This work investigates the interaction between a nonlinear slender clamped-clamped beam and a freely movable mass during the passive self-tuning process. The experimental and numerical results illustrate that the hardening nonlinearity caused by the beam stretch strain can broaden the frequency bandwidth. When the amplitude and curvature of the beam at the slider location are large enough, the slider could be driven to move from the side towards the centre and stop around the centre. The slider’s movement, in turn, changes the beam-slider structure’s mass distribution that shifts the frequency response functions to the lower frequency range. During this interaction between the beam and slider, the high energy orbit could be captured with amplified vibration response. Because the slider is driven by the beam vibration, the self-tuning process does not require external energy. Such a beam-slider structure could be used for the design of nonlinear energy harvesting system with the capability of passive self-tuning to acquire large amplitude vibration and thus higher efficiency.
Nonlinear internal resonance mechanism is exploited in piezoelectric vibration energy harvesting (PVEH) for the purpose of broadening the resonance band. Conventional linear energy harvester has narrow operating bandwidth. In this research, a buckled piezoelectric beam structure with preload under transverse excitation is investigated to demonstrate the superiority of internal resonance. The condition for 2:1 internal resonance could be established by truncating the continuum beam with geometrical nonlinearity. Integro–partial–differential equations are derived for governing transverse motion measured from a stable equilibrium position. At specific initial axial compressive force, two modes are coupled through the internal resonance interaction. For weak nonlinear perturbations, multiple scales method is used to explore the amplitude-frequency responses of the buckled beam system under primary resonance with 2:1 internal resonance. Numerical examples demonstrate that the resonance bandwidth is broadened thanks to the coexistence of softening and hardening nonlinear characteristics. Moreover, validity of the approximate analytical method is demonstrated by comparing with simulation. Furthermore, the optimal resistance is discussed with a pure resistive load. This research on the internal resonance of buckled beam provides a basis for structure design and optimization in broadband PVEH.