The objective of this thesis is to describe the design, construction, implementation and performance of a prototype adaptive pendulum tuned mass damper (APTMD). Furthermore the thesis aims at demonstrating the performance improvements obtained when the tuned mass damper (TMD) parameters are optimized. The study considers the effect of adjusting the APTMD tuned frequency and damping ratio on a two storey test structure subjected to broadband and narrowband excitation. An analytical model of the APTMD for a single-degree-of-freedom (SDOF) structure is used to demonstrate the performance improvements when the APTMD parameters are optimized. The optimized model considers the effects of adjusting the frequency ratio, damping ratio, and mass ratio of the combined system to reduce the maximum deflection when the structure is subjected to a harmonic excitation force. The analytical model is used to simulate the optimal performance of the APTMD system. The experimental APTMD is capable of identifying the structural vibration modes in real time and tuning to the desired mode. The structural vibration modes are identified by calculating the windowed power spectral density of the structure’s acceleration, followed by peak-picking algorithm to identify the modal frequencies. Tuning is performed by moving the pivot location of the pendulum arm via a tuning frame along a set of rails. The design also allows for changes in the external dampening force. An adjustable damper is attached to the pendulum mass to allow for control of the APTMD damping ratio. A prototype of the APTMD is built and tested in a modal testing setup. The test structure is a two-storey model of a building structure. The structure is excited using a shaker fixed to the lower storey of the structure. The performance of the APTMD under broadband and narrowband excitation is examined for various tuning and damping parameters. The performance of the APTMD system under optimally tuned and detuned conditions is investigated. The results of the experimental studies demonstrate the importance of optimizing the TMD tuned frequency and damping ratio to reduce structural vibrations. Since the APTMD is designed to autonomously update both parameters, it is an effective tool in mitigating structural vibrations where user interaction is either difficult or expensive. Further study on the performance of a prototype APTMD applied to a large scale structure is required before implementation on full-scale structures.

The large number of bridge collapses that have occurred in recent earthquakes has exposed the vulnerabilities in existing bridges. One of the emerging tools for protecting bridges from the damaging effects of earthquakes is the use of isolation systems. Seismic isolation is achieved via inserting flexible isolator elements into the bridge that shift the vibration period and increase energy dissipation. To date, the structural performance of bridges incorporating sliding seismic isolation is not well-understood, in part due to the lack of adequate models that can account for the complex behavior of the isolators. This study investigates and makes recommendations on the structural performance of bridges utilizing sliding type seismic isolators, based on the development of state-of-the-art analytical models. Unlike previous models, these models can account simultaneously for the variation in the normal force and friction coefficient, large deformation effects, and the coupling of the vertical and horizontal response during motion. The intention is to provide support for seismic risk mitigation and insight for the analysis and design of seismically isolated bridges by quantifying response characteristics. The level of accuracy required for isolator analytical models used in typical highway bridges are assessed. The comparative viability of the two main isolator types (i.e. sliding and elastomeric) for bridges is investigated. The influence of bridge and sliding isolator design parameters on the system s seismic response is illustrated.

This thesis aims to explain how the concepts of functional modeling are implemented in the development and validation of real-world hybrid dynamic systems. I also discuss how control theory is integrated with the design process in order to understand the significance of periodic orbits on a simple dynamic system. Two hybrid system applications with different levels of complexity will be considered in this thesis – an anthropomorphic Bipedal walking robot and a Double Pendulum with a mechanical stop. The primary objectives of this project are to demonstrate the phenomena of Zeno and zeno periodic orbits in hybrid dynamic systems involving impacts. Initially, I describe the salient features of the product design procedure and then explain the significance of functional modeling as a part of this process. We then discuss hybrid dynamic systems and the occurrence of Zeno behavior in their mathematical form. Also, the necessary conditions for existence of Zeno and zeno equilibrium points are provided. Then the theory of completed Lagrangian hybrid systems is explained in detail. We then examine the two hybrid dynamic systems being considered for this project. Prior research undertaken on bipedal walking is explored to understand their design and achievement of stable walking gaits with appropriate actuation mechanisms. Based on this insight, a suitable design procedure is employed to develop the bipedal robot model. The desired actuation mechanisms for all the configurations considered for this model as well as the challenges faced in employing optimal actuation will be discussed. However, due to the high level of complexity of the bipedal robot model, a simpler hybrid dynamic system is considered to simplify fabrication and control of the model. This is the motivation behind designing and building the Double Pendulum model with a mechanical stop in an attempt to observe zeno behavior in this system. We begin by formally demonstrating that the “constrained” double pendulum model displays Zeno behavior and complete this Zeno hybrid system to allow for solutions to be carried past the Zeno point. The end result is periods of unconstrained and constrained motions in the pendulum, with transitions to the constrained motion occurring at the Zeno point. We then consider the development of a real physical pendulum with a mechanical stop and introduce non-plastic impacts. Later, we verify through experimentation that Zeno behavior provides an accurate description of the behavior of the physical system. This provides evidence to substantiate the claim that Zeno behavior, while it does not technically occur in reality, provides an accurate method for predicting the behavior of systems undergoing impacts and that the theory developed to understand Zeno behavior can be applied to better understand these systems.

This thesis investigated a tip-over stability of mobile boom cranes with swinging payloads. Base and crane motion presents a tip-over problem. Attaching complex payloads further complicates the problem. They study began with a single-pendulum payload to analyze a tip-over stability characteristics under different conditions. A simple tip-over prediction model was developed with a goal of limiting a computational cost to a minimum. The stability was characterized by a tip-over stability margin method. The crane's tip-over stability was also represented by the maximum possible payload it can carry throughout the workspace. In a static stability analysis, mobile boom crane was assumed to be stationary, thus with no payload swing. The study provided basic understanding on the relationship between tip-over stability and boom configuration. In a pseudo-dynamic stability analysis, the method incorporated payload swing into the analysis by adding estimated maximum payload swing due to motions. To estimate the angles, differential equations of motions of payload swings were derived. The thesis extended the study to a double-pendulum payload. The maximum swing angles estimated in the single-pendulum case were directly applied to the double-pendulum case. To validate the analytical methods, a full dynamic multi-body simulation model of a mobile boom crane was developed. The predictions from the previous analysis were verified by the simulation results. The prediction model and the analytical methods in the thesis provide a significant tool for practical application of tip-over stability analysis on mobile boom cranes. The experimental results increase the confidence of the study's accuracy.

Vorgeschichte Mit Vorträgen von Professor Werner Wuttke und Professor Ullrich Reinhold wurde in der Hochschulbibliothek das im Lichtschacht des Glasgebäudes installierte Foucaultsche Pendel übergeben. Dies war schon wegen der Seltenheit der Installation in der Region eine Besonderheit. Die gleichzeitig in Betrieb genommene Webcam ermöglicht nun die Beobachtung weltweit rund um die Uhr: http://www.fh-zwickau.de/index.php?id=701 http://141.32.4.72/view/view.shtml

Edgar Allan Poe has long been considered one of the great writers in Gothic literature. His works, as he himself suggested in his essay “The Philosophy of Composition,” are intended to strike a unique balance between mainstream appeal and higher literary craft. In many ways, my goals as a composer are similar, not just in mitigating this often tenuous dynamic, but also in tapping into powerful emotional states. Poe is a master at creating moods, for instantly drawing the reader into his dynamic worlds. Many of his works spend a significant amount of time, sometimes paragraph upon paragraph as in the opening to The Fall of the House of Usher, simply detailing his specific vision of the story’s tenor. In this piece, I was interested in musically depicting the imagery, which Poe so eloquently writes. I have chosen three of Poe’s short stories: The Black Cat, The Pit and the Pendulum, and The Fall of the House of Usher. In each movement, I deliberately avoid any programmatic connection to the story, that is to say specific events in the music do not coincide with any actual depiction of an event within the intended story. Rather this piece examines and details the specific tone of each story. Midnight Drearies: Three Moods on Edgar Allan Poe was written for Dan Welcher and the University of Texas New Music Ensemble. / text

M. Tech. Mathematical Technology. / Discusses the main problems in terms of how to derive mathematical models for a free, a forced and a damped spring pendulum and determining numerical solutions using a computer algebra system (CAS), because exact analytical solutions are not obvious. Hence this mini-dissertation mainly deals with how to derive mathematical models for the spring pendulum using the Euler-Lagrange equations both in the Cartesian and polar coordinate systems and finding solutions numerically. Derivation of the equations of motion are done for the free, forced and damped cases of the spring pendulum. The main objectives of this mini-dissertation are: firstly, to derive the equations of motion governing the oscillatory and rotational components of the spring pendulum for the free, the forced and damped cases of the spring pendulum ; secondly, to solve these equations numerically by writing the equations as initial value problems (IVP); and finally, to introduce a novel way of incorporating nonlinear damping into the Euler-Lagrange equations of motion as introduced by Joubert, Shatalov and Manzhirov (2013, [20]) for the spring pendulum and interpreting the numerical solutions using CAS-generated graphics.

The restoration of arm-free standing in paraplegic individuals can be accomplished with the help of functional electrical stimulation (FES). The key component of such a system is a controller that can modulate FES induced muscle contractions in real-time, such that artificially produced forces in the legs and abdominal muscles are able to generate stable standing posture. A 57 year-old individual with chronic ASIA-A (American Spinal Injury Association), T3/4 level spinal cord injury (SCI) participated in this study. The objective was to determine if a proportional-derivative (PD) or proportional-integral-derivative (PID) controller could be used to regulate FES induced muscle contractions in the ankle joint to allow it to maintain balance of the entire body during quiet standing, while exhibiting physiological dynamics seen in able-bodied individuals while doing so.

The thesis presents comparative study of modern control methods for regulating under-actuates systems. The classical pendulum on a cart system, a 2-DOF under-actuated system was utilized as a benchmark system for analyzing controllers' performances. The work includes analysis, controller design and swing-up control simulation for the following three methods: Nonlinear state-space control The mathematical model based on the Lie theoretic approach with nonlinear output injection was developed. The controller accomplishes both swing-up and stabilization of the pendulum. The feasibility of the implementation is limited due to physical constraints (length of the cart rail). Fuzzy logic control A Sugeno type fuzzy inference engine implementing the control strategy was built over the system fuzzy model. The simulations showed successful controller behavior but the generated system control input exhibited some non-smoothness that could cause increase on the actuator demand. Method of embedded artificial constraints (EAC). The analysis reveals dependence between the pendulum motion and the cart acceleration. Using this artificial constraint a state link was developed and the nonlinear control problem was reduced to a linear controller design. A stabilizing linear state-space controller has been developed and methods for arbitrary pole placement and optimal linear quadratic regulator design were compared. A reduced order current estimator for velocity estimation has been studied and implemented. A software client/server controller application running on a QNX Neutrino 6.1 platform was developed. The real-time experiments conducted with the EAC/linear state-space controller confirmed good swing-up and stabilization system performance.

Most current space robotics vehicles use solar energy as their prime energy source. In spherical robotic vehicles the use of solar cells is very restricted. Focusing on the particular problem, an improved method to generate electrical power will be developed; the innovation is the use of an internal pendulum-generator mechanism to generate electrical power while the ball is rolling. This concept will enable spherical robots on future long-duration planetary exploration missions. Through a developed proof-of-concept prototype, inspired by the Russian thistle plant, or tumbleweed, this thesis will demonstrate power generation capabilities of such a mechanism. Furthermore, it will also present and validate a parametric analytical model that can be used in future developments as a design tool to quantify power and define design parameters. The same model was used to define the design parameters and power generation capabilities of such a system in Martian environment.