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.

A novel method based on entransy theory for setting energy targets of heat exchanger network

A T-Q diagram based on entransy theory is applied to graphically and quantitatively describe the irreversibility of the heat transfer processes.The hot and cold composite curves can be obtained in the T-Q diagram.The entransy recovery and entransy dissipation that are affected by temperature differences can be obtained through the shaded area under the composite curves.The method for setting the energy target of the HENs in T-Q diagram based on entransy theory is proposed.A case study of the diesel oil hydrogenation unit is used to illustrate the application of the method.The results show that three different heat transfer temperature differences is 10 K,15 K and 20 K,and the entransy recovery is 5.498×10~7k W·K,5.377×10~7k W·K,5.257×10~7k W·K,respectively.And the entransy transfer efficiency is 92.29%,91.63%,90.99%.Thus,the energy-saving potential of the HENs is obtained by setting the energy target based on the entransy transfer efficiency.

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.

Shock response mitigation of a large-scale structure by modal energy redistribution facilitated by a strongly nonlinear absorber

A lightweight geometrically nonlinear attachment,the strongly nonlinear absorber(SNA),is adopted to suppress the shock response of a linear,large-scale nine-story structure.The role of the SNA is not only to dissipate but also to redistribute the shock energy among the modes of the structure.In this study,single-and two-degree-of-freedom(SDOF and Two-DOF)SNAs are investigated.The quantitative results for shock energy redistribution indicate that with strong geometric nonlinearity,one can achieve low-to-high frequency nonlinear targeted energy transfer in this structure.Specifically,the percentages of shock energy dissipated by higher structural modes for the cases of locked SNA,SDOF SNA,and Two-DOF SNA are 0.08%,0.43%,and 30.04%,respectively.The results indicate that the Two-DOF SNA is capable of rapidly scattering far more energy to much higher frequencies than the SDOF SNA,thereby more quickly reducing the shock response of the primary structure.The robustness of the performance of the SNAs is also studied for varying shock intensities,where the Two-DOF SNA is shown to be significantly more robust at scattering shock energy from low to high frequencies.Last,an effective damping measure is employed to verify and quantify the redistribution of the modal energies in the primary structure.The potential applications of this new passive shock mitigation method are discussed.