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  • 1
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    Control of Limit Cycle Oscillations of a Two-Dimensional Aeroelastic System (2010)
    Hindawi
    Details
    Publication Date: 2010-01-01
    Description: Linear and nonlinear static feedback controls are implemented on a nonlinear aeroelastic system that consists of a rigid airfoil supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. The normal form is used to investigate the Hopf bifurcation that occurs as the freestream velocity is increased and to analytically predict the amplitude and frequency of the ensuing limit cycle oscillations (LCO). It is shown that linear control can be used to delay the flutter onset and reduce the LCO amplitude. Yet, its required gains remain a function of the speed. On the other hand, nonlinear control can be effciently implemented to convert any subcritical Hopf bifurcation into a supercritical one and to significantly reduce the LCO amplitude.
    Print ISSN: 1024-123X
    Electronic ISSN: 1563-5147
    Topics: Mathematics , Technology
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  • 2
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    Parametrically Excited Nonlinear Two-Degree-of-Freedom Systems with Repeated Natural Frequencies (1995)
    Hindawi
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    Publication Date: 1995-01-01
    Description: The method of normal forms is used to study the nonlinear response of two-degree-of-freedom systems with repeated natural frequencies and cubic nonlinearity to a principal parametric excitation. The linear part of the system has a nonsemisimple one-to-one resonance. The character of the stability and various types of bifurcation including the formation of a homoclinic orbit are analyzed. The results are applied to the flutter of a simply supported panel in a supersonic airstream.
    Print ISSN: 1070-9622
    Electronic ISSN: 1875-9203
    Topics: Mathematics
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  • 3
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    Neural Network Identification and Control of a Parametrically Excited Structural Dynamic Model of an F-15 Tail Section (2000)
    Hindawi
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    Publication Date: 2000-01-01
    Description: We investigated the design of a neural-network-based adaptive control system for a smart structural dynamic model of the twin tails of an F-15 tail section. A neural network controller was developed and tested in computer simulation for active vibration suppression of the model subjected to parametric excitation. First, an emulator neural network was trained to represent the structure to be controlled and thus used in predicting the future responses of the model. Second, a neurocontroller to determine the necessary control action on the structure was developed. The control was implemented through the application of a smart material actuator. A strain gauge sensor was assumed to be on each tail. Results from computer-simulation studies have shown great promise for control of the vibration of the twin tails under parametric excitation using artificial neural networks.
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    Electronic ISSN: 1875-9203
    Topics: Mathematics
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  • 4
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    Investigation of Subcombination Internal Resonances in Cantilever Beams (1998)
    Hindawi
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    Publication Date: 1998-01-01
    Description: Activation of subcombination internal resonances in transversely excited cantilever beams is investigated. The effect of geometric and inertia nonlinearities, which are cubic in the governing equation of motion, is considered. The method of time-averaged Lagrangian and virtual work is used to determine six nonlinear ordinary-differential equations governing the amplitudes and phases of the three interacting modes. Frequency- and force-response curves are generated for the caseω ≈ ω4≈ 1/2(ω2+ ω5). There are two possible responses: single-mode and three-mode responses. The single-mode periodic response is found to undergo supercritical and subcritical pitchfork bifurcations, which result in three-mode interactions. In the case of three-mode responses, there are conditions where the low-frequency mode dominates the response, resulting in high-amplitude quasiperiodic oscillations.
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    Electronic ISSN: 1875-9203
    Topics: Mathematics
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  • 5
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    Axial Vibration Confinement in Nonhomogenous Rods (2005)
    Hindawi
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    Publication Date: 2005-01-01
    Description: A design methodology for the vibration confinement of axial vibrations in nonhomogenous rods is proposed. This is achieved by a proper selection of a set of spatially dependent functions characterizing the rod material and geometric properties. Conditions for selecting such properties are established by constructing positive Lyapunov functions whose derivative with respect to the space variable is negative. It is shown that varying the shape of the rod alone is sufficient to confine the vibratory motion. In such a case, the vibration confinement requires that the eigenfunctions be exponentially decaying functions of space, where the notion of spatial domain stability is introduced as a concept dual to that of the time domain stability. It is also shown that vibration confinement can be produced if the rod density and/or stiffness are varied with respect to the space variable while the cross-section area is kept constant. Several case studies, supporting the developed conditions imposed on the spatially dependent functions for vibration confinement in vibrating rods, are discussed. Because variation in the geometric and material properties might decrease the critical buckling loads, we also discuss the buckling problem.
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    Electronic ISSN: 1875-9203
    Topics: Mathematics
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  • 6
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    Control of Rotary Cranes Using Fuzzy Logic (2003)
    Hindawi
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    Publication Date: 2003-01-01
    Description: Rotary cranes (tower cranes) are common industrial structures that are used in building construction, factories, and harbors. These cranes are usually operated manually. With the size of these cranes becoming larger and the motion expected to be faster, the process of controlling them has become difficult without using automatic control methods. In general, the movement of cranes has no prescribed path. Cranes have to be run under different operating conditions, which makes closed-loop control attractive.In this work a fuzzy logic controller is introduced with the idea of “split-horizon”; that is, fuzzy inference engines (FIE) are used for tracking the position and others are used for damping the load oscillations. The controller consists of two independent sub-controllers: radial and rotational. Each of these controllers has two fuzzy inference engines (FIE). Computer simulations are used to verify the performance of the controller. Three simulation cases are presented. In the first case, the crane is operated in the gantry (radial) mode in which the trolley moves along the jib while the jib is fixed. In the second case (rotary mode), the trolley moves along the jib and the jib rotates. In the third case, the trolley and jib are fixed while the load is given an initial disturbance. The results from the simulations show that the fuzzy controller is capable of keeping the load-oscillation angles small throughout the maneuvers while completing the maneuvers in relatively reasonable times.
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    Topics: Mathematics
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  • 7
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    Dynamic Analysis of Multilayers Based MEMS Resonators (2017)
    Hindawi
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    Publication Date: 2017-01-01
    Description: The dynamic behavior of a microelectromechanical system (MEMS) parallel and electrically coupled double-layers (microbeams) based resonator is investigated. Two numerical methods were used to solve the dynamical problem: the reduced-order modeling (ROM) and the perturbation method. The ROM was derived using the so-called Galerkin expansion with considering the linear undamped mode shapes of straight beam as the basis functions. The perturbation method was generated using the method of multiple scales by direct attack of the equations of motion. Dynamic analyses, assuming the above two numerical methods were performed, and a comparison of the results showed good agreement. Finally, a parametric study was performed using the perturbation on different parameters and the results revealed different interesting features, which hopefully can be useful for some MEMS based applications.
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    Topics: Mathematics , Technology
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  • 8
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    Control of 2D Flexible Structures by Confinement of Vibrations and Regulation of Their Energy Flow (2009)
    Hindawi
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    Publication Date: 2009-01-01
    Description: In this paper, we investigate the control of 2D flexible structures by vibration confinement and the regulation of their energy flow along prespecified spatial paths. A discretized-model-based feedback strategy, aiming at confining and suppressing simultaneously the vibration, is proposed. It is assumed that the structure consists of parts that are sensitive to vibrations. The control design introduces a new pseudo-modal matrix derived from the computed eigenvectors of the discretized model. Simulations are presented to show the efficacy of the proposed control law. A parametric study is carried out to examine the effects of the different control parameters on the simultaneous confinement and suppression of vibrations. In addition, we conducted a set of simulations to investigate the flow control of vibrational energy during the confinement-suppression process. We found that the energy flow can be regulated via a set of control parameters for different confinement configurations.
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    Topics: Mathematics
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  • 9
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    Thermally Induced Principal Parametric Resonance in Circular Plates (2002)
    Hindawi
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    Publication Date: 2002-01-01
    Description: We consider the problem of large-amplitude vibrations of a simply supported circular flat plate subjected to harmonically varying temperature fields arising from an external heat flux (aeroheating for example). The plate is modeled using the von Karman equations. We used the method of multiple scales to determine an approximate solution for the case in which the frequency of the thermal variations is approximately twice the fundamental natural frequency of the plate; that is, the case of principal parametric resonance. The results show that such thermal loads produce large-amplitude vibrations, with associated multi-valued responses and subcritical instabilities.
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    Topics: Mathematics
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  • 10
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    Nonlinear Response of Cantilever Beams to Combination and Subcombination Resonances (1998)
    Hindawi
    Details
    Publication Date: 1998-01-01
    Description: The nonlinear planar response of cantilever metallic beams to combination parametric and external subcombination resonances is investigated, taking into account the effects of cubic geometric and inertia nonlinearities. The beams considered here are assumed to have large length-to-width aspect ratios and thin rectangular cross sections. Hence, the effects of shear deformations and rotatory inertia are neglected. For the case of combination parametric resonance, a two-mode Galerkin discretization along with Hamilton’s extended principle is used to obtain two second-order nonlinear ordinary-differential equations of motion and associated boundary conditions. Then, the method of multiple scales is applied to obtain a set of four first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the two excited modes. For the case of subcombination resonance, the method of multiple scales is applied directly to the Lagrangian and virtual-work term. Then using Hamilton’s extended principle, we obtain a set of four first-order nonlinear ordinary-differential equations governing the amplitudes and phases of the two excited modes. In both cases, the modulation equations are used to generate frequency- and force-response curves. We found that the trivial solution exhibits a jump as it undergoes a subcritical pitchfork bifurcation. Similarly, the nontrivial solutions also exhibit jumps as they undergo saddle-node bifurcations.
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    Topics: Mathematics
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