The offshore wind industry is increasingly moving towards larger turbines. The growth in rotor size and aerodynamic loads necessitates larger monopile foundations. This increased foundation height results in a monopile that exhibits pronounced slenderness and flexibility. Consequently, the fixed-bottom monopile becomes more susceptible to wave loads, which can induce nonlinear vibrations in complex wave environments. Extensive physical model experiments have been conducted in a wave tank to study the nonlinear vibration characteristics of a fixed-bottom monopile under regular wave action. The experimental results demonstrate that when the wave period is close to twice the resonant period of the model, the vibration response of the monopile increases significantly. Under these conditions, a second harmonic resonance occurs, with the amplitude of the second harmonic component being more than twice that of the fundamental (wave frequency) component. Additionally, the maximum run-up around the model exhibits a W-shaped distribution in the circumferential direction, with the highest run-up observed on the incident wave side. The wave pressure at the water surface is the greatest and increases with wave height, while the pressure below the water surface gradually increases with the measurement height.

This study examines the sloshing of liquid with time-varying mass in a tank. A set of innovative experiments is carried out involving a shaking table supporting a water tank equipped with a drain pipe. Physical evidence of transient resonance is observed for the first time. Transient resonance occurs under specific excitation conditions when the instantaneous average water level (AWL) approaches a critical depth. During transient resonance, the oscillatory amplitude of the free-surface elevation increases sharply and then decreases in an envelope pattern. A bifurcation of the frequency band is first found in the Morlet-wavelet time–frequency spectrum, coinciding with the appearance of the maximum oscillatory amplitude. How the excitation conditions, drainage rate, and initial water depth affect transient resonance is recognized. Two mathematical models—one based on linear modal theory and the other based on nonlinear asymptotic theory and the Bateman–Luke variational principle—are derived to replicate the physical observations, by which application scopes of both models have been greatly broadened. The linear solution fails to predict the key feature of transient resonance, namely, the asymmetric envelopes of the oscillatory component about the AWL. By contrast, the nonlinear asymptotic solution captures this asymmetric feature accurately, and predicts both the steady and maximum oscillatory amplitudes well. The nonlinear solution is decomposed into terms of order 1/3, 2/3, and 1 using an asymptotic series for component analyses. A special nonlinear jump behavior is observed. The effects of draining and filling on transient resonance are compared.

The objective of this work is to establish a theoretical static force equilibrium equation of the semi-ellipsoidal droplet on a horizontal wall by analyzing the forces acting on the differential element and deducing the expressions of surface tension as well as the internal pressure acting on the droplet. The relationship between the static spreading radius, the density, the volume, the surface tension coefficient and the contact angle of the droplet is given. The results from the equation are compared with the experimental data and show a good agreement. The data from the numerical simulation using the volume of fluid method also agree well with those from the theoretical equation.

To address the two major inherent limitations of conventional wave-energy-harvesting (WEH) liquid tanks concerning hydrodynamic efficiency and sea-state adaptability, a sea-state-adaptive frequency control strategy is proposed. A dual-model smooth natural-frequency tuning strategy is designed. Specifically, the natural frequency of the floating platform is tuned via adjustment of its draft with ballast water, whereas the natural frequency of the WEH liquid tank is regulated by altering its horizontal cross-sectional area. A coupled hydrodynamic–liquid–pneumatic mathematical model is established to investigate the two natural-period tuning approaches. Systematic parameter studies are conducted to identify the optimal hydrodynamic efficiency of the sea-state adaptive WEH liquid tank, and its maximum power-generation performance under regular and irregular waves is quantitatively evaluated. The results demonstrate that natural-period tuning of the floating platform improves the overall power-generation capacity, yet it barely alters the high-power operating region within the range of incident-wave periods. Natural-period tuning of the liquid tank shifts the high-power and high-efficiency operating regions to distinct wave periods, which serves as the primary mechanism for sea-state adaptation. The optimal air-duct diameter governing the balance between the chamber pressure difference and airflow rate is also investigated. Under regular wave conditions, controlling the natural period of the liquid tank for each wave scenario broadens the high-power operating range, and the maximum wave-to-pneumatic power capture efficiency reaches 77.6%. Under JONSWAP irregular waves, a maximum capture efficiency of 34.1% is achieved by controlling the optimal natural period of the liquid tank. These results indicate that the proposed control strategies are capable of improving power generation and maintaining the efficient operation of the WEH liquid tank under variable sea-state conditions.

To address the limited hydrodynamic efficiency and sea-state adaptability of conventional wave-energy-harvesting (WEH) liquid tanks, a sea-state-adaptive frequency control strategy is proposed based on floating-body natural-period tuning and liquid-tank natural-period tuning. The former adjusts floating-platform draft using ballast water, while the latter varies the tank's horizontal cross-sectional area. A coupled hydrodynamic–liquid–pneumatic model and systematic parametric studies are used to assess hydrodynamic efficiency and quantify power-generation performance under regular and irregular waves. Results show that floating-body tuning improves overall power-generation capacity but barely changes the high-power operating region across incident-wave periods. Liquid-tank tuning shifts both high-power and high-efficiency operating regions toward different wave periods, providing the primary mechanism for sea-state adaptation. The optimal air-duct diameter is investigated to balance chamber pressure difference and airflow rate. Under regular waves, tuning the liquid-tank natural period for individual wave conditions broadens the high-power operating range, achieving a maximum wave-to-pneumatic power capture efficiency of 77.6%. Under JONSWAP irregular waves, selecting an appropriate liquid-tank natural period yields a maximum predicted wave-to-pneumatic power capture efficiency of 34.1%. These findings indicate that the proposed tuning approaches can enhance power-generation capability and support efficient WEH liquid-tank operation under varying sea states.