The integrated design of a structure and its control system was treated as a multiobjective optimization problem. Structural mass, a quadratic performance index, and the flutter speed constituted the vector objective function. The closed-loop performance index was taken as the time integral of the Hamiltonian. Constraints on natural frequencies and aeroelastic damping were also considered. Derivatives of the objective and constraint functions with respect to structural and control design variables were derived for a finite element beam model of the structure and constant feedback gains determined by Independent Modal Space Control. Pareto optimal designs generated for a simple beam and a tetrahedral truss demonstrated the benefit of solving the integrated structural and control optimization problem. The use of quasi-steady aerodynamic strip theory with a thin-wall box beam model showed that the integrated design for a high aspect ratio, unswept, straight, isotropic wing can be separable. Finally, an efficient modal solution of the flutter equation facilitated the aeroelastic tailoring of a low aspect ratio, forward swept, composite plate wing model. / Ph. D.

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Thesis (PhD (Industrial Engineering))--University of Stellenbosch, 2007. / Off-road working vehicles are subjected to high levels of vibration input on the rough terrain and irregular roads they work. The human operators are therefore exposed to high levels of whole body vibration (WBV) and at risk of developing health problems. A number of international standards address the matter of whole body vibration, and the European Union issued a directive which limits the exposure of workers in the EU to WBV. Unfortunately, to date there is no law in South Africa requiring compliance with any of these EU standards nor guidelines. There are vehicles which are not fitted with suspension and/or suspension seats. The three wheeled logger used in forestry is a highly manoeuvrable and effective bulk handler, but without any form of suspension and no space under the operator’s seat to install a suspension seat. However, a suspension cushion can be retrofitted to existing vehicles largely alleviating the problem. To isolate low frequency vibration large suspension travel is required which makes an air suspension cushion attractive, as it can fully collapse. Additionally, a Helmholtz resonator if added to the cushion in the form of a pipe and tank, provides anti-resonance at a specific frequency. The resonator can be tuned by adjusting the pipe’s length and diameter as well as the volume of the tank. Larger diameter pipes have less friction and give better reduction of the transmissibility curve at the anti-resonance frequency. The SEAT value is a single number used to compare suspension seats for a specific input vibration. It is calculated from the weighted input acceleration power spectral density curve and the suspension seat transmissibility curve. The former is obtained from the vehicle and is vehicle, path and speed dependent. The latter is the only variable that can be improved by using a better suspension seat/cushion. The input power spectral density often contains significant energy at frequencies where the human operator is most sensitive. The cushion resonator could be tuned to position the anti-resonance in the transmissibility curve at these frequencies. The resultant output vibration would thus be lower than the input vibration at that frequency. In this dissertation an analytical model describes the state variables in the cushion, pipe and tank. A Simulink model predicts the transmissibility curve with a solid mass as well as with a two degree of freedom seated human model. Initially the prototype was tested with a solid mass to compare the transmissibility curve produced by the simulation with the experimental results. It was required to evaluate the contribution of the resonator without the complexity of the human impedance. Subsequent tests were carried out with human subjects. Test results showed high inter subject similarity at the anti-resonance frequencies. Design guidelines are formulated that can be used by the suspension cushion designer to specify the pipe diameter and length and the volume of the tank to determine the optimal transmissibility. Input psd from ISO7096 class EM3 vehicles is used as an example during the design process. A prototype air suspension cushion was designed to reduce output vibration on the three wheeled logger. Laboratory tests with human subjects showed a significant improvement at the problematic frequencies through the tuning of the resonator. Using a Helmholtz resonator with the air suspension cushion the overall SEAT value improved by 25% compared with a 100mm foam cushion. However, the current tank and pipe need to be reduced in size for practical implementation to the vehicle. Future work would include finding an alternative mass to replace the air in the pipe. This should reduce the size of the tank and the pipe required. Additionally the simultaneous effect of multiple resonators at different frequencies should be investigated. This is required for vehicles having an input psd with significant energy at more than one frequency band.

Wavefront controller optimization is important in achieving the best possible image quality for adaptive optics systems on the current generation of large and very large aperture telescopes. This will become even more critical when we consider the demands of the next generation of extremely large telescopes currently under development. These telescopes will be capable of providing resolution which is significantly greater than the current generation of optical/IR telescopes. However, reaching the full resolving potential of these instruments will require a careful analysis of all disturbance sources, then optimizing the wavefront controller to provide the best possible image quality given the desired science goals and system constraints. Along with atmospheric turbulence and sensor noise, structural vibration will play an important part in determining the overall image quality obtained. The next generation of very large aperture telescopes currently being developed will require assessing the effects of structural vibration on closed loop AO system performance as an integral part of the overall system design. Telescope structural vibrations can seriously degrade image quality, resulting in actual spot full width half maximum (FWHM) and angular resolution much worse than the theoretical limit. Strehl ratio can also be significantly degraded by structural vibration as energy is dispersed over a much larger area of the detector. In addition to increasing telescope diameter to obtain higher resolution, there has also been significant interest in adaptive optics systems which observe at shorter wavelength from the near infrared to visible (VNIR) wavelengths, at or near 0.7 microns. This will require significant reduction in the overall wavefront residuals as compared with current systems, and will therefore make assessment and optimization of the wavefront controller even more critical for obtaining good AO system performance in the VNIR regime.

In recent years civil engineering structures such as floors, footbridges, and staircases, have reported unacceptable vibration when they are dynamically excited by pedestrians. When such structures have a particular combination of high structural flexibility and low inherent damping, there is potential for excessive vibration. Pedestrian-structure interaction (PSI) is especially noticeable when the lowest structural natural frequencies are close to the dominant pedestrian pace frequency or its harmonics. Although most of these structures are designed according to existing standards and guidelines, there are still many uncertainties in the human actions that may lead to unexpected structural behavior, increasing the vibration responses and exceeding serviceability limit states. How a pedestrian excites a structure and how that structure affects a pedestrian's gait is not fully understood. Therefore, a realistic analysis of PSI must be performed to properly incorporate these effects toward more rational structural designs. This study aims to identify, within this class of the walking-induced load problem, the vibration mechanisms, the mathematical models, and methods, to address excessive vibration in pedestrian structures. After conducting an in-depth evaluation of current guidelines and provisions for analysis and design of pedestrian structures, models to enable more realistic design under such uncertainties have been developed. The results establish a body of knowledge regarding human loads and structural responses, yielding the potential for more rational approaches to improve the analysis and design of pedestrian structures.

This thesis is concerned with disturbance amplification in interconnected systems which may consist of a large number of elements. The main focus is on passive control of a chain of interconnected masses where a single point is subject to an external disturbance. The problem arises in the design of multi-storey buildings subjected to earthquake disturbances, but applies in other situations such as bidirectional control of vehicle platoons. It is shown that the scalar transfer functions from the disturbance to a given intermass displacement can be represented as a complex iterative map. This description is used to establish uniform boundedness of the H∞-norm of these transfer functions for certain choices of interconnection impedance. A graphical method for selecting an impedance such that the H∞-norm is no greater than a prescribed value for an arbitrary length of the mass chain is given. A design methodology for a fixed length of the mass chain is also provided. A case study for a 10-storey building model demonstrates the validity of this method.

Active vibration control is a widely implemented method for the helicopter vibration control. Due to the significant progress in microelectronics, this technique outperforms the traditional passive control technique due to weight penalty and lack of adaptability for the changing flight conditions. In this thesis, an optimal controller is designed to attenuate the rotor blade vibration. The mathematical model of the triply coupled vibration of the rotating cantilever beam is used to develop the state-space model of an isolated rotor blade. The required natural frequencies are determined by the modified Galerkin method and only the principal aerodynamic forces acting on the structure are considered to obtain the elements of the input matrix. A linear quadratic regulator is designed to achieve the vibration reduction at the optimum level and the controller is tuned for the hovering and forward flight with different advance ratios.

This dissertation focuses on the design, modeling, characterization and experimental verification of a class of nonlinear energy sink, based on a cantilever beam vibrating laterally between two specially shaped surfaces that limit the vibration amplitude, thus providing a variable beam length throughout its deflection, therefore producing a smooth nonlinear restoring force. First, a methodology to evaluate and visualize the energy interactions between the nonlinear energy sink and its host structure is developed. Then, an semi-analytical dynamic model for simulating the device under actual working conditions is proposed, and finally, an experimental verification step is conducted where the numerical results are compared and correlated to the experimental results.<br>

This dissertation demonstrates that a magnetic-levitation (maglev) stage has the capabilities to control movements and reject vibration simultaneously. The mathematical model and vibration control scheme with a 6-degree-of-freedom (6-DOF) maglev stage for nanoscale positioning are developed for disturbance rejection. The derived full nonlinear dynamic equation of motions (EOMs) of the maglev stage include translational and rotational motions with differential kinematics. The derived EOMs and the magnetic forces are linearized to design a multivariable controller, a Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR), for vibration disturbance rejection in a multi-input multi-output (MIMO) system. For a more accurate model, the dynamics of an optical table with a pneumatic passive isolation system is also considered. The model of the maglev stage with the optical table is validated by experiments. Dual-loop controllers are designed to minimize the influence of the vibration disturbance between the moving platen and the optical table in the x-, y-, and z-axes motions. The inner-loop compensator regulates the velocity to reject vibration disturbance and the outer-loop compensator tracks positioning commands. When the vibration disturbances of 10 to 100 Hz are applied, the vibration-reduction ratios are about 30 to 65 percent in horizontal motion and 20 to 45 percent in vertical motion. In addition, the vibration disturbances of 45.45 Hz are attenuated by about 4 to 40 percent in angular motions. The vibration control schemes are effective in not only translational but rotational motions. In step responses, the vibration control schemes reduce the wandering range in the travel from the origin to another location. Positioning and tracking accuracies with the vibration controller are better than those without the vibration controller. In summary, these dual-loop control schemes with velocity feedback control improved the nanopositioning and vibration/disturbance rejection capabilities of a maglev system.

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