936,557 research outputs found

    Nonlinear output frequency response functions of MDOF systems with multiple nonlinear components

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    In engineering practice, most mechanical and structural systems are modeled as Multi-Degree-of-Freedom (MDOF) systems. When some components within the systems have nonlinear characteristics, the whole system will behave nonlinearly. The concept of Nonlinear Output Frequency Response Functions (NOFRFs) was proposed by the authors recently and provides a simple way to investigate nonlinear systems in the frequency domain. The present study is concerned with investigating the inherent relationships between the NOFRFs for any two masses of nonlinear MDOF systems with multiple nonlinear components. The results reveal very important properties of the nonlinear systems. One significant application of the results is to detect and locate faults in engineering structures which make the structures behave nonlinearly

    Resonances and resonant frequencies for a class of nonlinear systems

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    Resonant phenomena for a class of nonlinear systems, which can be described by a SDOF model with a polynomial type nonlinear stiffness, are investigated using Nonlinear Output Frequency Response Functions (NOFRFs). The concepts of resonance and resonant frequencies are proposed for the first time for a class of nonlinear systems. The effects of damping on the resonances and resonant frequencies are also analyzed. These results produce a novel interpretation of energy transfer phenomena in this class of nonlinear systems and show how the damping effect influences the system resonant frequencies and amplitudes. The results are important for the design and fault diagnosis of mechanical systems and structures which can be described by the SDOF nonlinear model

    Robust stabilization of nonlinear systems via stable kernel representations with L2-gain bounded uncertainty

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    The approach to robust stabilization of linear systems using normalized left coprime factorizations with H∞ bounded uncertainty is generalized to nonlinear systems. A nonlinear perturbation model is derived, based on the concept of a stable kernel representation of nonlinear systems. The robust stabilization problem is then translated into a nonlinear disturbance feedforward H∞ optimal control problem, whose solution depends on the solvability of a single Hamilton-Jacobi equation

    Accessibility of Nonlinear Time-Delay Systems

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    A full characterization of accessibility is provided for nonlinear time-delay systems. It generalizes the rank condition which is known for weak controllability of linear time-delay systems, as well as the celebrated geometric approach for delay-free nonlinear systems and the characterization of their accessibility. Besides, fundamental results are derived on integrability and basis completion which are of major importance for a number of general control problems for nonlinear time-delay systems. They are shown to impact preconceived ideas about canonical forms for nonlinear time-delay systems

    Towards deterministic subspace identification for autonomous nonlinear systems

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    The problem of identifying deterministic autonomous linear and nonlinear systems is studied. A specific version of the theory of deterministic subspace identification for discrete-time autonomous linear systems is developed in continuous time. By combining the subspace approach to linear identification and the differential-geometric approach to nonlinear control systems, a novel identification framework for continuous-time autonomous nonlinear systems is developed

    Relationships between the nonlinear output frequency response functions of multi- degree-of-freedom nonlinear systems

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    Nonlinear Output Frequency Response Functions (NOFRFs) are a new concept proposed by the authors for the analysis of nonlinear systems in the frequency domain. The present study is concerned with investigating inherent relationships between the NOFRFs of two masses in nonlinear MDOF systems. The results reveal very important properties of a class of nonlinear systems, and have considerable significance for the application of the NOFRF concept in engineering practices

    Parametric characteristic analysis for the output frequency response function of nonlinear volterra systems

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    The output frequency response function (OFRF) of nonlinear systems is a new concept, which defines an analytical relationship between the output spectrum and the parameters of nonlinear systems. In the present study, the parametric characteristics of the OFRF for nonlinear systems described by a polynomial form differential equation model are investigated based on the introduction of a novel coefficient extraction operator. Important theoretical results are established, which allow the explicit structure of the OFRF for this class of nonlinear systems to be readily determined, and reveal clearly how each of the model nonlinear parameters has its effect on the system output frequency response. Examples are provided to demonstrate how the theoretical results are used for the determination of the detailed structure of the OFRF. Simulation studies verify the effectiveness and illustrate the potential of these new results for the analysis and synthesis of nonlinear systems in the frequency domain
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