An experimental investigation into the dynamics of a string

Molteno, T. C. A.; Tufillaro, Nicholas B.

doi:10.1119/1.1764557

Cited by 40 publications

(27 citation statements)

References 32 publications

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“…with Indeed, Eqs. (10) and (11) show that the equilibria of the self-sustained Duffing oscillator are stable for any value of the phase shift φ 0 , i.e. along the whole resonance curve.…”

Section: Stability Under Phase-shift Controlmentioning

confidence: 96%

“…Much more recently, the Duffing oscillator acquired relevance in the realm of microtechnologies [7,8,9]. It has since long been known that the Duffing equation stands for the leading nonlinear correction to the oscillations of an elastic beam clamped at its two ends [10,11]. Minute vibrating silica beams, in turn, have been proposed as pacemakers for the design of time-keeping devices at the microscale, where traditional quartz crystals are difficult to build and operate [7].…”

Section: Introductionmentioning

confidence: 99%

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Duffing revisited: phase-shift control and internal resonance in self-sustained oscillators

Arroyo

Zanette

2016

Eur. Phys. J. B

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We address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, have intrinsic significance to the field of nonlinear oscillating systems.First, we study the stability of periodic motion when the phase shift between the external force and the oscillation is controlled -contrary to the standard case, where the control parameter is the frequency of the force. Phase-shift control is the operational configuration under which self-sustained oscillators -and, in par-

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“…with Indeed, Eqs. (10) and (11) show that the equilibria of the self-sustained Duffing oscillator are stable for any value of the phase shift φ 0 , i.e. along the whole resonance curve.…”

Section: Stability Under Phase-shift Controlmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Duffing revisited: phase-shift control and internal resonance in self-sustained oscillators

Arroyo

Zanette

2016

Eur. Phys. J. B

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“…Oplinger (1960) [20] compared numerical and experimental results of frequency response. Molteno and Tufillaro (2004) [15] checked qualitatively the agreement between the analytical results obtained via the truncated Kirchhoff string equation and the experimental results. The various numerical schemes, such as the Galerkin method [6] and finite difference methods [2,14,21], were developed to simulate the nonlinear Kirchhoff string model.…”

Section: Introductionmentioning

confidence: 88%

Two nonlinear models of a transversely vibrating string

Chen

Ding²

2007

Arch Appl Mech

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Modeling transverse vibration of nonlinear strings is investigated via numerical solutions of partialdifferential equations and an integro-partial-differential equation. By averaging the tension along the deflected string, the classic nonlinear model of a transversely vibrating string, Kirchhoff's equation, is derived from another nonlinear model, a partial-differential equation. The partial-differential equation is obtained via neglecting longitudinal terms in a governing equation for coupled planar vibration. The finite difference schemes are developed to solve numerically those equations. An index is proposed to compare the transverse responses calculated from the two models with the transverse component calculated from the coupled equation. A steel string and a rubber string are treated as examples to demonstrate the differences between the two models of transverse vibration and their deviation from the full model of coupled vibration. The numerical results indicate that the differences increase with the amplitude of vibration. Both models yield satisfactory results of almost the same precision for vibration of small amplitudes. For large amplitudes, the Kirchhoff equation gives better results.

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“…In 1990, Molteno and Tufillaro [15] carried out a simple experiment that explained the torus doubling transition to chaos in an axially travelling string. In addition, Molteno and Tufillaro [16] studied the nonlinear characteristics of a sinusoidally forced string and observed more complex phenomena not present in the solution of the equations of motion. However, as for the relationship between the transverse nonlinear vibration, the tension and the travelling speed of the belt, little experimental work has been reported.…”

Section: Introductionmentioning

confidence: 99%

Experimental investigation of the transverse nonlinear vibration of an axially travelling belt

Chen¹,

Lin²,

Ferguson³

2016

J. vibroeng.

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Abstract. From an experimental perspective, this paper investigates the transverse vibration present in an axially travelling belt undergoing uniform motion with constant travelling speed. Application of a control of the belt speed, using Matlab, a Code Composer Studio (CCS) and the available complementary embedded tools, a stepper motor DSP control was obtained automatically by using a graphical method to establish the stepper motor movement models within a Simulink environment. By changing the tension of the belt and the rotational speed of the stepper motor, the natural frequency of the travelling belt was studied. The response waveforms, spectral content and phase diagrams were obtained by measuring the transverse vibration displacement under different conditions. A nonlinear model for the experimental moving belt system was developed and numerical solutions calculated. Subsequently, the nonlinear response behavior of this model were validated by the results of the experiment. It was shown that there were many scenarios for which the system can exhibit periodic motion, chaotic motion and beat frequency phenomena to be present and measured in the vibration of the axially travelling belt.

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An experimental investigation into the dynamics of a string

Cited by 40 publications

References 32 publications

Duffing revisited: phase-shift control and internal resonance in self-sustained oscillators

Duffing revisited: phase-shift control and internal resonance in self-sustained oscillators

Two nonlinear models of a transversely vibrating string

Experimental investigation of the transverse nonlinear vibration of an axially travelling belt

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