Numerical optimisation of a classical stochastic system for targeted energy transfer

The paper studies stochastic dynamics of a two-degree-of-freedom system,where a primary linear system is connected to a nonlinear energy sink with cubic stiffness nonlinearity and viscous damping.While the primary mass is subjected to a zero-mean Gaussian white noise excitation,the main objective of this study is to maximise the efficiency of the targeted energy transfer in the system.A surrogate optimisation algorithm is proposed for this purpose and adopted for the stochastic framework.The optimisations are conducted separately for the nonlinear stiffness coefficient alone as well as for both the nonlinear stiffness and damping coefficients together.Three different optimisation cost functions,based on either energy of the system’s components or the dissipated energy,are considered.The results demonstrate some clear trends in values of the nonlinear energy sink coefficients and show the effect of different cost functions on the optimal values of the nonlinear system’s coefficients.

Fractional nonlinear energy sinks

The cubic or third-power(TP)nonlinear energy sink(NES)has been proven to be an effective method for vibration suppression,owing to the occurrence of targeted energy transfer(TET).However,TET is unable to be triggered by the low initial energy input,and thus the TP NES would get failed under low-amplitude vibration.To resolve this issue,a new type of NES with fractional nonlinearity,e.g.,one-third-power(OTP)nonlinearity,is proposed.The dynamic behaviors of a linear oscillator(LO)with an OTP NES are investigated numerically,and then both the TET feature and the vibration attenuation performance are evaluated.Moreover,an analogy circuit is established,and the circuit simulations are carried out to verify the design concept of the OTP NES.It is found that the threshold for TET of the OTP NES is two orders of magnitude smaller than that of the TP NES.The parametric analysis shows that a heavier mass or a lower stiffness coefficient of the NES is beneficial to the occurrence of TET in the OTP NES system.Additionally,significant energy transfer is usually accompanied with efficient energy dissipation.Consequently,the OTP NES can realize TET under low initial input energy,which should be a promising approach for micro-vibration suppression.

Response regimes of narrow-band stochastic excited linear oscillator coupled to nonlinear energy sink

This paper draws attention to the issue of the vibration absorption of nonlinear mechani- cal system coupled to nonlinear energy sink （NES） under the impact of the narrow band stochastic excitation. Firstly, based on the complex-averaging method and frequency detuning methodology, response regimes of oscillators have been researched under the linear impact of coupling a nonlinear attachment with less relativistic mass and an external sinusoidal forcing, of which results turn out that the quasi-periodicity response regime of system which occurs when the external excitation amplitude exceeds the critical values will be the precondition of the targeted energy transfer. Secondly, basing on the path integration method, vibration suppression of NES has been researched when it is affected by a main oscillator with a narrow band stochastic force in the form of trigono- metric functions, of which results show that response regimes are affected by the amplitude of stochastic excitation and the disturbance strength. Finally, all these conclusions have been approved by the numerical verification and coincided with the theoretical analysis; meanwhile, after the com- paring analysis with the optimal linear absorber, it turns out that the NES which is affected by the narrow band stochastic force could also suppress the vibration of system with a better effect.

利用强非线性减振器的模态能量再分配缓解大型结构的冲击响应

采用一种轻型几何非线性附件,强非线性减振器(SNA),以抑制线性大型九层结构的冲击响应.SNA的作用不仅是耗散能量,而且重新分配结构模态之间的冲击能量.本文研究单自由度(SDOF)和双自由度(Two-DOF)的SNAs.冲击能量再分配的定量结果表明,在强几何非线性的情况下,这种结构可以实现从低频到高频的非线性单向能量传递.具体而言,在锁定SNA、单自由度SNA和双自由度SNA的情况下,较高结构模态耗散的冲击能量百分比分别为0.08%,0.43%和30.04%.结果表明,与单自由度SNA相比,双自由度SNA能够将更多的能量快速散射到更高的频域,从而更快地降低主结构的冲击响应.还研究了在不同冲击强度下SNA性能的鲁棒性,其中双自由度SNA在从低频到高频散射冲击能量时表现出更强的鲁棒性.最后,采用等效阻尼技术来验证和量化主结构中模态能量的重新分布,并讨论这种新型被动减震方法的潜在应用.