Vibration Isolation Performance of an Inerter–Stiffness–Damping Isolator Mounted on a Flexible Base and Feedback Control

It has been commonly assumed that an inerter–stiffness–damping isolator mounts on a rigid foundation, however, there exists a strong interaction among the vibration source, isolator, and the base structure for systems with flexible or nonrigid bases. This paper investigates a system consisting of an isolation object, mounted on flexible base plate through an inerter–spring–damping isolator. The steady-state response of the plate-exerted point force excitation can be obtained by using the eigenfunction expansion theorem and expressed by the eigenfunctions and natural frequencies of the system. The four-pole parameter of the inerter can be modeled from the formula calculation or its properties. The transmissibility relation of the proposed system is obtained by using the four-pole parameter theory, which is validated by creating the simulation model in Abaqus software. The power transmission ratio as an isolation performance index is proposed by the mobility relationship among the isolation object, the isolator, and the base. The novelty of this study is that the vibration transmissibility with the flexible base has a much better roll-off rate and anti-resonance peak than that of the rigid base in the high-frequency range, although the resonant peak is generated. A comprehensive parameter analysis shows that the isolation performance can be designed and adjusted by the thickness, material of the plate and the position of the isolator. The effects of feedback control on the resonant peak mitigation of the proposed system are discussed in detail based on Resonant Control, Positive Position Feedback, and Fractional Order Positive Position Feedback. The [Formula: see text] optimization criterion is employed to obtain the optimal damping parameters of positive position feedback.