Nonstationary probability densities of strongly nonlinear single-degree-of-freedom oscillators with time delay

The primary and subharmonic resonances of a nonlinear single-degree-of-freedom system under feedback control with a time delay are studied by means of an asymptotic perturbation technique. Both external (forcing) and parametric excitations are included. By means of the averaging method and multiple scales method, two slow-flow equations for the amplitude and phase of the primary and subharmonic resonances and all other parameters are obtained. The steady state (fixed points) corresponding to a periodic motion of the starting system is investigated and frequency-response curves are shown. The stability of the fixed points is examined using the variational method. The effect of the feedback gains, the time-delay, the coefficient of cubic term, and the coefficients of external and parametric excitations on the steady-state responses are investigated and the results are presented as plots of the steady-state response amplitude versus the detuning parameter. The results obtained by two methods are in excellent agreement

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Loop Shaping for Transparency and Stability Robustness in Time-Delayed Bilateral Telemanipulation

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.1790539 ◽

2004 ◽

Vol 126 (3) ◽

pp. 650-656 ◽

Cited By ~ 10

Author(s):

Kevin B. Fite and ◽

Michael Goldfarb ◽

Angel Rubio

Keyword(s):

Time Delay ◽

Communication Channels ◽

Smith Predictor ◽

Degree Of Freedom ◽

Single Degree Of Freedom ◽

Single Degree ◽

Stability Robustness ◽

Loop Shaping ◽

And Performance ◽

Control Methodology

This paper presents a control methodology that provides transparency and stability robustness in bilateral telemanipulation systems that include a significant time delay in the communication channels. The method utilizes an adaptive Smith predictor to compensate for the time delay, and incorporates a previously published loop shaping approach to design a compensator for transparency and stability robustness of the loop. The method is experimentally demonstrated on a single degree-of-freedom telemanipulation system, and is shown to effectively provide stability and performance robustness.

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Passive Targeted Energy Transfers and Strong Modal Interactions in a Thin Plate With Strongly Nonlinear End Attachments of Different Configurations

Volume 1: 21st Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C ◽

10.1115/detc2007-34174 ◽

2007 ◽

Cited By ~ 1

Author(s):

F. Georgiades ◽

A. F. Vakakis

Keyword(s):

Wavelet Transforms ◽

Degree Of Freedom ◽

Vibration Energy ◽

Modal Interactions ◽

Single Degree Of Freedom ◽

Strongly Nonlinear ◽

Single Degree ◽

Energy Transfers ◽

Parametric Studies ◽

Underlying Mechanisms

In this paper we examine Targeted Energy Transfers (TETs) and nonlinear modal interactions occurring in a thin cantilever plate lying on an elastic foundation with strongly nonlinear lightweight attachments of different configurations. Under shock excitation of the plate we systematically study, nonlinear modal interactions and passive broadband targeted energy transfer phenomena between the plate and attachments of the following configurations: a single ungrounded, strongly (essentially) nonlinear single-degree-of-freedom (SDOF) NES; multiple SDOF attachments attached at different points of the plate; and a single multi-degree-of-freedom (MDOF) attachment with multiple essential stiffness nonlinearities. We perform parametric studies by varying the parameters and location of the attachments, in order to optimize TETs from the plate to the NES. We examine in detail the underlying mechanisms influencing TETs by means of Hilbert-Huang Transforms in combination with Wavelet Transforms. These transforms enable one to systematically study the strong modal interactions between the essentially nonlinear attachments and different plate modes. The efficacy of using this type of essentially nonlinear attachments as passive absorbers of broadband vibration energy is discussed.

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Optimization of PID controller parameters for active control of single degree of freedom structures

Challenge Journal of Structural Mechanics ◽

10.20528/cjsmec.2019.04.002 ◽

2019 ◽

Vol 5 (4) ◽

pp. 130

Author(s):

Serdar Ulusoy ◽

Sinan Melih Niğdeli ◽

Gebrail Bekdaş

Keyword(s):

Time Delay ◽

Active Control ◽

Pid Controller ◽

Structural Model ◽

Degree Of Freedom ◽

Control Force ◽

Single Degree Of Freedom ◽

Single Degree ◽

Near Fault ◽

Optimum Parameters

In active control of structures, the parameters of controllers used application must be perfectly tuned. In that case, a good vibration reduction performance can be obtained without a stability problem. During the tuning process, the limit of control force and time delay of controller system must be considered for applicable design. In the study, the optimum parameters of Proportional-Derivative-Integral (PID) type controllers that are proportional gain (K), integral time (Ti) and derivative time (Td) were optimized by using teaching learning-based optimization (TLBO). TLBO is a metaheuristic algorithm imitating the teaching and learning phases of education in classroom. The optimization was done according to the responses of the structure under a directivity pulse of near fault ground motions. In the study, time delay was considered as 20 ms and the optimum parameters of PID controller for a single degree of freedom (SDOF) structural model was found for different control force limits. The performances and feasibility of the method were evaluated by using sets of near fault earthquake records.

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A modified stochastic averaging method on single-degree-of-freedom strongly nonlinear stochastic vibrations

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2016.07.009 ◽

2016 ◽

Vol 91 ◽

pp. 469-477 ◽

Cited By ~ 4

Author(s):

Gen Ge ◽

ZePeng Li

Keyword(s):

Averaging Method ◽

Stochastic Averaging ◽

Stochastic Averaging Method ◽

Degree Of Freedom ◽

Single Degree Of Freedom ◽

Strongly Nonlinear ◽

Single Degree ◽

Stochastic Vibrations

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An Averaging Approach for Noisy Strongly Nonlinear Periodically Forced Systems

Design Engineering ◽

10.1115/imece2002-39384 ◽

2002 ◽

Author(s):

Seunggil Choi ◽

N. Sri Namachchivaya

Keyword(s):

Stochastic Averaging ◽

External Noise ◽

Degree Of Freedom ◽

Periodic Force ◽

Single Degree Of Freedom ◽

Strongly Nonlinear ◽

Single Degree ◽

Periodically Driven ◽

Statistical Measures ◽

Stochastic Bifurcations

The purpose of this work is to develop a unified approach to study the dynamics of single degree of freedom systems excited by both periodic and random perturbations. The near resonant motion of such systems is not well understood. We will study this problem in depth with the aim of discovering a common geometric structure in the phase space, and to determine the effects of noisy perturbations on the passage of trajectories through the resonance zone. We consider the noisy, periodically driven Duffing equation as a prototypical single degree of freedom system and achieve a model-reduction through stochastic averaging. Depending on the strength of the noise, reduced Markov process takes its values on a line or on graph with certain gluing conditions at the vertex of the graph. The reduced model will provide a framework for computing standard statistical measures of dynamics and stability, namely, mean exit times, probability density functions, and stochastic bifurcations. This work will also explain a counter-intuitive phenomena of stochastic resonance, in which a weak periodic force in a nonlinear system can be enhanced by the addition of external noise.

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