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Delay-controlled primary and stochastic resonances of the SD oscillator with stiffness nonlinearities

机译：具有刚度非线性的SD振荡器的延迟控制的主共振和随机共振

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摘要

This work presents analytical studies of the stiffness nonlinearities SD (smooth and discontinuous) oscillator under displacement and velocity feedback control with a time delay. The SD oscillator can capture the qualitative characteristics of quasi-zero-stiffness and negative-stiffness. We focus mainly on the primary resonance of the quasi-zero-stiffness SD oscillator and the stochastic resonance (SR) of the negative-stiffness SD oscillator. Using the averaging method, we have been analyzed the amplitude response of the quasi-zero-stiffness SD oscillator. In this regard, the optimum time delay for changing the control intensity according to the optimization standard proposed can be obtained. For the optimum time delay, increasing the displacement feedback intensity is advantageous to suppress the vibrations in resonant regime where vibration isolation is needed, however, increasing the velocity feedback intensity is advantageous to strengthen the vibrations. Moreover, the effects of time-delayed feedback on the SR of the negative-stiffness SD oscillator are investigated under harmonic forcing and Gaussian white noise, based on the Langevin and Fokker-Planck approaches. The time-delayed feedback can enhance the SR phenomenon where vibrational energy harvesting is needed. This paper established the relationship between the parameters and vibration properties of a stiffness nonlinearities SD which provides the guidance for optimizing time-delayed control for vibration isolation and vibrational energy harvesting of the nonlinear systems.
机译：这项工作提出了具有时滞的位移和速度反馈控制下的刚度非线性SD（光滑和不连续）振荡器的分析研究。 SD振荡器可以捕获准零刚度和负刚度的定性特征。我们主要关注准零刚度SD振荡器的主共振和负刚度SD振荡器的随机共振（SR）。使用平均方法，我们已经分析了准零刚度SD振荡器的幅度响应。在这方面，可以获得用于根据所提出的优化标准改变控制强度的最佳时间延迟。对于最佳时间延迟，增加位移反馈强度有利于抑制需要隔振的共振状态下的振动，但是，增加速度反馈强度有利于增强振动。此外，基于Langevin和Fokker-Planck方法，研究了在谐波强迫和高斯白噪声下，时滞反馈对负刚度SD振荡器SR的影响。延迟反馈可以增强需要振动能量收集的SR现象。本文建立了刚度非线性SD的参数与振动特性之间的关系，为优化非线性系统的隔振和振动能量采集的时滞控制提供了指导。

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