Nonlinear mirrored-stiffness design method for quasi-zero stiffness vibration isolators

The phenomenon of stiffness hardening has detrimental influence on the natural frequency and the width of vibration isolation frequency bands, which significantly confines the development of quasi-zero-stiffness vibration isolators (QZSVIs). To overcome this restriction, the nonlinear mirrored-stiffness design method (NMSM) is proposed and its applicable condition is revealed. Based on the mechanism of stiffness hardening, a nonlinear spring (NS) is designed by the NMSM. NS possesses nonlinear restoring force and a mirror-image relationship with the targeted negatives stiffness. The mathematical model of the NS is established based on Heaviside function. Coupled QZSVIs (CQZSVIs) are constructed by a concave metastructure with multiple stiffness properties and the NS to validate the NMSM. A prototype of the CQZSVI is fabricated to prove the correctness of the theoretical analysis. The practical tests of the CQZSVI demonstrate an obvious QZS region where the restoring force remains approximately constant and the stiffness is almost invariable and close to zero. The results of sweep-frequency experiments show that the CQZSVI has a natural frequency of about 0.8 Hz and a broad effective vibration isolation region starting from about 1.1 Hz. Its transmissibility is about − 15 dB at 3 Hz and is about − 20 dB at 3.5 Hz. The NMSM successfully breaks through the bottleneck of the development of QZSVIs and produces a new approach for the construction of low-frequency vibration isolators.