Fig. 1. (a) Prototype of bistable buckling beam; (b) spring oscillator structure.

Fig. 2. Numerical simulation model in Simulink.

Fig. 3. Comparison between analytical and numerical results.

Fig. 4. Comparison between analytical and numerical results with considering 1/2 sub-harmonics.

Fig. 5. Spectra for sub-harmonic resonance.

Fig. 6. Analytical results of the influence of amplitude on sub-harmonic resonance: (a) The Y coordinate of panel is logarithmic; (b) the Y coordinate of panel is linear.

Fig. 7. Numerical results of the impact of amplitude on sub-harmonic resonance: (a) Results without damping; (b) results with damping.

Fig. 8. Influence of amplitude on vibration isolation characteristics without damping.

Fig. 9. Influences of amplitude on frequency shifting (a) and the peaks of harmonic resonance (b) with damping.

Fig. 10. When k_n = 0.2 N/mm³, influence of k₀ on vibration isolation: (a) Analytical results; (b) numerical simulations.

Fig. 11. When k₀ = –7.5 N/mm, influence of k_n on vibration isolation: (a) Analytical results; (b) numerical simulations.

Fig. 12. (a) Experimental schematic diagram; (b) experimental setups.

Fig. 13. Response under sinusoidal excitation signal with frequency of 55 Hz: (a) Frequency domain; (b) time domain.

Fig. 14. Influence of excitation amplitude on the 1/2 sub-harmonic resonance.

Fig. 15. Sub-harmonic resonance phenomena at 40 Hz: (a) Response and excitation spectrum with U = 1.251 mm; (b), (c) response and excitation spectrum withU = 1.351 mm; (d) time-domain waveform with U = 1.351 mm.

Fig. 16. Comparison between numerical and experimental results.