This work investigates a self-tuning resonator composed of a slender clamped-clamped steel beam and a freely movable slider.The clamped-clamped beam exhibits hardening nonlinearity when it vibrates in large amplitude,providing a broad bandwidth of dynamic response.The moving slider changes the mass distribution of the whole structure,and provides a passive self-tuning approach for capturing the high-energy orbit of the structure.In the case without inclination,adequate inertial force that mainly depends on the vibration amplitude of the beam and the position of the slider can drive the slider to move from the side toward the centre of the beam.This movement amplifies the beam response when the excitation frequency is below 37 Hz in our prototyped device.In the multi-orbit frequency range(28-37 Hz),the self-tuning and magnification of beam response can be achieved when the slider is initially placed in an appropriate position on the beam.Once the beam is disturbed,however,the desired response in the high-energy orbit can be lost easily and cannot be reacquired without external assistance.In an improved design with a small inclination,the introduced small gravitational component enables the slider to move from the higher side toward the lower side when the beam amplitude is small.This property sacrifices the less efficient self-tuning region below 25 Hz,but can enable the beam to acquire and maintain the high-energy orbit response in the multi-orbit frequency range(28-39 Hz),which is resistant to disturbance.The proposed resonator in this paper not only broadens the frequency bandwidth of dynamic response,but also enables capture and maintenance of the high-energy orbit in a completely passive way.Such a passive self-tuning structure presents an advantage in the design of broadband vibration energy-harvesting systems.
