Current and future space exploration operations rely heavily on space-borne telescopes, of which mirrors are an integral component. However, traditional solid mirrors are heavy and require a big storage space. Deploying membrane mirrors can alleviate many of these obstacles. Membrane mirrors are light and can be compactly stowed resulting in cheap launching costs. It was also demonstrated that membrane mirror would provide quality optical imaging capabilities. However, membrane mirrors exhibit undesirable vibrations that can be caused by thermal gradients or internally-induced excitations. The undesirable vibration degrades the performance of these mirrors. Hence, it is proposed to augment membrane mirrors with smart actuators around their outer rim. Smart actuators can be used to suppress the undesirable vibration. More importantly, such a system provide the capability to form appropriate surfaces to correct for aberrations in an incoming wavefront. In this spirit, this work aims at modeling and control a membrane mirror augmented with smart actuators. The approach here to consider a membrane strip augmented with smart actuators as a prelude for studying circular membranes. We consider strips of membrane material, and treat two such structures: a membrane strip augmented with a single piezoceramic bimorph acting in bending, and a membrane strip augmented with multiple macro-fiber composite bimorphs. The later structure is studied under two actuation configurations. In the first configuration, both actuators act in bending. In the other configuration, one actuator acts in bending and the second acts in tension. The developed models of both structures were validated experimentally. Then, control laws were derived for both structures. An optimal proportional-integral controller is used for the membrane strip augmented with a single piezoceramic bimorph. For the membrane strip augmented with two macro-fiber composite bimorphs, a sliding mode controller with a switching command is used. Simulation results are presented to demonstrate the efficacy of the proposed control laws. Then, a circular membrane augmented with macro-fiber composite bimorph actuators is considered. We derive the governing equation of the structure for the general configuration, where actuators are producing bending moments and radial loading. Then, we seek a reduced order model of the structure. We work on obtaining a Galerkin expansion of the model where the test functions used are the mode shapes of the structure as obtained from a finite element analysis conducted in a commercial software package. Then the control problem is considered. The objective is to correct for optical aberrations, so the Zernike polynomial basis functions are used. A transformation from the optical modes to the mechanical modes is presented and an augmented adaptive controller is used to correct for image aberrations. The results presented show the efficacy of the controller. / Ph. D.

The analysis of engineering structures which are subjected to dynamic forces is an area of study which has received considerable attention in recent years. In some cases, an understanding of the behavior of a structure under its expected time-varying loads is imperative so that the designed facility fulfills its intended purpose. Such structures might be simple beams, columns, rigid frames, electrical, and mechanical equipment, etc. In general, there are three types of motion which the design engineer might be required to investigate due to certain prescribed loads, namely, transient response, steady-state vibrations, and random vibrations. The motion studied usually depends upon the expected or predicted load which is sometimes called the input of the system. In what follows, only transient responses of systems subjected to short time-duration loads are considered. These impulsive-type forces might arise from sources such as earthquake tremors, wind gust forces and pressure, and pressure waves from explosions. Of the various assumptions which the engineer must make when studying the dynamic response of structures, one of the most important is perhaps the model representation of the true structure. One method of representation is to judiciously idealize the structure into concentrated mass and to connect, each lumped mass to its neighbor by weightless springs and dashpots. The number of masses and the constraints or lack of them on each mass determine the number of degrees-of-freedom of the system. The differential equations which describe the motion of the model are either linear or nonlinear, depending upon the behavior of each mass, spring, and dashpot. / Ph. D.

Solving the inverse problem, finding the applied forces knowing the system characteristics and the response, has been a difficult problem in structural dynamics. Insufficient accuracy in the system identification and uncorrelated content in the response exacerbate the ill-conditioned nature of the indirect-force-determination problem. Numerical techniques for performing the force determination are exploited and compared. The characteristics of the force determination problems are investigated through least squares solution procedures and numerical examples. The credibility of the estimated forces are studied in the numerical examples using the correlations of the matrix condition number and the mode contribution factor with the resulting error. The focus of this research is the improved estimation of the applied forces. The two important factors in reducing the force determination error are accurate system identification and improved conditioning of the system matrix. A variety of techniques are examined to reduce the system identification error and control the response measurement uncertainty. The use of rotational or curvature degrees of freedom as an alternative to the translational degrees of freedom for the response measurements and for the structural dynamics model yields a quite differently conditioned system matrix. The choice of a particular degrees of freedom is shown to depend on the frequency contents of the applied forces. / Ph. D.

No description available.

A new method is developed for experimentally determining the system parameters of a structure that is suitable for implementation in microprocessor-based systems. It uses single degree-of-freedom models to describe a multi-degree-of-freedom system. The system is assumed to be describable by a linear, proportionally and lightly damped, lumped parameter model. Two types of damping models, viscous and structural damping, are provided. The effective mass, stiffness, and damping are obtained by fitting the experimental data in the inverse Nyquist plane. The effective mass, stiffness, and damping are convertible to global modal mass, stiffness, and damping through normal mode corrections. Then a physical space mathematical model may be assembled from the modal properties for complete and truncated modal vector system descriptions. Therefore, this method will deal with the general case where the number of degree-of-freedom exceeds the number of identified modes. After a mathematical model is developed, different ways of modifying the structure analytically are investigated. This modified model is used to predict the new dynamic characteristics of the modified structure due to changes in its mass, stiffness, or damping properties. There are three ways that modifications can be made. They are: l) modifications made in the physical coordinates model; 2) modifications made in both the physical and modal coordinates models; and 3) modifications made in the modal coordinates model. The last way is found to be the most efficient way; therefore, model modifications should be done totally in modal spaces, modal space I and II. The derivation of mass, stiffness, and damping modification matrices for general structure is also presented. The resonance specification and frequency response function synthesis are two useful techniques that aid in system modification and are, therefore, included. A resonant peak can be shifted to another frequency by making certain modifications to the structure, thus avoiding undesired vibration. The resonance specification will determine the amount of physical change needed. It is not practical to store all the frequency response function measurements of a structure during testing. Therefore, a frequency response function synthesis is needed, such that any one can be synthesized from the model developed. A theoretical three degree-of-freedom system and two experimental systems--a square plate and a C-clamp--were used to verify the techniques developed. / Ph. D.

published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy

Trial and error and the use of highly time-consuming methods are often necessary for investigation and characterization of nonlinear systems. However, for the rather common case where a nonlinear system has linear relations between many of its degrees of freedom there are opportunities for more efficient approaches. The aim of this thesis is to develop and validate new efficient simulation and experimental methods for characterization of mechanical systems with localized nonlinearities. The purpose is to contribute to the development of analysis tools for such systems that are useful in early phases of the product innovation process for predicting product properties and functionality. Fundamental research is combined with industrial case studies related to metal cutting. Theoretical modeling, computer simulations and experimental testing are utilized in a coordinated approach to iteratively evaluate and improve the methods. The nonlinearities are modeled as external forces acting on the underlying linear system. In this way, much of the linear theories behind forced response simulations can be utilized. The linear parts of the system are described using digital filters and modal superposition, and the response of the system is recursively solved for together with the artificial external forces. The result is an efficient simulation method, which in conjunction with experimental tests, is used to validate the proposed characterization methods. A major part of the thesis addresses a frequency domain characterization method based on broad-band excitation. This method uses the measured responses to create artificial nonlinear inputs to the parameter estimation model. Conventional multiple-input/multiple-output techniques are then used to separate the linear system from the nonlinear parameters. A specific result is a generalization of this frequency domain method, which allows for characterization of continuous systems with an arbitrary number of localized zero-memory nonlinearities in a structured way. The efficiency and robustness of this method is demonstrated by both simulations and experimental tests. A time domain simulation and characterization method intended for use on systems with hysteresis damping is also developed and its efficiency is demonstrated by the case of a dry-friction damper. Furthermore, a method for improved harmonic excitation of nonlinear systems using numerically optimized input signals is developed. Inverse filtering is utilized to remove unwanted dynamic effects in cutting force measurements, which increases the frequency range of the force dynamometer and significantly improves the experimental results compared to traditional methods. The new methods form a basis for efficient analysis and increased understanding of mechanical systems with localized nonlinearities, which in turn provides possibilities for more efficient product development as well as for continued research on analysis methods for nonlinear mechanical structures.

Vibration in metal cutting is a common problem in the manufacturing industry, especially when long and slender tool holders or boring bars are involved in the manufacturing process. Vibration has a detrimental effect on machining. In particular the surface finish is likely to suffer, but tool life is also most likely to be reduced. Tool vibration also results in loud noise that may disturb the working environment. The first part of this thesis describes the development of a robust and manually adjustable analog controller capable of actively controlling boring bar vibrations related to internal turning. This controller is compared with an adaptive digital feedback filtered-x LMS controller and it displays similar performance with a vibration attenuation of up to 50 dB. A thorough experimental investigation of the influence of the clamping properties on the dynamic properties of clamped boring bars is also carried out in second part of the thesis. In relation to this, it is demonstrated that the number of clamping screws, the clamping screw diameter size, the screw tightening torque and the order the screws are tightened, have a significant influence on a clamped boring bar’s eigenfrequencies as well as on its mode shape orientation in the cutting speed - cutting depth plane. Also, an initial investigation of nonlinear dynamic properties of clamped boring bars was carried out. Furthermore, vibration in milling has also been studied in relation to millingtool holders with a long overhang. A basic investigation concerning the spatial dynamic properties of the tool holders of milling machines, both when not cutting and during cutting, has been carried out. Also, active control of milling tool holder vibration has been investigated and a first prototype of an active milling tool holder was implemented and tested. The challenge of transferring electrical power while maintaining good signal quality to and from a rotating object is addressed and a solution to this is proposed. Finally, vibration is also a problem for the hydroelectric power industry. In Sweden, hydroelectric power plants stand for approximately half of Sweden’s electrical power production and are also considered to be a so-called green source of energy. When renovating water turbines in small-scale hydroelectric power plants and modifying them to optimize efficiency, it is not uncommon that disturbing vibrations occur in the power plant. These vibrations have a negative influence on the production capacity and will wear various components quickly. Occasionally, these vibrations may cause severe damage to the power plant. To identify this vibration problem, experimental modal analysis and operating deflection shape analysis were utilized. To reduce the vibration problem, active control using inertial mass actuators was investigated. Preliminary results indicate a significant attenuation of the vibrations.

No description available.

There is a risk that excessive vibration in long span cantilever grandstands can be triggered by the spectators synchronising their jumps to the music played. If the jumping frequency excites a resonance of the grandstand, large force could be generated. This thesis studies human-structure interaction in cantilever grandstands, with emphasis on modelling the passive and jumping crowds, and analysing the response of a single degree-of-freedom (SDOF) structural system. Preliminary work on analysing a cantilever occupied by seated humans shows that it is acceptable to use a SDOF structural system for analysis which meant emphasis of later work could be placed on understanding the interaction between a passive crowd and the structure. Human dynamic models from published biomechanics studies are used to develop a passive crowd model. A transfer function, fitted to the crowd apparent mass, is used to define the crowd model. It is found that the passive crowd can be approximated well by using a single 2DOF system. The combined passive crowd-structure system is modelled as a feedback system and a parametric study is conducted. It is found that the passive crowd adds significant mass and damping to the structure and these effects vary with the natural frequency of the structure. Records of forces of people jumping to a beat are used to develop a probabilistic model of crowd jumping loads. Key parameters are introduced to characterise the timing and shape of the jumping impulses. An analytical function is used to approximate the impulse shape. All parameters are characterised with probability distribution functions. Using the fitted probability distribution functions, the Monte Carlo method is used to simulate individual jumping load-time histories and to obtain the structural responses due to group jumping loads. The variations of the structural response with the natural frequency of the empty structure and the size of the active crowd are presented in charts. As expected, the worst response is found on structures with natural frequencies coinciding with the first three harmonics of the crowd jumping loads. For structures occupied by passive crowds, a significant reduction in the structural response is found at resonance excited by the second and third harmonics, due to high levels of damping provided by the passive crowds. On variation of the structural response with the crowd size, it is found that the structural response becomes asymptotic for groups larger than 16 people. Experimental individual jumping and bobbing tests are conducted at six distinct beat frequencies to look at the variations of the impulse shape and degree of synchronisation with the beat frequency. The bobbing action is found to have a higher inherent variability between individuals compared to jumping. Jumping tests involving two people facing each other are also conducted. The results show that there is a better synchronisation when two people are jumping together compared to when jumping alone.