Optimal grounded inerter-based dynamic vibration absorber for controlling inertial force-induced vibrations in rotating machines

ABSTRACT

This paper proposes the optimal design of GIDVA for inertial force-induced vibrations reduction in rotating machinery considered as primary system. For this purpose, simple-to-use closed-form suboptimal design solutions were first derived based on the extended fixed point theory (EFPT). Then, the $H_{\mathrm{\infty }}$ optimization problem was formulated, which was reduced to solving a constrained system of multi-variable nonlinear equations. Thus, by considering the analytical solutions based on the EFPT as a starting point in order to accelerate the convergence of the system, the Newton-Raphson method was applied to numerically solve the nonlinear system equations for the range values of the mass ratio $1\mathrm{\%}\le \mathit{\mu }\le 10\mathrm{\%}$. For this range of values, the proposed GIDVA was compared with the traditional dynamic vibration absorber (TDVA) and the non-traditional dynamic vibration absorber (NDVA). The results of comparison shown that the proposed GIDVA is 47.76–70.66% and 44.82–70.54% superior to the optimized TDVA and NDVA, respectively, in the steady state vibrations suppression of primary system under inertial excitation, and can widen the effective frequency band 70.22–80.98% and 64.07–80.95% superior to TDVA and NDVA, respectively. These results were confirmed in the time domain simulation of the primary system response considered as a centrifuge pump. For this range of values, the proposed GIDVA was compared with the TDVA and the NDVA. The results of comparison shown that the proposed GIDVA is 47.76–70.66% and 44.82–70.54% superior to the optimized TDVA and NDVA, respectively, in the steady state vibrations suppression of primary system under inertial excitation and can widen the effective frequency band 70.22–80.98% and 64.07–80.95% superior to TDVA and NDVA, respectively. These results were confirmed in the time domain simulation of the primary system response considered as a centrifuge pump.

KEYWORDS:

• Inerter
• dynamic vibration absorber
• inertial force
• extended fixed point theory
• $H_{\mathrm{\infty }}$ optimization

Acknowledgments

The authors would like to thanks the associate editor and the anonymous referees for their valuable comments and suggestions, which helped us to improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).