“…Hence, the inerter-based (Petrini et al, 2020; Wagg, 2021) vibration absorbers (Chen and Hu, 2019b) are applied to mitigate the dynamic responses of the mechanical engineering machinery (De Domenico et al, 2019) and parts, notably automotive and train suspensions (Shen et al, 2016; Wang et al, 2006), buildings (Chowdhury et al, 2022b), wind turbines (Hu et al, 2018; Zhang and Fitzgerald, 2020; Zhang et al, 2019; Zhang and Høeg, 2021), and bridges (Song et al (2021); Liang et al (2021)). There are different types of inerter-inspired (Chowdhury and Banerjee, 2022a) TMD which were developed, such as tuned mass damper inerter (De Domenico and Ricciardi, 2018a; Su et al, 2022), tuned inerter damper (Shen et al, 2019; Wang et al, 2021), tuned viscous mass damper (Ma et al, 2021; Ikago et al, 2012), inerter-based dynamic vibration absorber (Hu and Chen, 2015), angular mass damper (Pradono et al, 2008), gyro-mass dampers (Hessabi and Mercan, 2016), rotational inertia viscous damper (Javidialesaadi and Wierschem, 2019a), viscous inertial mass damper (Lu et al, 2021), electromagnetic inertial mass dampers (Nakamura et al, 2014), rotational inertia dampers (Hwang et al, 2007), clutching inerter damper (Wang and Sun, 2018), tuned inertial mass electromagnetic transducers (Asai et al, 2018), spring-dashpot-inerter (Basili et al, 2019), rotational inertial double tuned mass dampers (Javidialesaadi and Wierschem, 2018), tuned heave plate inerter (Ma et al, 2018), inerter-enhanced nonlinear energy sink (Javidialesaadi and Wierschem, 2019b), tuned liquid inerter system (Zhao et al, 2019b), tuned liquid column damper inerter (Di Matteo et al, 2022), shape memory alloy-tuned mass damper inerter (Tiwari et al, 2021), inerter-based isolators (Hu et al, 2015), inerter-based vibration isolation (Liu et al, 2022), friction pendulum inerter system (…”