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∞ 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%≤μ≤10%. 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.