Nonlinear complex response of a parametrically excited tuning fork

Lee, Yongsik; Pai, P. Frank; Feng, Z. C.

doi:10.1016/j.ymssp.2007.11.015

Cited by 10 publications

(4 citation statements)

References 20 publications

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“…The other system parameters are obtained as x0 ¼ 3:1712, P ¼ À0:0445, g ¼ 27:5099 and a ¼ 6:6884 using Eqs. ( 18)- (22). For the frequency range considered g Ã MVA is negative, leading to a softening behaviour.…”

Section: Effect Of Tip Massmentioning

confidence: 97%

“…Parametrically excited cantilever beams (PECBs) have been studied extensively in various applications to investigate the dynamic behaviour of parametrically excited systems [17][18][19][20][21][22][23]. Two different aspects of these systems have been of interest to researchers: avoiding or controlling the unwanted effects due to parametric excitation and exploiting parametric excitation, particularly parametric resonance, in these systems to increase their performance.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear dynamics of parametrically excited cantilever beams with a tip mass considering nonlinear inertia and Duffing-type nonlinearity

2023

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The response of a parametrically excited cantilever beam (PECB) with a tip mass is investigated in this paper. The paper is mainly focused on accurate prediction of the response of the system, in particular, its hardening and softening characteristics when linear damping is considered. First, the method of varying amplitudes (MVA) and the method of multiple scales (MMS) are employed. It is shown that both Duffing nonlinearity and nonlinear inertia terms govern the hardening or softening behaviour of a PECB. MVA results show that for frequencies around the principal parametric resonance, the term containing a linear combination of nonlinear inertia and Duffing nonlinearity in the frequency response equation can tend to zero, resulting in an exponential growth of the vibrations, and results are validated by numerical results obtained from direct integration (DI) of the equation of motion, while the MMS fails to predict this critical frequency. A criterion for determining the hardening and softening characteristics of PECBs is developed and presented using the MVA. To verify the results, experimental measurements for a PECB with a tip mass are presented, showing good agreement with analytical and numerical results. Furthermore, it is demonstrated that the mass added at the cantilever tip can change the system characteristics, enhancing the softening behaviour of the PECB. It is shown that, within the frequency range considered, increasing the value of the tip mass decreases the amplitude response of the system and broadens the frequency range in which a stable response can exist.

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Section: Effect Of Tip Massmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of parametrically excited cantilever beams with a tip mass considering nonlinear inertia and Duffing-type nonlinearity

2023

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“…Here, the investigation was based the behavior for the macro system. The (TFB) is modeled by two inverted pendulums of motion in the opposite directions hung by the same rods of vertical and horizontal motion according to suggestions by [28,29].Recently, the researcher in [29] investigate the interaction of the dynamics of the electro-shaker with the gyroscope, demonstrated that under certain parameters the system can exhibit complex dynamic behavior such as chaotic motion [30], analyze the influence on the electrical charge, between the cantilever beam and the wide electrode by using numerical methods. For the analysis, the authors used the mathematical model of a Duffing oscillator, under electrostatic effects, with variable capacitor, investigating the dynamic interaction, between a micro machined rate gyroscope and variable force actuators.…”

Section: Nis Emergent Problemsmentioning

confidence: 99%

Dynamics behaviour of an elastic non-ideal (NIS) portal frame, including fractional nonlinearities

Balthazar

Brasil

Félix

et al. 2016

J. Phys.: Conf. Ser.

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Abstract. This paper overviews recent developments on some problems related to elastic structures, such as portal frames, taking into account the full interactions of the vibrating systems, with an energy source of limited power supply (small motors, electro-mechanical shakers). We include a discussion on fractional (rational) damping and stiffness effects on the adopted modelling. This was a plenary lecture, delivered in the event titled: Mechanics of Slender Structures, organized in Northampton, England from 21-22, September 2015. IntroductionThis paper shows a series of problems related to nonlinear dynamics and control, correlated to Electromechanical Systems [1] using an elastic support. Here, we analyzed such systems those fall into three groups: the conventional MACRO, MEMS and NEMS electro-mechanical systems, taking into account the existence of a full interaction between mechanical and electrical field quantities. The aim of this paper is to describe a large number of phenomena caused by the action of vibrations on nonlinear electro-mechanical systems and the energy source supply to it. This paper gives a general description of this class of phenomena which has been discussed in recent years.

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“…Lee [2] has demonstrated the response of a tuning fork beam subject to parametric excitation in an experiment. He has shown that parametric excitation can be taken advantage of, in order to increase the sensitivity of the tuning fork gyroscopes [3]. Vibrations of a parametrically excited system with ideal and non-ideal energy sources have been investigated [4,5].…”

Section: Introductionmentioning

confidence: 99%

Periodic and Chaotic Response of a Macro-Scale Tuning Fork Gyroscope

Tehrani

Silveira

Balthazar

2016

AMM

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In this paper, the dynamic behaviour of a macro-scale tuning fork gyroscope is presented. The gyroscope consists of two inverted pendulums on a suspension mass. The suspension mass is subjected to force excitation generated by an electromagnetic shaker. The dynamics of the shaker are included in the analysis. It is shown that the system is a parametrically excited system. Parametric excitation can lead to vibration in the horizontal motion of the suspension mass, when the two pendulums are in phase. The problem is particularly interesting for energy harvesting. Due to the interaction between the system’s degrees of freedom, the energy is transferred from vertical (base excitation) to horizontal direction. Initial parametric studies are carried out to analyse the dynamic behaviour of the system by varying the initial conditions, base excitation frequency and amplitude. It is demonstrated that under certain parameters the system can exhibit complex dynamic behaviour such as chaotic motion.

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Nonlinear complex response of a parametrically excited tuning fork

Cited by 10 publications

References 20 publications

Nonlinear dynamics of parametrically excited cantilever beams with a tip mass considering nonlinear inertia and Duffing-type nonlinearity

Nonlinear dynamics of parametrically excited cantilever beams with a tip mass considering nonlinear inertia and Duffing-type nonlinearity

Dynamics behaviour of an elastic non-ideal (NIS) portal frame, including fractional nonlinearities

Periodic and Chaotic Response of a Macro-Scale Tuning Fork Gyroscope

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