Experimental nonlinear dynamics is an important area of study in the modern engineering field, with engineering applications in structural dynamics, structural control, and structural health monitoring. As a result, the discipline has experienced a great influx of research efforts to develop a versatile and reliable experimental methodology. A technical challenge in many experimental studies is the procurement of a device that exhibits the desired nonlinear behavior. As a result, many researchers have longed for a versatile, but accurate, testing methodology that has complete freedom to simulate a wide range of nonlinearities and stochastic behaviors. The objective of this study is to develop a reconfigurable test setup as a tool to be used in a wide range of nonlinear dynamic studies. The main components include a moving mass whose restoring force can accurately be controlled and reprogrammed (with software) based upon measured displacement and velocity readings at each time step. The device offers control over nonlinear characteristics and the equation of dynamic motion. The advantage of having such an experimental setup is the ability to simulate various types of nonlinearities with the same test setup. As a result, the data collected can be used to help validate nonlinear modeling, system identification, and stochastic analysis studies. A physical test apparatus was developed, and various mechanical, electrical, and programming calibrations were performed for reliable experimental studies. To display potential uses for the reconfigurable approach, examples are presented where the device has been used to create physical data for use in change detection and deterioration studies. In addition, a demonstration is presented of the device’s ability to physically simulate a large-scale orifice viscous damper, commonly used in vibration mitigation in bridges and buildings. For a large-scale viscous damper, physical testing is required to ensure structural design properties. However, due to the large scale of the dampers, expensive dynamic loading tests can be carried out at a very iii limited number of facilities. Using the reconfigurable test setup, the dynamic signature of the large-scale viscous damper can accurately be simulated with pre-collected data. The development of a system capable of emulating the restoring force of a nonlinear device with software is a novel approach and requires further calibration for increased reliability and accuracy. A discussion regarding the challenges faced when developing the methodology is presented and possible solutions are recommended. The methodology introduced by this apparatus is very promising. The device is a valuable experimental tool for researchers and designers, allowing for physical data collection, modeling, analysis, and validation of a wide class of nonlinear phenomena that commonly occur in a wide variety of engineering applications.

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published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

A theory is presented which describes the global reflection and transmission characteristics of a self-focused channel propagating at an oblique angle of incidence to an interface separating two or more self-focusing nonlinear dielectric media. A complete characterization of the different behavior of the channel is given in the proper parameter space. In the dominant region, the nonlinear wavepacket representing the self-focused channel is represented as an equivalent particle moving in an equivalent potential. The dynamics of the particle is described by Newton's equations of motion, with the asymptotic propagation paths of the channel being read off from the associated phase planes of the equivalent potential. This theory provides therefore, the nonlinear Snell's Laws of refleciton or transmission since the particle dynamics gives the critical angle of total reflection and in the case of transmission, the corresponding angle of transmission. This theory also gives the stability characteristics of nonlinear surface waves, which had only been partially established in the past through numerical simulations. Finally, some applications of the theory are presented such as the design of an all-optical power adjustable spatial scanning element and an all optical switch. Extensions of the theory to waveguides with multiple interfaces are also given and possible new directions are also suggested.

Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERO. / Vita. / Bibliography: p. 232-237. / by W. Michael Bowles. / Sc.D.

在實際分析數據的時候,我們經常遇到二元時間序列數據。在許多情況下，由於普通線性二元時間序列模型未必足以說明較複雜的社會和自然現象，許多分析家認為，多元非線性時間序列模型可以提供一個可行的解決方案。在許多不同類型的多元非線性時間序列中，一個重要的類別是二元門限自回歸（BTAR）模型。BTAR 模型可以充分捕到時間序列數據中的極限週期跳躍現象及振幅頻率。Tsay (1998) [37] 提出了多元的門限型的非線性檢驗。然而，這種檢驗對被異常點污染了的時間序列數據的表現不太令人滿意。為了糾正Tsay (1998) [37]檢驗的缺點，我們提出一個穩健的檢驗程序。本論文的重點是二元時間序列數據。重新加權二元最小消平方法被採用從而推出一個穩健的門限型非線性檢驗。亦得出該檢驗的統計量在原假設下的漸近分怖。透過模擬實驗,找出提出的檢驗的性能，並且與根據最小消平方法建立的Tsay (1998) [37]的檢驗作出比較，我們也會提供實際的數據例子給予說明。 / Bivariate time series data are frequently encountered in practical situations. In many cases, since ordinary linear bivariate time series models may not be sufficient to de-scribe complex social and natural phenomena, many analysts believe that vector non-linear time series models could provide a viable solution. Among many different types of vector non-linear time series processes, an important class is the bivariate threshold autoregressive (BTAR) model. BTAR model can be employed to capture limit cycles, jump phenomenon and amplitude-frequency in the time series data. A test for threshold-type non-linearity in a vector time series was proposed by Tsay (1998) [38]. However, this test does not perform satisfactorily if the data are contaminated by outliers. To remedy the drawback of the Tsay' s (1998) [38] test, we propose a robust testing procedure. The focus of this thesis is on bivariate time series data. The reweighted bivariate least trimmed squares method is adopted to derive a robust test for threshold-type non-linearity. The asymptotic null distribution of the proposed test statistic is dervied. Simulation studies are conducted to investigate the performance of the proposed test and to compare it with the least squares method based on the Tsay's (1998) [38] test. Numerical examples are provided for illustrative purposes. / Detailed summary in vernacular field only. / Chow, Wai Kit. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 40-44). / Abstracts also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Linear Time Series Models and Their Applications --- p.1 / Chapter 1.2 --- Non-linear Time Series Models and Their Applications --- p.3 / Chapter 1.3 --- Threshold Autoregressive Model (TAR) and the Self-exciting Threshold Autoregressive Model (SETAR) --- p.4 / Chapter 1.4 --- Outliers in Univariate Time Series --- p.5 / Chapter 1.5 --- Bivariate Autoregressive Model (BAR) --- p.6 / Chapter 1.6 --- Bivariate Threshold Autoregressive Model (BTAR) --- p.7 / Chapter 1.7 --- Outliers in Bivariate Time Series --- p.8 / Chapter 1.8 --- Objectives of the Thesis --- p.9 / Chapter 1.9 --- Organisation of the Thesis --- p.10 / Chapter 2 --- The Proposed Test --- p.11 / Chapter 2.1 --- Tsay's Test --- p.11 / Chapter 2.2 --- Reweighted Multivariate Least Trimmed Squares Method --- p.14 / Chapter 2.3 --- The Proposed Test --- p.18 / Chapter 3 --- Simulation Study --- p.24 / Chapter 3.1 --- Under the Null Hypothesis --- p.24 / Chapter 3.2 --- Under the Alternative Hypothesis --- p.26 / Chapter 3.3 --- The Choice of γ and δ --- p.28 / Chapter 4 --- Examples --- p.31 / Chapter 4.1 --- Simulated Data --- p.31 / Chapter 4.2 --- Gas-Furnace Data --- p.33 / Chapter 4.3 --- Blowfly Data --- p.35 / Chapter 5 --- Conclusions and Further Research --- p.38 / Bibliography --- p.40

Yuen, Kin Pong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 93-95). / Yuen, Kin Pong. / Contents --- p.i / Abstract --- p.iv / Acknowledgement --- p.v / List of Figures --- p.vi / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Optically Bistable Behavior --- p.5 / Chapter 2.1 --- Bistable behavior of two component composites --- p.5 / Chapter 2.1.1 --- Formalism --- p.6 / Chapter 2.1.2 --- Results and Discussion --- p.7 / Chapter 2.1.3 --- Stability analysis --- p.9 / Chapter 2.2 --- Bistable behavior of three component composites: Nonlinear dielec- tric core embedded in a metallic shell --- p.11 / Chapter 2.2.1 --- Spectral representation of the local field --- p.11 / Chapter 2.2.2 --- The onset of bistable behavior --- p.20 / Chapter 2.2.3 --- The extinction coefficient and reflectance at normal incidence --- p.24 / Chapter 2.2.4 --- Discussion and Conclusion --- p.28 / Chapter 2.3 --- Bistable behavior of three component composites: Metallic core em- bedded in a nonlinear dielectric shell --- p.30 / Chapter 2.3.1 --- Linear response of spherical inclusions and concentric spheres --- p.31 / Chapter 2.3.2 --- Onset of bistable behavior --- p.35 / Chapter 2.3.3 --- Results and Discussion --- p.41 / Chapter 2.4 --- Possible development of the spectral representation --- p.44 / Chapter Chapter 3. --- Optical Repsonse of a Nonlinear Composite Film --- p.45 / Chapter 3.1 --- Enhanced nonlinear response of coated spheres --- p.46 / Chapter 3.2 --- Solution of nonlinear wave equation --- p.48 / Chapter 3.3 --- Results and Discussion --- p.49 / Chapter 3.4 --- Conclusion --- p.52 / Chapter 3.5 --- Transfer matrix formalism for transmittance: Possible control over the size of a photonic band gap --- p.52 / Chapter 3.5.1 --- Transfer matrix method --- p.54 / Chapter Chapter 4. --- Bounds and Estimates for Nonlinear Composites --- p.59 / Chapter 4.1 --- Linear response of spherical inclusions --- p.60 / Chapter 4.2 --- Strongly nonlinear response of spherical inclusions --- p.61 / Chapter 4.3 --- Linear response of concentric spheres --- p.64 / Chapter 4.4 --- Strongly nonlinear response of concentric spheres --- p.66 / Chapter 4.5 --- Some exactly solvable cases --- p.68 / Chapter 4.6 --- Concentric spheres with nonlinear shell embedded in a linear dielec- tric host --- p.71 / Chapter 4.7 --- Discussion and Conclusion --- p.73 / Chapter 4.8 --- Small contrast expansion --- p.75 / Chapter 4.9 --- Hashin-Shtrikman microgeometry --- p.78 / Chapter 4.10 --- Exact bounds for linear composites --- p.79 / Chapter 4.11 --- Variational approach for Hashin-Shtrikman microstructure --- p.82 / Chapter 4.12 --- Improved variational approach --- p.85 / Chapter 4.13 --- Discussion and Conclusion --- p.87 / Appendix A. Derivation of the Energy Functional --- p.88 / Chapter A.1 --- The energy functional --- p.88 / Chapter A.2 --- Effect of higher order terms to the energy functional --- p.91 / Bibliography --- p.93

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Bibliography: leaves 170-173. / by Daniel Ocone. / Ph.D.

Martin Schetzen. / "July 6, 1962." "Submitted to the Department of Electrical Engineering, M.I.T., May 20, 1961, in partial fulfillment of the requirements for the degree of Doctor of Science." / Bibliography: p. 53. / Army Signal Corps Contract DA 36-039-sc-78108 Department of the Army Task 3-99-20-001 and Project 3-99-00-000. Army Signal Corps Contract DA-SIG-36-039-61-G14.