Free Vibration Identification of the Geometrically Nonlinear Isolator with Elastic Rings by Using Hilbert Transform

Abstract

The geometrically nonlinear isolator formed by a pair of elastic circular springs in the push-pull configuration has the symmetrical hardening stiffness under static compression and tension. Thus, it could be a potential solution to satisfy the dual isolation requirements of steady-state vibrations and transient shocks in the engineering application. The nonlinear transmissibility of this isolator under large-amplitude sinusoidal excitations has been investigated theoretically and experimentally in our previous research. In this paper, the Hilbert transform is applied to identify the geometrically nonlinear isolator with measured free vibration responses in the time domain. The measured responses are acquired by a laser vibrometer with large initial deformations. Since all the involved instantaneous modal parameters contain fast oscillations around their average values, the empirical mode decomposition is employed to smooth the identified results of the instantaneous frequency and damping coefficient. It is found that the backbone curve obtained experimentally conforms well to the previously measured frequency responses. The identified nonlinear stiffness and damping force characteristics of this geometrically nonlinear isolator have good agreements with the results from the theoretically calculation and the frequency-domain test in our previous research. Therefore, this research provides an efficient approach to analyze the dynamic characteristics of the geometrically nonlinear isolator with push-pull configuration rings and is also beneficial to design the parameters of this isolator.