VTechWorks Repository :: Browsing by Author "Meirovitch, Leonard"

Browsing by Author "Meirovitch, Leonard"

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The accelerated characterization of viscoelastic composite materials
Griffith, William I. (Virginia Tech, 1980-04-05)
A brief review of necessary fundamentals relative to composite materials and viscoelasticity is provided. Subsequently the accelerated characterization techniques of Time Temperature Superposition and Time Temperature Stress Superposition are treated in detail. An experimental procedure for applying the latter to composites is given along with results obtained on a particular T300/934 graphite/epoxy. The accelerated characterization predictions are found in good agreement with actual long term tests. A postcuring phenomenon is discussed that necessitates thermal conditioning of the specimen prior to testing. A closely related phenomenon of physical aging is described. The effect of each on the glass transition temperature and strength is discussed. Creep rupture results are provided for a variety of geometries and temperatures for T300/934 graphite/epoxy. The results are found to compare reasonably with a modified kinetic rate theory.
Active vibration control of composite structures
Chang, Min-Yung (Virginia Tech, 1990-07-07)
The vibration control of composite beams and plates subjected to a travelling load is studied in this dissertation. By comparing the controlled as well as uncontrolled responses of classical and refined structural models, the influence of several important composite structure properties which are not included in the classical structural model is revealed. The modal control approach is employed to suppress the structural vibration. In modal control, the control is effected by controlling the modes of the system. The control law is obtained by using the optimal control theory. Comparison of two variants of the modal control approach, the coupled modal control (CMC) and independent modal-space control (IMSC), is made. The results are found to be in agreement with those obtained by previous investigators. The differences between the controlled responses as well as actuator outputs that are predicted by the classical and the refined structural models are outlined in this work. In conclusion, it is found that, when performing the structural analysis and control system design for a composite structure, the classical structural models (such as the Euler-Bernoulli beam and Kirchhoff plate) yield erroneous conclusions concerning the performance of the actual structural system. Furthermore, transverse shear deformation, anisotropy, damping, and the parameters associated with the travelling load are shown to have great influence on the controlled as well as uncontrolled responses of the composite structure.
Aeroelastic modeling and flutter control in aircraft with low aspect ratio composite wings
Morris, Russell A. (Virginia Tech, 1996)
A comprehensive study including modeling and control of aeroelastic instabilities in free flying aircraft with flexible wings has been completed. The structural model of the wing consists of a trapezoidal composite plate rigidly attached to a fuselage with rigid-body degrees of freedom. Both quasi-steady and quasi-static aerodynamic strip theories were used to analyze several different flutter mechanisms for a variety of low aspect ratio wing configurations. The most critical flutter mechanism was found to be body-freedom flutter, a coupling of aircraft pitching and wing bending motions, for wings in a forward-sweep configuration. In addition, a modal approximation to the flutter eigenvalue problem was used to substantially reduce computation cost, making the resulting model very attractive for use in larger multiobjective design packages. Composite ply angle tailoring was investigated as a passive method of increasing the body-freedom flutter airspeed of an aircraft model. In addition, wing mounted piezoelectric sensor and induced-strain actuator patches were used in conjunction with active feedback control laws to increase the airspeed at which body-freedom flutter occurs. Two control laws were tested, coupled and independent modal position feedback, to delay frequency coalescence and thus increase the flutter airspeed.
Analysis and Design of Variable Stiffness Composite Cylinders
Tatting, Brian F. (Virginia Tech, 1998-10-13)
An investigation of the possible performance improvements of thin circular cylindrical shells through the use of the variable stiffness concept is presented. The variable stiffness concept implies that the stiffness parameters change spatially throughout the structure. This situation is achieved mainly through the use of curvilinear fibers within a fiber-reinforced composite laminate, though the possibility of thickness variations and discrete stiffening elements is also allowed. These three mechanisms are incorporated into the constitutive laws for thin shells through the use of Classical Lamination Theory. The existence of stiffness variation within the structure warrants a formulation of the static equilibrium equations from the most basic principles. The governing equations include sufficient detail to correctly model several types of nonlinearity, including the formation of a nonlinear shell boundary layer as well as the Brazier effect due to nonlinear bending of long cylinders. Stress analysis and initial buckling estimates are formulated for a general variable stiffness cylinder. Results and comparisons for several simplifications of these highly complex governing equations are presented so that the ensuing numerical solutions are considered reliable and efficient enough for in-depth optimization studies. Four distinct cases of loading and stiffness variation are chosen to investigate possible areas of improvement that the variable stiffness concept may offer over traditional constant stiffness and/or stiffened structures. The initial investigation deals with the simplest solution for cylindrical shells in which all quantities are constant around the circumference of the cylinder. This axisymmetric case includes a stiffness variation exclusively in the axial direction, and the only pertinent loading scenarios include constant loads of axial compression, pressure, and torsion. The results for these cases indicate that little improvement over traditional laminates exists through the use of curvilinear fibers, mainly due to the presence of a weak link area within the stiffness variation that limits the ultimate load that the structure can withstand. Rigorous optimization studies reveal that even though slight increases in the critical loads can be produced for designs with an arbitrary variation of the fiber orientation angle, the improvements are not significant when compared to traditional design techniques that utilize ring stiffeners and frames. The second problem that is studied involves arbitrary loading of a cylinder with a stiffness variation that changes only in the circumferential direction. The end effects of the cylinder are ignored, so that the problem takes the form of an analysis of a cross-section for a short cylinder segment. Various load cases including axial compression, pressure, torsion, bending, and transverse shear forces are investigated. It is found that the most significant improvements in load-carrying capability exist for cases which involve loads that also vary around the circumference of the shell, namely bending and shear forces. The stiffness variation of the optimal designs contribute to the increased performance in two ways: lowering the stresses in the critical areas through redistribution of the stresses; and providing a relatively stiff region that alters the buckling behavior of the structure. These results led to an in-depth optimization study involving weight optimization of a fuselage structure subjected to typical design constraints. Comparisons of the curvilinear fiber format to traditional stiffened structures constructed of isotropic and composite materials are included. It is found that standard variable stiffness designs are quite comparable in terms of weight and load-carrying capability yet offer the added advantage of tailorability of distinct regions of the structure that experience drastically different loading conditions. The last two problems presented in this work involve the nonlinear phenomenon of long tubes under bending. Though this scenario is not as applicable to fuselage structures as the previous problems, the mechanisms that produce the nonlinear effect are ideally suited to be controlled by the variable stiffness concept. This is due to the fact that the dominating influence for long cylinders under bending is the ovalization of the cross-section, which is governed mainly by the stiffness parameters of the cylindrical shell. Possible improvement of the critical buckling moments for these structures is investigated using either a circumferential or axial stiffness variation. For the circumferential case involving infinite length cylinders, it is found that slight improvements can be observed by designing structures that resist the cross-sectional deformation yet do not detract from the buckling resistance at the critical location. The results also indicate that bucking behavior is extremely dependent on cylinder length. This effect is most easily seen in the solution of finite length cylinders under bending that contain an axial stiffness variation. For these structures, the only mechanism that exhibits improved response are those that effectively shorten the length of the cylinder, thus reducing the cross-sectional deformation due to the forced restraint at the ends. It was found that the use of curvilinear fibers was not able to achieve this effect in sufficient degree to resist the deformation, but that ring stiffeners produced the desired response abmirably. Thus it is shown that the variable stiffness concept is most effective at improving the bending response of long cylinders through the use of a circumferential stiffness variation.
Analysis for Taylor vortex flow
Li, Rihua (Virginia Polytechnic Institute and State University, 1986)
Taylor vortex flow is one of the basic problems of nonlinear hydrodynamic stability. In contrast with the wide region of wavenumber predicted by the linear theory, experiments show that Taylor vortex flow only appears in a small region containing the critical wavenumber ß_er This phenomenon is called wave selection. In this work, several high-order perturbation methods and a numerical method are established. Both evolution and steady state of the How caused by single or several disturbances are studied. The existence of multiple steady states for disturbances with small wavenumber is discovered and proved. The stable and unstable steady state solutions and some associated phenomena such as jump phenomenon and hysteresis phenomenon are found. and explained. In the small region, the wavenumbers and initial amplitudes of disturbances determine the wavenumber of the flow. But outside this region, only the wavenumbers of the disturbances have effect on the wave selection. These results indicate that unstable solutions play a key role in wave selection. The side-band stability curve produced by the high-order perturbation methods is accurate at low Taylor numbers but incorrect at relatively high Taylor numbers. The relation of the unstable solutions and side-band stability is discussed. Besides, the overshoot and the oscillation phenomena during evolution are studied in detail. Connections between this work and experiments are discussed.
Buckling and postbuckling of flat and curved laminated composite panels under thermomechanical loadings incorporating non-classical effects
Lin, Weiqing (Virginia Tech, 1997-04-05)
Two structural models which can be used to predict the buckling, post buckling and vibration behavior of flat and curved composite panels under thermomechanical loadings are developed in this work. Both models are based on higher-order transverse shear deformation theories of shallow shells that include the effects of geometric nonlinearities and initial geometric imperfections. Within the first model (Model I), the kinematic continuity at the contact surfaces between the contiguous layers and the free shear traction condition on the outer bounding surfaces are satisfied, whereas in the second model (Model II), in addition to these conditions, the static interlaminae continuity requirement is also fulfilled. Based on the two models, results which cover a variety of problems concerning the postbuckling behaviors of flat and curved composite panels are obtained and displayed. These problems include: i) buckling and postbuckling behavior of flat and curved laminated structures subjected to mechanical and thermal loadings; ii)frequency-load/temperature interaction in laminated structures in both pre-buckling and post buckling range; iii) the influence of a linear/nonlinear elastic foundation on static and dynamic post buckling behavior of flat/curved laminated structures exposed to mechanical and temperature fields; iv) implication of edge constraints upon the temperature/load carrying capacity and frequencyload/ temperature interaction of flat/curved structures; v) elaboration of a number of methodologies enabling one to attenuate the intensity of the snap-through buckling and even to suppress it as well as of appropriate ways enabling one to enhance the load/temperature carrying capacity of structures.
Contact stress analysis and fatigue life prediction for a cam-roller follower system
Girardin, Benoit (Virginia Tech, 1994-06-05)
An analytical treatment of the fatigue performance of a cam-roller followler system as influenced by residual stresses induced by grinding, is developed. An approach based on an extended Hertzian analysis is used to determine the 3-D contact stress fields, which are then combined by elastic superposition with the residual stress fields. These residual stresses were measured previously by the x-ray diffraction technique and represent a range of grinding protocols from mild to abusive. The maximum cyclic component, generally occurring subsurface, is then identified in terms of an effective stress amplitude and mean which are used with a fatigue damage model to predict fatigue crack initiation. Results, pending experimental confirmation, appear reasonable and provide a useful basis for optimizing cam performance in terms of manufacturing and design parameters.
Control of a flexible space robot tracking a moving target
Chen, Yifeng (Virginia Tech, 1993-04-29)
This dissertation is concerned with a space robot consisting of a rigid platform, two articulated flexible arms and a rigid end-effector. The task is to ferry some payload and to dock smoothly with an orbiting target whose motion is either known or not known a priori. The dynamical equations for planar motion of the space robot are derived by means of Lagrange’s equations. They are then separated into two sets of equations suitable for rigid-body maneuver control design and vibration suppression control design. A perturbation method is used when the target motion is known a priori and direct partitioning is used when the target motion is not known. Both approaches are under the assumption that maneuver motions are much larger than elastic motions. As far as the rigid-body maneuver control is concerned, optimal trajectory planning is carried out off-line by means of the global optimization method under the assumption that the target motion is known a priori. In contrast, when the target motion is not known a priori, on-line feedback tracking control is carried out by means of an algorithm based on Liapunov-like methodology and using on-line measurements of the target motion. As far as the vibration suppression control is concerned, the use of the piezoelectric sensor/actuator pairs dispersed along the flexible arms is proposed. Collocated sensors/actuators for vibration control exhibit good performance. The actuators are designed to compensate for the disturbances caused by the rigid-body maneuver and to realize the LQR feedback control. Assuming that the number of actuators along each flexible arm is equal to the number of modes used to model the beam, the LQR control design is based on a linear time-varying system without persistent disturbances. Problems related to the digital implementation of the control algorithms are also discussed. Some undesirable effects, such as the bursting phenomenon and even system instability, can occur if the control algorithms are realized in discrete-time. To prevent these problems, the modified discrete-time control schemes are developed. Numerical examples are used to demonstrate the control algorithms.
Control of flexible spacecraft during a minimum-time maneuver
Sharony, Yaakov (Virginia Polytechnic Institute and State University, 1988)
The problem of simultaneous maneuver and vibration control of a flexible spacecraft can be solved by means of a perturbation approach whereby the slewing of the spacecraft regarded as rigid represents the zero-order problem and the control of elastic vibration, as well as of elastic perturbations from the rigid-body maneuver, represents the first-order problem. The zero-order control is to be carried out in minimum time, which implies on-off control. On the other hand, the perturbed model is described by a high-order set of linear time-varying ordinary differential equations subjected to persistent, piecewise-constant disturbances caused by inertial forces resulting from the maneuver. This dissertation is concerned primarily with the control of the perturbed model during maneuver. On-line computer limitations dictate a reduced-order compensator, thus only a reduced-order model (ROM) is controlled while the remaining states are regarded as residual. Hence, the problem reduces to 1) control in a short time period of a linear time-varying ROM subject to constant disturbances and 2) mitigation of control and observation spillover effects, as well as modeling errors, in a way that the full modeled system remains finite-time stable. The control policy is based on a compensator, which consists of a Luenberger observer and a controller. The main features of the control design are: (1) the time-varying ROM is stabilized within the finite-time interval by an optimal linear quadratic regulator, (2) a weighted norm spanning the full modeled state is minimized toward the end of the time interval, and (3) the supremum"time constant" of the full modeled system is minimized, while (1) serves as a constraint, thus resulting in a finite-time stable modeled system. The above developments are illustrated by means of a numerical example.
Control of sound radiation from submerged plates
Meirovitch, Leonard; Thangjitham, Surot (Acoustical Society of America, 1990-07-01)
In many applications, the radiation pressure is an undesirable effect, so that the object is to suppress it. This paper is concerned with radiation pressure suppression through active control. The general idea of active control of a structure is to suppress the vibration by applying suitable feedback control forces, which requires sensors capable of measuring the state of the system and actuators capable of applying control forces. A control technique capable of suppressing the far-field radiation pressure is developed. Copyright 1990 Acoustical Society of America
A controller design procedure for nonlinear stochastic systems
Lucas, William Henry (Virginia Polytechnic Institute and State University, 1984)
An improved method for designing controllers for nonlinear stochastic systems is developed and analyzed. The resulting controller consists of a nonlinear control law coupled with an adaptive state estimator. The nonlinear control law is developed first. Using Taylor series expansion, linear approximations to the nonlinear systems are generated at selected points in the operating region. Then a control law which will produce the desired response is developed for each linearized configuration using conventional techniques for linear systems. The resulting control law parameters are treated as tabulated values from a set of unknown continuous functions of the nonlinear system parameters. These unknown functions are approximated at all points in the operating region by fitting curves to the tabulated data. The stability and convergence aspects of this nonlinear control law are analyzed in detail, with several derivations given and theorems proved. Two examples are given to illustrate the design procedure and evaluate its performance. The design procedure is extended to stochastic systems by incorporating a suitable state estimator. Two members of the class known as partitioned adaptive estimators (PAE's) are evaluated and their performance compared. The formulation known as the modified semi-Markov PAE is shown to be superior. The design, execution, and analysis of the experiments comprising the evaluation are discussed in detail, with particular attention given to correlating the performance of the estimators with the behavior of the weighting coefficients. Numerous figures and tables which amplify the discussions, along with some suggestions for further research, are also included.
Discrete-time control of a spacecraft with retargetable flexible antennas
France, Martin E. B. (Virginia Polytechnic Institute and State University, 1989)
This dissertation considers the discrete-time control of a spacecraft consisting of a rigid-platform with retargetable flexible antennas. The mission consists of independent minimum-time maneuvers of each antenna to coincide with pre-determined lines of sight, while the platform is stabilized in an inertial space and elastic vibration of the antennas is suppressed. The system is governed by a set of linearized, time-varying equations of motion. A discrete-time approach permits consideration of the time-varying nature of the system in designing the control law. Both global and decentralized controls are proposed for a noise-free system with full-state feedback. Initially, a time-varying linear-quadratic regulator (LQR) is implemented, followed by two types of decentralized controllers. First, a collocated control law is devised in which actuator forces are based on the position and velocity at the actuator locations. Next, a new method called Substructure-Decentralized Control is proposed, where each flexible substructure is controlled based on state measurements associated with the substructure modes of the separately modeled appendages. In both global and decentralized cases, a linear control law is first implemented coupled with an open-loop disturbance-accommodating control based on the known inertial disturbances caused by the maneuver. Elastic motion is next controlled using nonlinear (on-off) antenna controllers for each decentralized case. For Substructure-Decentralized Control, the controls translate into quantized actual controls. Lastly, nonlinear (on-off) control laws are also used to control the rigid-body motion for each case. Next, the problem of controlling the time-varying system in the presence of noisy actuators and sensors is examined. It is assumed that only displacements, not velocities, are sensed for both rigid-body and elastic motion, making state reconstruction also necessary. A discrete-time, full-order Kalman filter is constructed for the time·varying system. A pseudo-decentralized control is proposed whereby feedback controls are based on system state estimates. As before, both linear and nonlinear controls are implemented. For each case mentioned, a numerical example is presented involving a spacecraft with a single flexible maneuvering antenna.
Dynamic Response of Linear/Nonlinear Laminated Structures Containing Piezoelectric Laminas
Liang, Xiaoqing (Virginia Tech, 1997-03-17)
The three-dimensional linear theory of piezo-elasticity is used to analyse steady state vibrations of a simply supported rectangular laminated composite plate with piezoelectric (PZT) actuator and sensor patches either embedded in it or bonded to the its surfaces. It is assumed that different layers are perfectly bonded to each other. The method of Fourier series is used to find an analytical solution of the problem. The analytical solution is then applied to study the shape control of a steadily vibrating composite plate by exciting different regions of a PZT actuator. Numerical results for a thin and a thick plate containing one embedded actuator layer and one embedded sensor layer are presented. For the former case, the optimum location of the centroid of the excited rectangular region that will require minimum voltage to control the out-of-plane displacements is determined. Keeping the location of the centroid and the shape of the excited region fixed, we ascertain the voltage required as a function of the length of its diagonal to nullify the deflections of the plate. The maximum shear stress at the interface between the sensor and the lamina is found to be lower than that between the actuator and the lamina. The point of maximum output voltage from the sensor coincides with that of its peak out-of-plane displacement. The variations of displacement and stress components through the thickness for the thin and thick plates are similar. The transient finite deformations of a neo-Hookean beam or plate with PZT patches bonded to its upper and lower surfaces are simulated by the finite element method. The constitutive relation for the piezoelectric material is taken to be linear in the Green-Lagrange strain tensor but quadratic in the driving voltage. A code using 8-noded brick elements has been developed and validated by comparing computed results with either analytical solutions or experimental observations. The code is then used to study flexural waves generated by PZT actuators and propagating through a cantilever beam both with and without a defect in it. The computed results are compared with test observations and with the published results for the linear elastic beam. The effects of both geometrical and material nonlinearities are discussed. A simple feedback control algorithm is shown to annul the motion of a neo-Hookean plate subjected to an impulsive load.
Dynamics and Control of Flexible Aircraft
Tuzcu, Ilhan (Virginia Tech, 2001-12-19)
This dissertation integrates in a single mathematical formulation the disciplines pertinent to the flight of flexible aircraft, namely, analytical dynamics, structural dynamics, aerodynamics and controls. The unified formulation is based on fundamental principles and incorporates in a natural manner both rigid body motions of the aircraft as a whole and elastic deformations of the flexible components (fuselage, wing and empennage), as well as the aerodynamic, propulsion, gravity and control forces. The aircraft motion is described in terms of three translations (forward motion, sideslip and plunge) and three rotations (roll, pitch and yaw) of a reference frame attached to the undeformed fuselage, and acting as aircraft body axes, and elastic displacements of each of the flexible components relative to corresponding body axes. The mathematical formulation consists of six ordinary differential equations for the rigid body motions and one set of ordinary differential equations for each elastic displacement. A perturbation approach permits division of the problem into a nonlinear "zero-order Problem" for the rigid body motions, corresponding to flight dynamics, and a linear "first-order problem" for the elastic deformations and perturbations in the rigid body translations and rotations, corresponding to "extended aeroelasticity." Due to computational speed advantages, the aerodynamic forces are derived by means of strip theory. The control forces for the flight dynamics problem are obtained by an "inverse" process. On the other hand, the feedback control forces for the extended aeroelasticity problem are derived by means of LQG theory. A numerical example corresponding to steady level flight and steady level turn maneuver is included.
Dynamics and Control of Flexible Multibody Structures
Stemple, Timothy J. (Virginia Tech, 1998-03-19)
The goal of this study is to present a method for deriving equations of motion capable of modeling the controlled motion of an open loop multibody structure comprised of an arbitrary number of rigid bodies and slender beams. The procedure presented here for deriving equations of motion for flexible multibody systems is carried out by means of the Principle of Virtual Work (often referred to in the dynamics literature as d'Alembert's Principle). We first consider the motion of a general flexible body relative to the inertial space, and then derive specific formulas for both rigid bodies and slender beams. Next, we make a small motions assumption, with the end result being equations for a Rayleigh beam, which include terms which account for the axial motion, due to bending, of points on the beam central axis. This process includes a novel application of the exponential form of an orthogonal matrix, which is ideally suited for truncation. Then, the generalized coordinates and quasi-velocities used in the mathematical model, including those needed in the spatial discretization process of the beam equations are discussed. Furthermore, we develop a new set of recursive relations used to compute the inertial motion of a body in terms of the generalized coordinates and quasi-velocities. This research was motivated by the desire to model the controlled motion of a flexible space robot, and consequently, we use the multibody dynamics equations to simulate the motion of such a structure, providing a demonstration of the computer program. For this particular example we make use of a new sequence of shape functions, first used by Meirovitch and Stemple to model a two dimensional building frame subjected to earthquake excitations.
Dynamics and control of spacecraft with retargeting flexible antennas
Kwak, Moon Kyu (Virginia Polytechnic Institute and State University, 1989)
This dissertation is concerned with the dynamics and control of spacecraft consisting of a rigid platform and a given number of retargeting flexible antennas. The mission consists of maneuvering the antennas so as to coincide with preselected lines of sight while stabilizing the platform in an inertial space and suppressing the elastic vibration of the antennas. The dissertation contains the derivation of the equations of motion by a Lagrangian approach using quasi-coordinates, as well as a procedure for designing the feedback controls. Assuming that antennas are flexible, distributed parameter members, the state equations of motion are hybrid. Moreover, they are nonlinear. Following spatial discretization and truncation, these equations yield a system of nonlinear discretized state equations, which are more practical for numerical calculations and controller design. Linearization is carried out based on the assumption that the inertia of the rigid body is large relative to that of flexible body. The equations of motion for a two-dimensional model are also given. The feedback controls are designed in several ways. Disturbance-minimization control plus regulation is considered by using constant gains obtained on the basis of the premaneuver configuration of the otherwise time-varying system. ln the case of unknown constant disturbance, proportional-plus integral (PI) control has proven very effective. Pl control is used to control the perturbed motions of the platform with multi-targeted flexible appendages. A new control law is obtained for the system with small time-varying configuration during a specified time period by applying a perturbation method to the Riccati equation obtained for Pl control. According to the the proposed perturbation method, the control gains consist of zero-order time-invariant gains obtained from the solution of the matrix algebraic Riccati equation (MARE) for the post-maneuver state and first order time-varying gains obtained from the solution of the matrix differential Lyapunov equation (MDLE). The solution of the MDLE has an integral form, which can be approximated by a matrix difference equation. The adiabatic approximation, which freezes the matrix differential Riccati equation or Lyapunov equation is also discussed. Comparisons are made based on system stability by Lyapunov’s second method. A spacecraft consisting of a rigid platform and a single flexible antenna is used to illustrate disturbance-minimization control, and a spacecraft consisting of a rigid platform and two flexible antennas reorienting into different directions is used to demonstrate the effectiveness of the disturbance-accommodating control. A time-varying spring-mass-damper and a two-dimensional model, representing a reduced version of the original spacecraft model, are considered to demonstrate the perturbation and adiabatic approximation methods. To illustrate the effect of nonlinearity on the dynamic response during reorientation, a numerical example of the spacecraft having a membrane-type antenna ls presented.
Effects of earthquakes on partially-filled water tanks
Koyama, Junji (Virginia Tech, 1994-08-05)
This thesis is concerned with the effects of earthquakes on partially-filled water tanks. The analysis is applicable to rectangular water tanks, which have received little attention to date. The analysis is relatively involved and includes the derivation of the equations of motion for the vibration of the whole of tank by means of substructure synthesis, a stochastic analysis relating the random ground motion caused by earthquakes to the random vibration of the tank, a stochastic characterization of the fluid pressure and computation of the probability of failure of the tank.
Experimental verification and development of structural identification techniques on a grid
Kahn, Steven Phillip (Virginia Tech, 1990-04-05)
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.
Feedback Control of Multi-Story Structures under Seismic Excitations
Dai, Yang (Virginia Tech, 2002-04-04)
This dissertation studies the feedback control of the dynamic response of multi-story structures to seismic excitations. The seismic excitations are represented by arbitrary unknown stochastic disturbances. The research consists of modeling of the structure with a control system and a control design in the state space. A combination of the extended Hamilton's principle and the Hierarchical Finite Element Method (HFEM) was used to derive the discrete differential equations of motion. This method exhibits superior accuracy with fewer degrees of freedom (DOF). The discrete equation were realized in the state space, where the Multiple Channel Control (MCC) model, the Single Channel Control (SCC) model and the Special Single Channel Control (SSCC) model were proposed. The MCC model is a general multiple input/multiple output (MIMO) dynamic system; the SSCC model is a single input/multiple output (SIMO) dynamic system; which requires only one actuator acting on the base; the SCC model has duality. On one hand, the system can be classified as MIMO when control actuators are regarded as the input. On the other hand, it can be regarded as a SIMO system when control signal as the input. Moreover, three different types of control methodologies, the Linear Quadratic Gaussian (LQG) control, the Disturbance Accommodating Control (DAC), and the hybrid LQG/DAC approaches, were successfully developed to actively mitigate the vibration of the multi-story structures subjected to the seismic disturbance. In addition, the Kalman filter was used as an optimal observer to estimate the state of the system in the LQG and the LQG/DAC design. Finally a numerical simulation of a four-story structure was carried out under nine cases. The cases covered various combinations of the three models and the three control designs to verify the effectiveness of control technique developed in this study. The simulation results found were quite encouraging. The results show each combination has its preponderance corresponding to special priority. In general, the hybrid LQG/DAC control in conjunction with the SSCC model is the best choice.
Finite difference approach for predicting probabilistic life of a composite cylinder subjected to thermal random loads
Con, Vu Ngoc (Virginia Tech, 1979-03-05)
A long hollow cylinder with five layers, subjected to a random thermal environment is analyzed. The random thermal environment includes the ambient air temperature, solar radiation and wind speed. The location of interest is Phoenix, Arizona. The governing differential equation is the so-called one-dimensional Fourier heat conduction equation in cylindrical coordinates. An implicit finite difference scheme is developed to obtain temperature responses inside the cylinder. Given the linear elastic behavior of materials involved, induced stresses and strains are evaluated at the end of each time step of the finite difference scheme. A statistical analysis is then carried out to determine the probability of failure of the propellant and hence the service life of the motor can be computed.

Browsing by Author "Meirovitch, Leonard"

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