Active–Passive Vibration Control of Cantilever Beam Based on Magnetic Spring with Negative Stiffness and Piezoelectric Actuator

To enhance the low-frequency vibration suppression capability of cantilever beams, a magnetically tunable piezoelectric cantilever beam structure (MTPCBS) is proposed in this paper. A magnetic spring with negative stiffness (NSMS) is fixed at the free end of a cantilever beam, forming a quasi-zero-stiffness structure. Meanwhile, a macro-fiber composite (MFC) patch is bonded near the root of the beam to implement active skyhook damping control for active vibration control. A theoretical model of the cantilever beam, NSMS, and MFC is established, and the displacement transmissibility of the MTPCBS is derived. The influences of the magnet distance of the NSMS and the control gain of the controller are investigated via simulation. Experimental results indicate that compared to the single beam, the effective vibration isolation frequency of the proposed MTPCBS shifts from 15.3 Hz to 4.6 Hz. When subjected to random vibration excitation ranging from 1 to 80 Hz, the root mean square (RMS) value of vibration decreases from 0.03 g to 1.77 × 10^-3 g, with the vibration attenuation rate improving from -50% to 91%. The proposed MTPCBS and active-passive vibration control method for cantilever beams significantly enhances low-frequency vibration suppression capabilities, providing a feasible strategy for achieving broadband vibration suppression.