cases, be used. Thus, observability and identifiability methods enable the design of experimental setups that would at least work if the measurements were free of noise and the rejection of those that would not work even in this ideal scenario. In this work, three methods for the observability and identifiability of nonlinear dynamic systems are studied and compared against each other. For a system whose state and measurement equations are analytic, geometric observability methods based on Lie Derivatives may be used. Moreover, if the equations are rational, algebraic methods are also available. For this last category of systems, identifiability methods may be used to investigate not only the finiteness of the possible parameter values, but their uniqueness as well.