• Title/Summary/Keyword: Oscillator perturbation

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Perturbation method for the dynamic analysis of a bistable oscillator under slow harmonic excitation

  • Luongo, Angelo;Casciati, Sara;Zulli, Daniele
    • Smart Structures and Systems
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    • v.18 no.1
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    • pp.183-196
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    • 2016
  • In this paper a nonlinear, bistable, single degree of freedom system is considered. It consists of a Duffing oscillator externally excited by a non-resonant, harmonic force. A customized perturbation scheme is proposed to achieve an approximate expression for periodic solutions. It is based on the evaluation of the quasi-steady (slow) solution, and then on a variable change followed by two perturbation steps which aim to capture the fast, decaying contribution of the response. The reconstructed solution, given by the sum of the slow and fast contributions, is in a good agreement with the one obtained by numerical integration.

The analytic solution for parametrically excited oscillators of complex variable in nonlinear dynamic systems under harmonic loading

  • Bayat, Mahdi;Bayat, Mahmoud;Pakar, Iman
    • Steel and Composite Structures
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    • v.17 no.1
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    • pp.123-131
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    • 2014
  • In this paper we have considered the vibration of parametrically excited oscillator with strong cubic positive nonlinearity of complex variable in nonlinear dynamic systems with forcing based on Mathieu-Duffing equation. A new analytical approach called homotopy perturbation has been utilized to obtain the analytical solution for the problem. Runge-Kutta's algorithm is also presented as our numerical solution. Some comparisons between the results obtained by the homotopy perturbation method and Runge-Kutta algorithm are shown to show the accuracy of the proposed method. In has been indicated that the homotopy perturbation shows an excellent approximations comparing the numerical one.

surface acoustic wave oscillator hymidity sensor using hexafluoropropene plasma thin film (헥사플루오르프로펜 플라즈마박막을 이용한 표면탄성파발진기 습도센서)

  • 박남천;서은덕
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 1992.05a
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    • pp.144-146
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    • 1992
  • Surface acoustic wave(SAW) oscillator offers many attractive features for application to vapor sensors. The perturbation of SAW velocity by the hexafluoropropence plasma polymer thin film has been studied for relative humidity sensing. adsorption of moisture produces rapid aid changes in the properties of the film, resulting in a change in the velocity of surface acoustic waves and, hence, in the frequency of one SAW oscillator. The device used in our experiments have 55 MHZ SAW oscillator fabricated on a LiNbO substrate.

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A Variant of the Brillouin-Wigner Perturbation Theory with Epstein-Nesbet Partitioning

  • Lee, Sangyoub;Choi, Cheol Ho;Kim, Eunji;Choi, Young Kyun
    • Bulletin of the Korean Chemical Society
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    • v.34 no.11
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    • pp.3279-3283
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    • 2013
  • We present an elementary pedagogical derivation of the Brillouin-Wigner and the Rayleigh-Schr$\ddot{o}$dinger perturbation theories with Epstein-Nesbet partitioning. A variant of the Brillouin-Wigner perturbation theory is also introduced, which can be easily extended to the quasi-degenerate case. A main advantage of the new theory is that the computing time required for obtaining the successive higher-order results is minimal after the third-order calculation. We illustrate the accuracy of the new perturbation theory for some simple model systems like the perturbed harmonic oscillator and the particle in a box.

Analytical Proof of Equivalence of ISF, and Floquet Vector-Based Oscillator Phase Noise Theories (ISF와 Floquet 벡터에 기초한 발진기 위상잡음 이론의 등가성에 대한 해석적 증명)

  • Jeon, Man-Young
    • Journal of IKEEE
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    • v.17 no.4
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    • pp.559-563
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    • 2013
  • This paper analytically proves the equivalence between two main oscillator phase noise theories, which are based on the ISF, and Floquet vector, respectively. For this purpose, this study obtains the power spectral density matrix from the ISF-based phase noise theory. As a result, one can prove that the power spectral density matrix obtained from the ISF-based phase noise theory is essentially equivalent to the power spectral density matrix presented by the Floquet vector-based phase noise theory, which manifests the equivalence of the two main theories. This study is intended to provide deeper insight into the relations between the two main theories.

Practical formula for determining peak acceleration of footbridge under walking considering human-structure interaction

  • Cao, Liang;Zhou, Hailei;Chen, Y. Frank
    • Structural Engineering and Mechanics
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    • v.83 no.6
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    • pp.729-744
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    • 2022
  • In this paper, an analytical formulation is proposed to predict the vertical vibration response due to the pedestrian walking on a footbridge considering the human-structure interaction, where the footbridge and pedestrian are represented by the Euler beam and linear oscillator model, respectively. The derived coupled equation of motion is a nonlinear fourth-order partial differential equation. An uncoupled solution strategy based on the combined weighted residual and perturbation method) is proposed to reduce the tedious computation, which allows the separate integration between the bridge and pedestrian subsystems. The theoretical study demonstrates that the pedestrian subsystem can be treated as a structural system with added mass, damping, and stiffness. The analysis procedure is then applied to a case study under the conditions of single pedestrian and multi pedestrians, and the results are validated and compared numerically. For convenient vibration design of a footbridge, the simplified peak acceleration formula and the idea of decoupling problem are thus proposed.

Analysis of the nonlinear oscillator using ampifiers with arctangent funtional characeriatics. (Arctangent특성의 증폭기를 사용한 비선발진기의 해석)

  • 김수중;홍재근
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.13 no.4
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    • pp.18-23
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    • 1976
  • We have obtained the solution of van der Pol's equation characterized by an arctangent nonlinearity, using the perturbation method by writing periodicity conditions: $$X^{(n)}(2{\pi})-X^{(n)}(0)=0$$ $$X^{(n)'}(2{\pi})-X^{(n)'}(0)=0 (n=0,1,2......)$$ together with the starting condition: $$X^{(n)}(\frac{\pi}{2})=0,\;X^{(n)}'(\frac{\pi}{2})=-R^{(n)}$$. Our results agree with Liapunov's theorem and our calculated value is more similar to Murata's measured value than Murata's calculated value.

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Dynamics and instability of the Karman wake mode induced by periodic forcing

  • Mureithi, Njuki W.
    • Wind and Structures
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    • v.7 no.4
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    • pp.265-280
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    • 2004
  • This paper presents some fundamental results on the dynamics of the periodic Karman wake behind a circular cylinder. The wake is treated like a dynamical system. External forcing is then introduced and its effect investigated. The main result obtained is the following. Perturbation of the wake, by controlled cylinder oscillations in the flow direction at a frequency equal to the Karman vortex shedding frequency, leads to instability of the Karman vortex structure. The resulting wake structure oscillates at half the original Karman vortex shedding frequency. For higher frequency excitation the primary pattern involves symmetry breaking of the initially shed symmetric vortex pairs. The Karman shedding phenomenon can be modeled by a nonlinear oscillator. The symmetrical flow perturbations resulting from the periodic cylinder excitation can also be similarly represented by a nonlinear oscillator. The oscillators represent two flow modes. By considering these two nonlinear oscillators, one having inline shedding symmetry and the other having the Karman wake spatio-temporal symmetry, the possible symmetries of subsequent flow perturbations resulting from the modal interaction are determined. A theoretical analysis based on symmetry (group) theory is presented. The analysis confirms the occurrence of a period-doubling instability, which is responsible for the frequency halving phenomenon observed in the experiments. Finally it is remarked that the present findings have important implications for vortex shedding control. Perturbations in the inflow direction introduce 'control' of the Karman wake by inducing a bifurcation which forces the transfer of energy to a lower frequency which is far from the original Karman frequency.

Nonlinear Tuned Mass Damper for self-excited oscillations

  • Gattulli, Vincenzo;Di Fabio, Franco;Luongo, Angelo
    • Wind and Structures
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    • v.7 no.4
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    • pp.251-264
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    • 2004
  • The effects of a class of nonlinear Tuned Mass Dampers on the aeroelastic behavior of SDOF systems are investigated. Unlike classical linear TMDs, nonlinear constitutive laws of the internal damping acting between the primary oscillator and the TMD are considered, while the elastic properties are keept linear. The perturbative Multiple Scale Method is applied to derive a set of bifurcation equations in the amplitude and phase and a parametric analysis is performed to describe the postcritical scenario of the system. Both cubic- and van der Pol-type dampings are considered and the dependence of the limit-cycle amplitudes on the system parameters is studied. These new results, compared with the previously obtained bifurcation scenario of a SDOF aeroelastic oscillator equipped with a linear TMD, show a detrimental effect on the maximum limit-cycle amplitude reduction of the nonlinear TMD. However, the analyses evidence that in the parameter region away from the perfect tuning condition the nonlinear connection can be used to tune the system with an enhancement of the limit-cycle amplitude reduction.

Optimal extended homotopy analysis method for Multi-Degree-of-Freedom nonlinear dynamical systems and its application

  • Qian, Y.H.;Zhang, Y.F.
    • Structural Engineering and Mechanics
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    • v.61 no.1
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    • pp.105-116
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    • 2017
  • In this paper, the optimal extended homotopy analysis method (OEHAM) is introduced to deal with the damped Duffing resonator driven by a van der Pol oscillator, which can be described as a complex Multi-Degree-of-Freedom (MDOF) nonlinear coupling system. Ecumenically, the exact solutions of the MDOF nonlinear coupling systems are difficult to be obtained, thus the development of analytical approximation becomes an effective and meaningful approach to analyze these systems. Compared with traditional perturbation methods, HAM is more valid and available, and has been widely used for nonlinear problems in recent years. Hence, the method will be chosen to study the system in this article. In order to acquire more suitable solutions, we put forward HAM to the OEHAM. For the sake of verifying the accuracy of the above method, a series of comparisons are introduced between the results received by the OEHAM and the numerical integration method. The results in this article demonstrate that the OEHAM is an effective and robust technique for MDOF nonlinear coupling systems. Besides, the presented methods can also be broadly used for various strongly nonlinear MDOF dynamical systems.