Double mechanical frequencies locking phenomenon in a piezoelectric driven 3-DOF magnetic coupling resonator

Frequency locking phenomenon induced by modal coupling can effectively overcome the dependence of peak frequency on driving strength in nonlinear resonant systems and improve the stability of peak frequency, which has a fundamental role in improving the dynamic performance of resonant devices. Most research has been focused on a single mechanical frequency locking, but less research has been done on the double frequencies locking phenomenon. In this study, the double frequencies locking phenomenon is first proposed through a 1:3:3 internal resonance of a three degrees of freedom (3-DOF) magnetic coupled resonant system driven by piezoelectricity. Firstly, the resonator is designed using three cantilever beams, permanent magnets and piezo-electric actuator. The nonlinear governing equations, representing the first, second and third modes, are obtained by a 3-DOF lumped parameter model of the resonator. The double frequencies locking phenomenon in a 3-DOF resonant system is measured experimentally and studied theoretically. Both theoretical predictions and experimental results show that with the increase of driving force, the first frequency locking phenomenon occurs due to the coupling vibration between the first and second modes. Interestingly, as the drive force continues to in-crease, the first frequency locking switches to the second frequency locking, accompanied by the transfer of vibration energy from the first mode to the third mode. Typically, the physical conditions of the first and second frequencies locking are deduced theoretically. Besides, a synchronous linear mass sensing scheme for double analytes is proposed by using double frequencies locking phenomenon. By measuring the shifts of the first and second locking frequencies, the mass detection of the double analytes can be carried out simultaneously.