Before the beginning of digital-computers era, a lot of research was carried out in order to find electric circuits the governing equations of which were analogous to the ones of mechanical systems. The mentioned circuits were called ectro-mechanical analogs. They were used as analogical computers for the simulation and the design of mechanical systems. The actual technological development of piezoelectric actuators, which are devices able to efficiently transduce energy between the electrical and mechanical form, induced us to consider again those electro-mechanical analogs in order to create coupled piezo-electro-mechanical systems. Our idea is that the coupling between electro-mechanical phenomena is maximum when the propagation of both electrical and mechanical waves are governed by similar equations. Let us remark that because of the propagating mechanical wave-speed is much lower than the light-speed for every material, it is not possible to search for an efficient electro-mechanical coupling inside a piezoelectric continuum. Consequently circuits able to support the propagation of electric-potential waves have been considered. In this work, the equations for the elastica and for the plate are considered and their circuital analogs are derived using their finite-difference approximation. Afterwards, the coupling between the two structures is modelled considering piezoelectric actuators uniformly distributed on the mechanical system and connected to the nodes of the electric circuit. Then the electro-mechanical coupled equations are derived, and an analytical solution is found for a particular case. Finally some numerical simulations showing the efficiently energy exchange is presented. / Master of Science

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A dual approach integrating structural tailoring and adaptive materials technology and designed to control the dynamic response of cantilever beams subjected to external excitations is addressed. The cantilevered structure is modeled as a thin-walled beam of arbitrary cross-section and incorporates a number of non-classical effects such as transverse shear, warping restraint, anisotropy of constituent materials and heterogeneity of the construction. Whereas structural tailoring uses the anisotropy properties of advanced composite materials, adaptive materials technology exploits the actuating/sensing capabilities of piezoelectric materials bonded or embedded into the host structure. Various control laws relating the piezoelectrically-induced bending moment with combined kinematical variables characterizing the response at given points of the structure are implemented and their effects on the closed-loop frequencies and dynamic response to external excitations are investigated. The combination of structural tailoring and control by means of adaptive materials proves very effective in damping out vibration. In addition, the influence of a number of non-classical effects characterizing the structural model on the open and closed-loop dynamic responses have been considered and their roles assessed. / Ph. D.

As power demand across communities increases, focus has been given to the maintenance of power lines against harsh environments such as wind-induced vibration (WIV). Currently, Inspection robots are used for maintenance efforts while fixed tuned mass dampers (FTMDs) are used to prevent structural damages. However, both solutions are facing many challenges. Inspection robots are limited by their size and considerable power demand, while FTMDs are narrowband and unable to adapt to changing wind characteristics, and thus are unable to reposition themselves at the antinodes of the vibrating loop. In view of these shortcomings, we propose a mobile damping robot (MDR) that integrates inspection robots' mobility and FTMDs WIV vibration control to help maintain power lines. In this effort, we model the conductor and the MDR by using Hamilton's principle and we consider the two-way nonlinear interaction between the MDR and the cable. The MDR is driven by a Proportional-Derivative controller to the optimal vibration location (i.e, antinodes) as the wind characteristics vary. The numerical simulations suggest that the MDR outperforms FTMDs for vibration mitigation. Furthermore, the key parameters that influence the performance of the MDR are identified through a parametric study. The findings could set up a platform to design a prototype and experimentally evaluate the performance of the MDR. / Master of Science / Power lines are civil structures that span more than 160000 miles across the United States. They help electrify businesses, factories and homes. However, power lines are subject to harsh environments with strong winds, which can cause Aeolian vibration. Vibration in this context corresponds to the oscillation of power lines in response to the wind. Aeolian vibration can cause significant structural damages that impact public safety and result in a significant economic loss. Today, different solutions have been explored to limit the damages to these key structures. For example, the lines are commonly inspected by foot patrol, helicopters, or inspection robots. These inspection techniques are labor intensive and expensive. Furthermore, Stockbridge dampers, mechanical vibration devices, can be used to reduce the vibration of the power line. However, Stockbridge dampers can get stuck at location called nodes, where they have zero efficiency. To tackle this issue, we propose a mobile damping robot that can re-adjust itself to points of maximum vibration to maximize vibration reduction. In this thesis, we explore the potential of this proposed solution and draw some conclusions of the numerical simulations.

In the first part of this study, the dynamic behavior of a cracked rotating shaft with a rigid disk is analyzed, with an ideal and a nonideal motor, passing through its critical speed. The shaft contains a single transverse crack that is assumed to be either completely open or completely closed at any given time, depending on the curvature of the shaft at the cross section containing the crack. Flexible, damped supports and overhangs with a mass at one end are included. The supports are modeled with elastic springs and dashpots. The influence of gyroscopic moments of the disk (with an ideal motor) is investigated. For a nonideal motor, there is an interaction between the shaft and the motor. Eccentricity of the disk, gravitational forces, and internal and external damping are included. The equations of motion and boundary conditions are derived by Hamilton's Principle. To eliminate the spatial dependence, the Extended Galerkin Method is applied. Longitudinal vibration, shear deformation and torsional vibration are neglected. In the second part of this study, the vibration suppression of a cracked, simply supported, rotating shaft with a rigid disk is discussed, with an ideal and a nonideal motor, passing through the critical speed. The use of a flexible internal constraint is introduced to suppress the vibration. By activating this additional internal support, the shaft is prevented from passing its critical speed. Transient motions occur at the time of activation or deactivation of the constraint. The maximum displacement of the shaft during acceleration (run-up) or deceleration (coast-down) can be reduced significantly by appropriate application of this flexible internal support. / Ph. D.

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.

Yes / This paper presents an investigation into the development of an intelligent active vibration control (AVC) system. Evolutionary Genetic algorithms (GAs) and Adaptive Neuro-Fuzzy Inference system (ANFIS) algorithms are used to develop mechanisms of an AVC system, where the controller is designed on the basis of optimal vibration suppression using the plant model. A simulation platform of a flexible beam system in transverse vibration using finite difference (FD) method is considered to demonstrate the capabilities of the AVC system using GAs and ANFIS. MATLAB GA tool box for GAs and Fuzzy Logic tool box for ANFIS function are used for AVC system design. The system is then implemented, tested and its performance assessed for GAs and ANFIS based design. Finally a comparative performance of the algorithm in implementing AVC system using GAs and ANFIS is presented and discussed through a set of experiments.

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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.