The investigation of the dominant-energy-regime map and broadband energy transfer characteristics of waves and flow by applying quasi-zero variable stiffness

Abstract

By investigating the pattern of pivoted vertical cylinders interacting with water waves and flow, this paper obtains the dominant-energy-regime map and realizes broadband energy transfer with the use of quasi-zero variable stiffness. First, a rigid circular cylindrical mass-damper-spring oscillator system is investigated experimentally in regular waves and uniform flow to determine the energy transfer characteristics in the frequency domain. Second, a general form of energy transfer distribution dominant-energy-regime map is built to reveal how the dominant load governs the energy transfer in its region and what the size of the region is. Finally, through numerical simulation this study explores a new approach to broadband energy transfer by applying quasi-zero variable stiffness, but the quasi-zero stiffness stroke must be greater than the critical value. The interaction of cylinder and flow dominates the energy transfer in the low-frequency range f* = fosc/ωv = 0.48–0.9, with an energy transfer efficiency of a few percent. On the other hand, the interaction of cylinder and waves dominates the energy transfer in the high-frequency range f* = 0.9–2.5, with an energy transfer efficiency of tenths of a percent. In the very high-frequency range f* = 2.5–3.5, the cylinder's interaction with flow still allows energy transfer, with an energy transfer efficiency of thousandths of a percent. These frequency ranges and transfer efficiency constitute the dominant-energy-regime of waves and flow. The frequency f* = 0.9 is the point where the dominant-energy factors are transferred, and the hybrid of wave and flow energy in the frequency domain is able to generate a broadband energy band. The critical value of the quasi-zero stiffness stroke decreases as reduced flow velocity U* increases, from about 0.6 times the response amplitude of constant stiffness with U* = 4.347 to about 0.2 times the response amplitude of constant stiffness with U* = 11.152. Only if the quasi-zero stiffness stroke exceeds the critical stroke value, the initial frequency of energy transfer and the energy transfer power will be reduced to a significantly low level. The applied quasi-zero variable stiffness in the vibration stroke expands the energy transfer frequency bandwidth, so the environmental adaptability of energy harvesting with quasi-zero variable stiffness is greatly increased. Waves load dominates the motion magnitude and energy transfer power efficiency in the frequency domain. The findings of this paper can be used to adjust the energy transfer and motion magnitude of the cylinder by taking advantage of the dominant-energy-regime map in the frequency domain.