Passive targeted energy transfer in the steady state dynamics of a nonlinear plate with nonlinear absorber

In this work, the inducement of passive nonlinear sink for vibration control of nonlinear plate model was studied. The considered system was composed of simply supported thin plate under harmonic excitation with a nonlinear attachment. By varying parameters and locations of the nonlinear energy (NES), an optimized passive targeted energy transfers (TETs) from the plate to the attachments was performed. Moreover, comparative studies of the performance of NESs and linear tuned mass dampers (TMDs) are given. By performing complex averaging and arclength continuations techniques, semi-analytical approximations for nonlinear steady-state response was developed. To justify the averaging method, numerical simulation was also performed. The obtained results show that the NES designed for specific amplitude of excitation has better performance with respect to TMD, but with increase in amplitude of excitation force, NES has lower robustness with respect to TMD. The obtained results show that, if the phase differences of plate and NES with exciting force are ±π2 and ±π respectively, then the best condition for energy transfer from plate to NES will occurs, but if both the plate and NES have π with exciting force, the amplitude of vibration for both of them are considerably high.