A novel high-performance passive non-traditional inerter-based dynamic vibration absorber

Abstract

This paper presents the performance evaluation for a novel high-performance nontraditional inerter-based dynamic vibration absorber called NIDVA-C4. For the easy physical parameter tuning for the proposed device, the Extended Fixed-Points Technique (EFPT) is applied, and then short closed-form solutions are provided for the undamped systems. Subsequently, performance evaluation is carried out by computing two performance measures, which are the H∞ and H2 performance indices. For both H∞ and H2 criteria, constrained and unconstrained multivariable non-linear optimization problems are formulated, which are solved through the formulation of sets of high-order nonlinear equations. For H∞ optimization, the nondimensional FRF function of NIDVA-C4 is minimized at resonant frequencies considering the harmonic force excitation case. For H2 optimization, two random vibration excitation cases are considered which are the following; random force and ground motion excitation cases. For both random vibration excitation cases, the variances of the squared modulus of the frequency response function are computed for undamped primary structure. Considering the mass ratio range from 1% to 10%, from H∞ performance evaluation, the numerical results revealed that the proposed device yields improvements of 2–15% and 23–33% when compared to the inerter-based dynamic vibration absorber (IDVA-C6) or rotational inertial double tuned mass dampers and classic DVA, respectively. On the other hand, for the random force excitation case, improvements of 1–16% and 14–27% can be obtained. Furthermore, for the random acceleration excitation case, the NIDVA-C4 provides dynamic performances of 2–6% and 15–20% compared with the IDVA-C6 and classic dynamic vibration absorber (DVA), respectively. Finally, to appreciate the vibration attenuation in the time domain, numerical simulations were carried out considering the randomly excited mechanical systems.