Theoretical analysis of 2D meta-structure with inertia amplification

This study proposed a square-grid structure (SGS) attached with inertial amplification mechanisms (IAMs) to obtain a better vibration isolation effect with low frequency and wide band gaps. According to the different stiffness assumptions of the IAM connecting rods, the proposed meta-structure is defined as two different types, 10 of freedom (DOF) elastic system (E-IAM) and 2-DOF rigid system (R-IAM). The motion equations of the two systems are given based on Newton's motion theorem and Lagrange's theorem, respectively. Dispersion relations and motion modes of the infinite system are discussed to obtain lower and wider band gaps. Vibration trans-mission characteristics of 20 x 20 meta-structures are also conducted. For the E-IAM system, ultra-low frequency vibration isolation can be achieved when the stiffness ratio of the connecting rod is the same in both vertical and horizontal directions and less than the main spring. The approximate analytical expression of the dispersion curve of the R-IAM system is given. Because the denominator is always greater than 1, it is proved that the cut-off frequency of the R-IAM system is always lower than that of the SGS. For finite R-IAM structures, when the longitudinal stiffness is asymmetric in both directions, multiple local resonant band gaps can be obtained in the passband, which is very beneficial to vibration reduction.

Automated summary

This study proposes a square-grid structure with inertial amplification mechanisms to achieve better vibration isolation at low frequencies and wide band gaps. The motion equations and dispersion relations of two different types of meta-structure are derived and discussed. The results show that ultra-low frequency vibration isolation and multiple local resonant band gaps can be achieved under certain conditions.