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.

Ballistic performance of spherical fragments penetrating PCrNi3MoV target plates

PCrNi3MoV steel is a medium-carbon,low-alloy quenched and tempered steel that finds its applications in military gun barrels due to the high wear resistance and ablation resistance.To study the penetration and failure modes of PCrNi3MoV plates impacted by tungsten spheres,tungsten spheres of various diameters(5 mm,8 mm,and 10 mm)were used to impact PCrNi3MoV steel plates with thicknesses of 6 mm,9 mm,and 14 mm.The penetration performance of the spheres was analyzed for different velocities,and the ultimate penetration velocity of the plate was obtained.It was found that the primary failure modes of the PCrNi3MoV plate were compression pitting failure and shear failure.Using the dimensional analysis method,a relationship between the bulge height of the steel plate and the fragment velocity,an equation for the ultimate penetration velocity,and a relationship between the target penetration energy and the fragment velocity were obtained.Then,a projectile-target action index was proposed to describe the process of tungsten spheres with different velocities impacting target plates.The results suggested that under the same thickness of the target plate,a larger-diameter fragment required more kinetic energy to obtain the same ultimate penetration effect as a smaller-diameter fragment.The equations obtained through dimensional analysis predicted values that agreed well with experimental values,indicating that these equations can be applied to engineering applications.

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.

Investigation of availability,demand,targets,and development of renewable energy in 2017-2050:a case study in Indonesia

Abundant potential of renewable energy(RE)in Indonesia is predicted to replace conventional energy which continues to experience depletion year by year.However,until now,the use of RE has only reached 2%of the existing potential of 441.7 GW.The main overview of this work is to investigate the availability of RE that can be utilized for electricity generation in Indonesia.National energy demand and targets in the long run during the 2017-2050 period are also discussed.Besides,government policies in supporting RE development are considered in this work.The results show that the potential of RE in Indonesia can be utilized and might replace conventional energy for decades.The use of RE for electricity generation can be achieved by employing a government policy that supports the investor as the executor of RE development.The selling price of electricity generated from RE is cheaper than electricity generated from fossils;this makes economy is more affordable for people.Finally,the target set by the government for utilizing RE as the main energy in Indonesia can be done by implementing several policies for the RE development.Thus,greenhouse gas emissions and the use of petroleum fuels can be reduced.

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.

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.