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1

Steady state vibration of the periodically forced and damped pure nonlinear two-degrees-of-freedom oscillator

Cveticanin Livija, Zukovic Miodrag, Cveticanin Dragan

Journal of Theoretical and Applied Mechanics

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2019

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Vol. 57 nr 2

445--460

EN

In the paper, a pure nonlinear and damped two-mass oscillator excited with a periodical force is considered. The oscillator is modelled with a system of two coupled second order nonlinear and non-homogenous equations. Using the model, two problems are investigated: one, identification of the excitation force for the known vibrating response of the system, and the second, determination of vibrations of the system excited with the known periodical force. Using the steady-state motion of the nonlinear oscillator, a method for identification of the excitation force is developed. For the pure nonlinear oscillator, it is obtained that the forcing function has the form of the Ateb function. However, if the excitation force is known, the procedure for computing the steady-state vibration of the system is introduced. The solution corresponds to steady-state vibrations of the free oscillator, but the amplitude and phase are assumed to be time variable. The averaged solutions are obtained for the pure nonlinear oscillator with an additional linear elastic force and for the van der Pol oscillator. Analytically obtained solutions are compared with numerical ones. They are in good agreement.

2

Analysis and design of CMOS coupled multivibrators

Casaleiro J., Lopes H. F., Oliveira L. B., Filanovsky I.

International Journal of Microelectronics and Computer Science

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2010

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Vol. 1, nr 3

249-256

EN

In this paper a wideband MOS quadrature oscillator constituted by two multivibrators is presented. Two different forms of coupling, named here as soft and hard, are investigated. Simulations are performed in a 0.13 žm CMOS technology to obtain the tuning range, the synchronization transients, and the influence of mismatches in timing capacitors and charging currents on synchronization. It is found that hard coupling reduces the quadrature error (about 1°, with 5% mismatches in timing capacitors and charging currents) and results in a low phase-noise (about 2 dB improvement) with respect to soft coupling. Either a single multivibrator or coupled multivibrators can be locked to an external synchronizing harmonic frequency, and the locking range is investigated by simulations. The simulations are done for oscillators covering the WTMS frequency bands.

3

Second order optimality conditions for bang-bang control problems

Maurer H., Osmolovskii N. P.

Control and Cybernetics

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2003

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Vol. 32, no 3

555-584

EN

Second order necessary and sufficient optimality conditions for bang-bang control problems have been studied in Milyutin, Osmolovskii (1998). These conditions amount to testing the positive (semi-)definiteness of a quadratic form on a critical cone. The assumptions are appropriate for numerical verification only in some special cases. In this paper, we study various transformations of the quadratic form and the critical cone which will be tailored to different types of control problems in practice. In particular, by means of a solution to a linear matrix differential equation, the quadratic form can be converted to perfect squares. We demonstrate by three practical examples that the conditions obtained can be verified numerically.