The partial differential equations of motion for an uncontrolled distributed structure can be transformed into a set of independent modal equations by means of the system eigenfunctions. In vibration analysis, the modal coordinates are referred to as natural coordinates. Active control forces generally recouple the modal equations so that the natural coordinates for the open-loop (uncontrolled) system cease to be natural coordinates for the closedloop (controlled) system. Control of this form is known as coupled control. In contrast, it is shown that a method known as the independent modal-space control method is a natural control method; i.e., the natural coordinates of the open-loop system and of the closed-loop system are identical. Furthermore, it is shown that natural control provides a unique and globally optimal closed-form solution to the linear optimal control problem for the distributed structure. The optimal control forces are ideally distributed. If implementation of distributed control is not feasible, then the distributed control forces can be approximated by finite-dimensional control forces. The class of self-adjoint systems are first considered following a treatment of non-self-adjoint systems. Numerical examples of a beam, a membrane and a whirling shaft are presented. In general, the eigenquantities for a distributed structure cannot be computed in closed-form, so that spatial discretization of the differential eigenvalue problem is necessary. A common discretization method is the finite element method leading to a discrete eigenvalue problem. Two bracketing theorems characterizing convergence of the discrete eigenvalue problem derived by the finite element method to the differential eigenvalue problem are formulated. The independent modal-space control method requires as many actuators as controlled modes. In contrast, coupled control is capable of controlling any number of modes using a single actuator, provided controllability is ensured. However, coupled control is sensitive to errors in the system parameters. As a compromise between coupled control and independent mbdal-space control, a block-independent control method is developed in which blocks of modes are controlled independently. The performances of independent modal-space control, coupled control and block-independent control are compared. / Ph. D.

The objectives of this experimentally and to simulate study were to implement theoretically a method of active vibration control, known as modal-space control, on a relatively simple beam-cable structure. The control was implemented in analog form and provided modal viscous damping in each of the three modes of the structure. Transient response to initial conditions was analyzed experimentally and theoretically. Control hardware included permanent magnet-coil systems for the three control force actuators and the single velocity sensor, and an analog controller built around integrated circuit operational amplifiers. This thesis compares open-loop experimental response and closed-loop experimental and theoretical response on the basis of Fast Fourier Transforms of transient time data. / M.S.

The cyclic trajectory described here exemplifies a loosely defined, continuously evolving set of questions, results, and methodologies that have emerged during the process of design by making. Through a series of prototypical building components and assemblies this collection presents a design process that began with a top-down program-specific design process that informed the development of a unique building system and enabled a bottom up formal exploration. As the design thesis for the first professional Master of Architecture degree, this exploration surrounds the design, fabrication, and deployment of a series of component-based building assemblies. One example, the SEEDS Pavilion At Hawks Ridge, serves as a remote base of operations for a local youth organization that supports field-based environmental education. The pavilion continues an investigation of user assembled construction and is based on a component group that can be assembled on-site by camp children. Each building component was manufactured using on campus fabrication laboratories and was assembled on-site by a group of supervised SEEDS camp student-volunteers during a two-day design-build workshop at the Hawk's Ridge Preserve in Floyd, Virginia. The form of the structure is derived by the limitation of component number, size, and assembly sequence and represents the conflict between a parametrically derived prescriptive shape and the forms that result from the bottom up exploration of the physical system itself. The component-based construction is made possible by a series of nodal linkage assemblies designed to accommodate variations in on-site conditions using a strategic 'sloppy detail' that enables a high degree of assembly and deployment tolerance. The following collection of sequential images outlines construction of several prototypical components and assemblies and is intended to represent a continuance, not an end, to a long-term effort. / Master of Architecture

Interest in large flexible space structures has grown considerably over the last decade. These distributed parameter systems exhibit vibration characteristics such as low, closely spaced natural frequencies and light damping, which, when coupled with the stringent pointing accuracy and vibration control requirements imposed on these systems, bring about interesting control problems. Addressing these problems has called for the use of active vibration control. Up to now, two of the most popular means for active vibration control of large space structures have been proof mass and reaction wheel actuators. These actuators are inertial-type actuators in that they operate by applying forces or moments to masses whose reaction forces, imposed on the structure, act to dampen the vibrations of the structure. A new class of actuators, variable geometry trusses (VGT's), has been recently introduced. These actuators are actually built into the structure, and they operate by varying their link lengths to apply forces to the structure or to change the shape of the structure itself. This study compared the effectiveness of four actuators in controlling the planar vibrations of a cantilevered truss-beam. The actuators chosen for the study were a proof mass actuator, a reaction wheel actuator, and two VGT's, the planar truss actuator, and the planar truss proof mass actuator (a combination VGT/inertial type actuator). Numerical simulations of each beam/actuator system were performed in response to initial condition inputs. A full-state, LQR optimal feedback control law was used with each system. These simulations provided information such as time response of the closed-loop system, damping provided to the beam, and power required by each actuator. This information can be used to determine the "best" actuator for a given purpose. The results of these simulations show that the VGT's are preferable in terms of damping added to the beam. The proof mass actuator is more efficient as far as power required to do the control, however, the efficiencies for all actuators are very similar. / Master of Science

Ever since the advent of the Moment-Distribution procedure (1) for analyzing continuous frames, it has been possible to solve many problems conveniently which previously had required laborious solutions. Indeed, the current literature of the engineering profession finds the Cross method being adopted in new fields and being applied to new problems. The classical methods of analysis, while still retaining some measure of their former utility, are being superseded by this and other methods involving less time and labor. Yet, even with this new impetus to the field of structural analysis, the rigid space frame has received far less attention than seems justified. Here is a class of structure devoid of practically any analytical investigation and even less experimental research. The desired characteristic of all current designs has been continuity, and yet there exists this paradoxical neglect of the third dimension, without which all structures would be non-existent. The reasons for this apparent indifference are not difficult to ascertain. Practicing engineers are practical men and as such require reasonably accurate results, obtained with a minimum of effort. Economy has dictated that refinements of analysis be saved for the classroom. A two-plane analysis is generally substituted for the more complex three-dimensional case. The write feels that the interaction of members in different planes of certain structures may be quite important in some cases and that a complete, convenient analysis is justified to determine the extent of such action. / Master of Science

The control problem of a large-order flexible system in the form of a beam-lattice is presented using the Independent Modal-Space Control (IMSC) method. The method is based on a transformation of the system equations of motion to modal space, yielding internally independent modal equations of motion. The control laws are designed in the modal space, permitting independent control of each mode, providing complete decoupling of the equations of motion. Linear optimal control with quadratic performance index is designed to control the response of the elastic as well as the rigid body modes, using the IMSC method. Actuators placement is of fundamental importance in the control of two-dimensional domains if IMSC is used. A method is presented as to the selection of actuators configuration in order to avoid singularity in the mode participation matrix, guaranteeing system controllability. The minimum-fuel problem is a very important one in the design of various space structures. Solution of the minimum-fuel problem is feasible in a coupled form for a fourth order system at most, but will be of insurmountable computational difficulty in the control of a flexible structure, since the model of such system will require a large number of degrees of freedom. A reformulation of the problem in the framework of "Modal Minimum-Fuel Problem" is presented, using the IMSC method. By this method, the complexity inherent in a high-order system is reduced, thus treatment of the coupled high-order system is avoided. Numerical examples for linear optimal control, with quadratic performance index, as well as for the minimum-fuel problem, are presented. / Ph. D.

In this thesis, we examine the Linear DC Motor in a configuration such that it provides the forces necessary to damp vibrations in a large flexible structure. The design is broken down into three steps where in each step, a feedback loop is placed around the actuator and/or the structure. The first loop is a motor compensation loop which effectively decouples the motor model from the structure model by removing the effect of the velocity of the structure on the motor's performance. The second loop stabilizes the relative position response of the combined actuator/structure model. This loop also shapes the magnitude response of the system, thus determining the bandwidth of the actuator. Two designs are developed: a narrow bandwidth design and a wide bandwidth design. The third loop is the vibration suppression design loop and can be designed a number of ways. In this thesis, we develop two decentralized designs and a centralized design. The final system is simulated to check design results. The various nonlinearities of the proof mass actuator are considered and their effect on results noted. These nonlinearites, the stroke and current limits, determine the effectiveness of each vibration suppression design. The linear model is checked for robustness to parameter uncertainty. Results for the various designs are tabulated and discussed. / M.S.

The work that is reported herein deals with system identification methods for large flexible structures. Proposed space missions for the future include the deployment of large flexible structures, e.g., NASA's proposed space station. These structures must be controlled to maneuver the structure to desired locations and to suppress unwanted vibration. Before controlling any structure, it is necessary to have an accurate model which may include accurate estimates of the structure's natural frequencies and mode shapes. System identification is an important process that precludes system control. Precision structures such as those proposed for the Space Based Laser or the Aerospace Plane require high performance control systems which will require robust, computationally efficient system identification algorithms. This work attempts to experimentally verify, develop, and compare existing identification algorithms to determine their properties and improve their efficiency towards potential applicability in a space environment. To this end, we consider the Temporal Correlation Method and the Eigensystem Realization Algorithm. The algorithms are implemented on the Astronautics Laboratory Grid structure, and the results of the algorithms are compared in the presence of damping, noise, and residual modes. In addition, the Temporal Correlation Method is shown to be a constrained version of the Eigensystem Realization Algorithm for cases of light damping. / Master of Science

Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2016-04-05T18:07:42Z No. of bitstreams: 2 dissertacao - Leandro Rodrigues da Silva Souza - 2015.pdf: 16210462 bytes, checksum: 475bed9248c2dcb7bf0346adfc69a5f0 (MD5) license_rdf: 19874 bytes, checksum: 38cb62ef53e6f513db2fb7e337df6485 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-04-06T12:44:50Z (GMT) No. of bitstreams: 2 dissertacao - Leandro Rodrigues da Silva Souza - 2015.pdf: 16210462 bytes, checksum: 475bed9248c2dcb7bf0346adfc69a5f0 (MD5) license_rdf: 19874 bytes, checksum: 38cb62ef53e6f513db2fb7e337df6485 (MD5) / Made available in DSpace on 2016-04-06T12:44:50Z (GMT). No. of bitstreams: 2 dissertacao - Leandro Rodrigues da Silva Souza - 2015.pdf: 16210462 bytes, checksum: 475bed9248c2dcb7bf0346adfc69a5f0 (MD5) license_rdf: 19874 bytes, checksum: 38cb62ef53e6f513db2fb7e337df6485 (MD5) Previous issue date: 2015-02-20 / In order to collaborate with technology and accessibility, this work proposes the development of a Space Frame chassis, constructed with polyvinyl Chloride (PVC). To the development were used PVC tubes and fittings, commonly used in civil builders. The essential parameters of the PVC were obtained experimentally and used to simulate the chassis. Along the development, analyses of tension and deformation were made in the proposed structure. Using computer simulation, the finite element analysis could provide the structure behaviour in different scenarios, as bending, tension and deformation. / Com o intuito de colaborar com o campo da tecnologia e acessibilidade, este trabalho propõe o desenvolvimento de uma estrutura veicular do tipo Space Frame, construída a partir de tubos de policloreto de Vinila (PVC). Para tanto, foram utilizados tubos e conexões de PVC normalmente empregados na construção civil. Os parâmetros essenciais do PVC para a simulação foram obtidos experimentalmente. São realizadas análises de tensões e deformações da estrutura, por meio de simulação computacional, utilizando um solver de Elementos Finitos, propiciando análise do protótipo, sob condições de solicitação a flexão devido a cargas distribuídas sobre as suas regiões.

Due to the environmental issues related with fuel consumption and additionally passenger safety, aluminum space frame chassis is promising a big opportunity to design a lightweight structure with a high stiffness. Despite the lower stiffness and strength of aluminum in comparison to the conventional steel chassis, it can be compensated with changing thickness and design of structure by space frame geometry In this study, instead of using steel for automobile chassis, main goal is producing a space frame structure with using aluminum in an extrusion and sand casting processes and improve the stiffness. Chassis is designed according to calculations for moment of inertia, torsional and bending stiffness and in sufficient structural stiffness which can compete with steel chassis. Static finite element analysis was carried out to understand the chassis bending, torsional stiffness and fatigue behaviors. For frontal collisions, dynamic finite element analysis was also done to determine increases in the energy absorbance, specific energy absorbance and peak force for passenger safety. Aluminum profiles were produced by hot extrusion and joined with sand casting parts by TIG welding to manufacture a space frame structure. For main chassis profile, 6063 series of aluminum alloy was selected due to availability for extrusion process, weldability and having sufficient tensile strength and percent elongation and treatment response. Three point bending test was carried out to determine flexural strength. Moment of inertia calculations were done. Some parts such as side frame and shock absorber tower were produced by sand casting method. A similar composition to Silafont &ndash / 36 aluminum alloy was selected because of its high fluidity and good mechanical properties / despite it is a die cast alloy. Tensile, hardness and Charpy impact test were conducted to determine the mechanical characteristics of Silafont - 36 sand cast alloy. In addition to microstructure features and thermal analysis were also carried out to achieve sufficient alloy properties. Heat affected z one was investigated by hardness and tensile test to determine the mechanical properties change after welding process. In this space frame development study, A, B and C pillar parts were produced by Al &ndash / Si sand casting and T6 heat treatment then welded together by TIG welding and finally assembled on the bottom chassis frame produced by using 6063 extrudes welded by 4000 series electrodes. The space frame chassis was studied by also computer simulation to test and see critical points which must be modified during manufacturing. Besides the experimental and theoretical studies, space frame was also produced at the same time. According to the experimental results, the feasibility of the production of lightweight and solid chassis structure was achieved.