A concave X-shaped structure supported by variable pitch springs for low-frequency vibration isolation

Based on the known X-shaped structure, a concave X-shaped structure (CXSS) featuring custom-designed variable pitch springs (VPS) is proposed. This design aims to enhance the displacement range of the quasi-zero stiffness (QZS) system and improve its performance in isolating low-frequency vibrations. The CXSS is obtained by merging two semi-X-shaped structures. The negative stiffness property of the concave structure can be improved by utilizing the motion limitations of the mechanical structure. Of particular concern is the VPS, it can provide nonlinear restoring force and variable stiffness by self-adjusting the effective number of coils. This special spring is suitable to neutralize the negative stiffness of the concave structure, enabling a wider range of QZS properties than linear springs and magnets. The average error between the practical and theoretical restoring force of the VPS is less than 10 %. Based on a special compression coefficient, the objective-load design method (OLDM) is proposed to obtain the stiffness conditions implementing QZS properties against rated mass. The stiffness obtained by the OLDM is considerably accurate. Under this condition, the vibration transmissibility is about 0.45 at 3.5 Hz and 0.1 at 14 Hz, which is lower than that of the unmatched load and stiffness coefficients. Compared with the X-shaped structure, the proposed structure has better low-frequency vibration isolation performance with a natural frequency of about 2 Hz. The vibration transmissibility is about 0.2 at 5 Hz and is about 0.1 at 10 Hz. Pulse excitations with an amplitude of 16 g can be attenuated to about 0.51 g through the CXSS compensated by VPS. It is convenient and efficient to implement QZS properties using the VPS to compensate negative stiffness.