A grounded inerter-based oscillating TMD for suppressing harmonic and random vibrations

Inspired by the lightweight passive vibration control technology, in this work a new anti-vibration device is proposed to significatively improve the protection for stationary mechanical structures subjected to different kinds of vibratory loads. Such a device is herein termed as the grounded inerter-based two-degree-of-freedom tuned mass damper (GI-TDOF-TMD) composed by a grounded inerter and TDOF-TMD with rotational and translational motions, which controls the primary structure's dominant modal shape by using the synergistic dynamic effects of both devices. In order to fairly evaluate the GI-TDOF-TMD's vibration mitigation effectiveness with respect to other devices, the damped and undamped primary structure's nondimensional compliance and mobility transfer functions are firstly computed from a generalized mathematical model that considers four types of random and harmonic excitation inputs which are the following: force general case, base acceleration excitation, base displacement input and inertial force generated by the unbalance in rotary machinery. For harmonically excited mechanical systems, the H∞ performance measure is applied to minimize the maximum resonant peaks of the displacement and velocity dimensionless frequency response functions (FRFs). As the Extended Fixed-Points Technique (EFPT) is analogous to the H∞ criterion, quasi-optimal solutions are firstly computed to perfectly calibrate the FRF's invariant points. After performing this, the evolution of the FRF's control invariant frequencies revealed that GI-TDOF-TMD performs well at low inertance values. Therefore, the GI-TDOF-TMD's maximum control performance is obtained when the inerter's inertial force is the same as that yielded by the TMD's physical mass. In view of such a dynamic behavior, the GI-TDOF-TMD approximately provides 40% and 17% improvements when compared with respect to the classic dynamic vibration absorber (DVA) and TMD-inerter (TMDI), respectively. Then, the GI-TDOF-TMD's power dissipation capability is demonstrated by applying the H2 norm approach to the randomly excited damped mechanical structures. Additionally, it is also revealed through the stochastic energy balance that the GI-TDOF-TMD's internal power dissipation effectiveness is directly reflected on the minimization of the primary structure's kinetic energy. Moreover, for random inputs, the proposed device can broaden the effective operating bandwidth in approximately 45% and 19% when compared to the classic DVA and TMDI, respectively. Therefore, the GI-TDOF-TMD works better than the TMDI in terms of structural displacement and velocity response mitigation, which can be useful in civil engineering applications.