Asymptotic motions and stability of the elastoplastic oscillator studied via maps

Capecchi, Danilo

doi:10.1016/0020-7683(93)90115-n

Cited by 18 publications

(5 citation statements)

References 10 publications

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“…As already shown in [11] for a one DOF oscillator, more efficient algorithms are obtained if the constitutive relations of nonlinear springs are represented in incremental form. This representation turns out to be very simple in the specific case in which the nonlinear springs are elastoplastic.…”

Section: General Aspectsmentioning

confidence: 89%

“…In [9], for instance, it is shown that results obtained in [5] for one DOF oscillator, by assuming four branches per cycle, are in some cases not correct. Many difficulties associated with the multivaluedness of hysteretic force can be overcome by adding dimensions to the state variables space where the restoring force can be formulated in incremental form by means of only ordinary functions [10,11].…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic response of a two DOF elastoplastic system under harmonic excitation. Internal resonance case

Capecchi

Vestroni

1995

Nonlinear Dyn

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The study of a two DOF elastoplastic system is formulated in a suitable phase space, velocity and force, in which an originally multi-valued restoring force is represented by a proper function. The asymptotic response can thus be studied using the Poincar6 map concept and avoiding approximate analytical techniques. On account of the peculiarity of this hysteretic system, which has a well-defined yielding point, its dynamics is studied in a reduced dimension phase space using an efficient numerical algorithm. It is shown that the asymptotic response is always periodic with the period of the driven frequency and is always stable. Thus the response of the oscillator is described by its frequency response curves at various intensities of the excitation. The results presented refer to a system with two linear frequencies in a ratio of 1 : 3. The response is highly complex with numerous peaks corresponding to higher harmonics. The effect of coupling in conditions of internal resonance is a strong modification of the frequency response curves and of the oscillation shape of the structure.

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Section: General Aspectsmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Asymptotic response of a two DOF elastoplastic system under harmonic excitation. Internal resonance case

Capecchi

Vestroni

1995

Nonlinear Dyn

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“…Whenever the magnitude of the force on the spring reaches a predefined threshold, the joints slide and the force remains constant. The response of the EPO (and its generalizations) to both harmonic forcing [28][29][30][31][32][33][34][35][36][37][38][39][40][41] and random forcing [42][43][44][45][46][47][48][49][50][51][52] has been extensively studied before. Figure 5 shows a possible force-displacement response for the asymmetric EPO, starting at the equilibrium position at x = 0.…”

Section: Analysis Of the Dynamics Of Rotationmentioning

confidence: 99%

Sustained rotation in a vibrated disk with asymmetric supports

Peraza‐Mues

Moukarzel

2019

J. Stat. Mech.

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A single frictional elastic disk, supported against gravity by two others, rotates steadily when the supports are vibrated and the system is tilted with respect to gravity. Rotation is here studied using molecular dynamics simulations, and a detailed analysis of the dynamics of the system is made. The origin of the observed rotational ratcheting is discussed by considering simplified situations analytically. This shows that the sense of rotation is not fixed by the tilt but depends on the details of the excitation as well.

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“…This approach follows the work on nonsmooth dynamical systems of Shaw & Holmes [3], for single degree of freedom systems. Capecchi [4] has studied the elastoplastic oscillator using a nonsmooth mapping approach. Capecchi and others [5,6,7] have extended this approach to two degree of freedom hysteretic oscillators.…”

Section: Introductionmentioning

confidence: 99%

“…Then in section 3 we consider the bifurcation diagrams and phase portraits for the asymmetric oscillator. Examples of chaotic motions are considered using a discontinuity crossing map [2,4]. Then we consider the regions of periodic and chaotic motion in a two dimensional parameter space of forcing amplitude and forcing frequency.…”

Section: Introductionmentioning

confidence: 99%