Energy dissipation mechanism of inerter systems

Abstract Inerter systems have been proven to be effective vibration control devices. The energy-input-dissipation flow offers an alternative perspective to reveal the working mechanism of inerter-based systems for vibration control. In this study, the energy-based method is used to analytically explain the discovered benefits of inerter systems including the reduction in input energy and the enhancement of energy dissipation, which further yields optimal design for the inerter systems. Closed-form energy equations are derived for structures equipped with a basic inerter system composed of a grounded or ungrounded inerter. These energy equations theoretically establish the quantified relationship between the powers of input and dissipation and the key parameters of the inerter system in an analytical form. Furthermore, the differences in working mechanisms between inerter systems composed of grounded or ungrounded inerters are characterized via comparative analysis in terms of the displacement control, enhanced energy dissipation efficiency, and input energy reduction. Based on the revealed energy working basis, a unified energy-dissipation-based optimization strategy is developed to simultaneously control the displacement and energy responses. Finally, numerical examples are presented to validate the derived energy equations and the proposed optimization strategy. The findings of this study show that the energy equation supplies an analytical measurement for evaluating the input power of inerter-based structures and quantifies the energy dissipation effect of the inerter system. In particular, the derived energy equation explicitly reveals the dual benefits of an inerter system with a grounded inerter, which reduces the input power of the entire inerter-based structure and simultaneously dissipates the vibrational energy. Following the energy-dissipation-based optimal design strategy, which directly applies the grounded inerter to reduce input power or potentially uses the ungrounded inerter to enhance the energy dissipation effect, the target displacement can be quantitively achieved by the optimized inerter systems.