Rotating vector solving method applied for nonlinear oscillator

Significant number of procedures for solving of the finite degree-of-freedom forced nonlinear oscillator are developed. For all of them it is common that they are based on the exact solution of the corresponding linear oscillator. For technical reasons, the aim of this paper is to develop a simpler solving procedure. The rotating vector method, developed for the linear oscillator, is adopted for solving of the nonlinear finite degree-of-freedom oscillator. The solution is assumed in the form of trigonometric functions. Assuming that the nonlinearity is small all terms of the series expansion of the function higher than the first are omitted. The rotating vectors for each mass are presented in the complex plane. In the paper, the suggested rotating vector procedure is applied for solving of a three-degree-of-freedom periodically excited oscillator. The influence of the nonlinear stiffness of the flexible elastic beam, excited with a periodical force, on the resonant properties of the system in whole is investigated. It is obtained that the influence of nonlinearity on the amplitude and phase of vibration is more significant for smaller values of the excitation frequency than for higher ones.

Light-powered Self-excited Coupled Oscillators in Huygens ’ Synchrony

Self-excited motions have the advantages of actively collecting energy from the environment, autonomy, making equipment portable and so on, and a great number of self-excited motion modes have recently been developed which greatly expand the application in active machines. However, there are few studies on the synchronization and group behaviors of self-excited coupled oscillators, which are common in nature. Based on light-powered self-excited oscillator composed of liquid crystal elastomer (LCE) bars, the synchronization of two self-excited coupled oscillators is theoretically studied. Numerical calculations show that self-excited oscillations of the system have two synchronization modes: in-phase mode and anti-phase mode. The time histories of various quantities are calculated to elucidate the mechanism of self-excited oscillation and synchronization. Furthermore, the effects of initial conditions and interaction on the two synchronization modes of the self-excited oscillation are investigated extensively. For strong interactions, the system always develops into in-phase synchronization mode, while for weak interaction, the system will evolve into anti-phase synchronization mode. Meanwhile, the initial condition generally does not affect the synchronization mode and its amplitude. This work will deepen people's understanding of synchronization behaviors of self-excited coupled oscillators, and provide promising applications in energy harvesting, signal monitoring, soft robotics and medical equipment.

Amplification of useful vibration using on-off damping

This paper points out how much useful vibration can be extracted from a base-excited oscillator, which is controlled by the on-off electrical damping. We study the class of on-off electrical damping controller, which switches the damping level from high to low and back at fixed times every quarter of period. The problem reduces to the maximization of a single-variable function. This result can open the new direction to amplify the useful vibration using controllable dampings.

Оn the structure of the device for measuring residual stresses

Тhe article deals with a relevant problem – improvement of the accuracy of measurement of residual stresses in the elements of machines and structures with the use of attachable transducers.Analysis of flexible current-vortex transducers designed in the form of a single-layer coil has been performed. To solve the problem, the method of eddy currents is proposed, which can be used to set the calibration value of the magnetic resistance of the air gap between the transducer and the object.This method implementation based on the scheme of the oscillator with a reactive circuit has been demonstrated. The design of the residual stress measurement unit in the form of «capacitive three-point» self-excited oscillator has been substantiated. The structure of the device for measuring stresses has been proposed. The core element of the calibration value setting unit is a self-excited oscillator with a reactive frequency oscillating circuit, the inductance thereof been the excitation coil of the current-vortex transducer.Magnetic resistance of the gap is measured by moving the transducer vertically versus the surface of the object in the measurement area. The circuit of the proposed device consists of a block for setting the gap magnetic resistance, eddy-current transducer, electron-counting frequency meter, and residual stress measuring unit.