Periodic Response of Yielding Oscillators

DebChaudhury, Amitabha

doi:10.1061/(asce)0733-9399(1985)111:8(977)

Cited by 13 publications

(2 citation statements)

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“…The base to of Pro, which because of the periodicity of the excitation varies in [0, T], is instead unknown. As a consequence of the overdeterminate nature of the fixed point equations, being n + m the relations and r < n + m the unknowns, the solution is obtained as a minimum problem defined by the objective function: l(to,pP) = IlP~o(pP) -p011 (7) with p to indicate that p has p + 1 known components.…”

Section: The Poincari~ Map Techniquementioning

confidence: 99%

“…Bilinear and Ramberg-Osgood restoring forces have been studied in [3][4][5][6][7][8][9]; a softening frequency-amplitude dependence and the existence of unbounded resonance above a certain level of excitation have been found. The frequency response curves obtained were always single-valued and stable, suggesting that this is a result of hysteresis and excluding the possibility that these systems could produce the variety of phenomena found in nonlinear elastic models.…”

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: The Poincari~ Map Techniquementioning

confidence: 99%