Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaf 82).

Not available / text

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references (leaves 177-180). Also available in an electronic version.

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis--Massachusetts Institute of Technology. / Includes bibliography.

No description available.

The identification of the dynamic characteristics of nonlinear systems is of increasing interest in the field of modal testing. In this work an investigation has been carried out into the force-state mapping approach to identification of nonlinear systems proposed by Masri and Caughey. They originally suggested a nonparametric identification technique based on curve fitting the restoring force in terms of the velocity and displacement using two dimensional Chebyshev polynomials. It has been shown that the use of Chebyshev polynomials is unnecessarily restrictive and that a simpler approach based on ordinary polynomials and special functions provides a simpler, faster and more accurate identification for polynomial and nonpolynomial types of nonlinearity. This simpler approach has allowed the iterative identification technique for multi-degree of freedom systems to be simplified and a direct identification approach, which is not subject to bias errors, has been suggested. A new procedure for identifying both the type and location of nonlinear elements in lumped parameter systems has been developed and has yielded encouraging results. The practical implementation of the force-state mapping technique required the force, acceleration, velocity and displacement signals to be available at the same instants of time for each measurement station. In order to minimise the instrumentation required, only the force and acceleration are measured and the remaining signals are estimated by integrating the acceleration. The integration problem has been investigated using several approaches both in the frequency and time domains. An analysis of the sensitivity of the estimated parameters with respect to any amplitude and phase measurement errors has been carried out for single-d.o.f. linear systems. Estimates are shown to be extremely sensitive to phase errors for lightly damped structures. The estimation of the mass or generalised mass and modal matrices required for the identification of single or multi-d.o.f. nonlinear systems respectively, has also been investigated. Initial estimates were obtained using a linear multi-point force appropriation method, normally used for the excitation of normal modes. These estimates were then refined using a new technique based on studying the sensitivity of the mass with respect to the estimated system parameters obtained using a nonlinear model. This sensitivity approach seemed promising since accurate results were obtained. It was also shown that accurate estimates for the modal matrix were not essential for carrying out a force-state mapping identification. Finally, the technique has been applied experimentally to the identification of a cantilevered T-beam structure with stiffness and damping nonlinearity. The cases of two well separated and then two fairly close modes were considered. Reasonable agreement between the behaviour of the nonlinear mathematical model and the structure was achieved considering inaccuracies in the measurement set-up. Conclusions have been drawn and some ideas for future work presented.

Response behavior of a nonlinear structural system subject to environmental loadings is investigated in this study. The system contains a nonlinear restoring force due to large geometric displacement. The external excitation is modeled as a narrowband stochastic process possessing dynamic characteristics of typical environmental loadings. A semi-analytical method is developed to predict the stochastic nonlinear response behavior under narrowband excitations in both the primary and the subharmonic resonance regions. Preservation of deterministic response characteristics under the narrowband random field is assumed. The stochastic system response induced by variations in the narrowband excitations is considered as a sequence of successive transient states. Due to the system nonlinearity, under a combination of excitation conditions, several response attraction domains may co-exist. Presence of co-existence of attraction domains and variations in the excitation amplitude often induce complex response inter-domain transitions. The response characteristics are found to be attraction domain dependent. Among different response attraction domains, their corresponding response amplitude domains overlap. In addition, within an individual attraction domain, response amplitude domains corresponding to different excitation amplitudes also overlap. Overlapping of response amplitude domains and the time-dependent variations in the excitation parameters induce response intra-domain transitions. Stationary Markovian assumption is employed to characterize the stochastic behavior of the response amplitude process and the excitation parameter processes. Based on the stochastic excitation properties and the deterministic response characteristics, governing equations of the response amplitude probability inter- and intra-domain transitions are formulated. Numerical techniques and an iteration procedure are employed to evaluate the stationary response amplitude probability distribution. The proposed semi-analytical method is validated by extensive numerical simulations. The capability of the method is demonstrated by good agreements among the predicted response amplitude distributions and the simulation results in both the primary and the subharmonic resonance regions. Variations in the stochastic response behavior under varying excitation bandwidth and variance are also predicted accurately. Repeated occurrences of various subharmonic responses observed in the numerical simulations are taken into account in the proposed analysis. Comparisons of prediction results with those obtained by existing analytical methods and simulation histograms show that a significant improvement in the prediction accuracy is achieved. / Graduation date: 1999

This work presents a control algorithm developed from the mammalian emotional processing network. Emotions are processed by the limbic system in the mammalian brain. This system consists of several components that carry out different tasks. The system level understanding of the limbic system has been previously captured in a discrete event computational model. This computational model was modified suitably to be used as a feedback mechanism to regulate the output of a continuous-time first order plant. An extension to a class of nonlinear plants is also discussed. The combined system of the modified model and the linear plant are represented as a set of bilinear differential equations valid in a half space of the 3-dimensional real space. The bounding plane of this half space is the zero level of the square of the plant output. This system of equations possesses a continuous set of equilibrium points which lies on the bounding plane of the half space. The occurrence of a connected equilibrium set is uncommon in control engineering, and to prove stability for such cases one needs an extended Lyapunov-like theorem, namely LaSalle's Invariance Principle. In the process of using this Principle, it is shown that this set of equations possesses a first integral as well. A first integral is identified using the compatibility method, and this first integral is utilized to prove asymptotic stability for a region of the connect equilibrium set.

This work presents a control algorithm developed from the mammalian emotional processing network. Emotions are processed by the limbic system in the mammalian brain. This system consists of several components that carry out different tasks. The system level understanding of the limbic system has been previously captured in a discrete event computational model. This computational model was modified suitably to be used as a feedback mechanism to regulate the output of a continuous-time first order plant. An extension to a class of nonlinear plants is also discussed. The combined system of the modified model and the linear plant are represented as a set of bilinear differential equations valid in a half space of the 3-dimensional real space. The bounding plane of this half space is the zero level of the square of the plant output. This system of equations possesses a continuous set of equilibrium points which lies on the bounding plane of the half space. The occurrence of a connected equilibrium set is uncommon in control engineering, and to prove stability for such cases one needs an extended Lyapunov-like theorem, namely LaSalle's Invariance Principle. In the process of using this Principle, it is shown that this set of equations possesses a first integral as well. A first integral is identified using the compatibility method, and this first integral is utilized to prove asymptotic stability for a region of the connect equilibrium set.