Fore Aft Research Articles

Experimental Study on Identification of Aerodynamic Damping Matrix for the Tower of an Operating Wind Turbine by Artificial Excitation

ABSTRACTQuantitation of damping is of great significance for the design and condition assessment of wind turbines. The authors' previous theoretical and numerical studies showed that compared with damping ratios, a modal aerodynamic damping matrix can better describe the damping coupling in the fore‐aft (FA) and side‐side (SS) tower motions. In the present study, an improved damping identification method was first proposed to identify this damping matrix with artificial exciters and then verified by using OpenFAST simulations under different excitation frequencies, excitation force amplitudes, and turbulent wind fields. Following the numerical study, a scaled wind turbine model with a geometric scale ratio of 1/75 was carefully designed based on the NREL 5‐MW wind turbine prototype, in which the scaled blade design follows the rule in thrust coefficient similarity. An identification study was performed with this scaled model by a series of wind tunnel tests. The modal aerodynamic damping matrix was identified under steady‐state harmonic excitation in the operating state and compared with the identified results by a free decay method and the theoretical values. The results experimentally confirm the correctness of the aerodynamic damping matrix theory under uniform wind and the feasibility of the improved identification method in practice.

Tractor Three-Point Hitch Control for an Independent Lower Arms System

The three-point hitch, found on agricultural tractors, facilitates the raising and lowering of an attached implement. Some tractors include a rock shaft that comprises a physical shaft that interconnects and facilitates the raising and lowering of the lower arms of the three-point hitch in a synchronized manner. In this study, we deal with a hitch system with the lower arms actuated by two independent hydraulic cylinders. This innovative tractor hitch system design allows the implement to follow the terrain, instead of the tractor, about the fore–aft (roll) axis of the tractor. However, since the two lower arms are independent, a specialized controller is needed to move these arms in unison. First, we present a position controller for individual arms and a roll controller to move these arms together. Second, we present a unique algorithm to emulate a physical rock shaft while the implement is operating in float mode. The algorithm ensures that the implement does not roll around the fore–aft axis while making sure it moves up and down vertically to follow the terrain. We present experimental results from the step response of the hitch system’s height while tracking a velocity reference. With the roll of the implement defined as the difference between the left arm’s position in percentage and that of the right arm in percentage, we observe that the largest mean roll was 0.23% with a flail mower attached and 0.26% without any implement. We then present results from the implement’s position in the float mode when the software rock shaft was activated and compare them with the case without the software rock shaft. The experiments showed that, when the software rock shaft was turned on, the mean roll reduced from 4.64% to 0.58% with a seed drill implement and from −3.99% to −0.59% with a flail mower implement. The standard deviations in these two implement cases improved from 16.77% to 2.79% and 6.45% to 3.53%, respectively, proving the effectiveness of the software rock shaft and its potential to replace the physical rock shaft found on the traditional tractors.

Vibration control and stroke evaluation of bi-directional bistable nonlinear energy sinks applied in monopile offshore wind turbines during emergency shutdown

Monopile offshore wind turbines (OWTs) in complex wind and wave environments can generate more excessive vibrations in the fore-aft (FA) and side-to-side (SS) directions when emergency shutdowns occur, and therefore damping techniques to alleviate such vibrations are essential. Due to the potential frequency detuning (reduced damping effectiveness) of traditional tuned mass dampers (TMDs) and stroke issues (such as large strokes of TMDs and limited maximum strokes of unidirectional nonlinear energy sinks (NESs)) in existing absorbers, this paper proposes a bi-directional bistable nonlinear energy sink (BBNES) to mitigate the vibration of the OWT in the FA and SS directions during the emergency shutdown. First, the proposed device and its operation mechanism are elaborated, and an optimization method for the device is introduced. Then, the dynamic analysis model of the BBNES is developed for vibration control of the OWT and incorporated into a fully coupled numerical simulation tool with high fidelity, FAST v8. Subsequently, the responses of the OWT without and with the proposed BBNES and the bi-directional tuned mass damper (BTMD) are exhaustively investigated under diverse conditions (including mass ratios, wind-wave loadings, emergency shutdown times, wind-wave misalignments, and 1st mode natural frequencies of the OWT) to reveal their performances and compare them. The research results show that under most conditions, the BBNES and BTMD have a similar damping performance in the FA direction, whereas the BBNES has a slightly lower damping performance in the SS direction than the BTMD. In addition, except for the wind velocity of 8 m/s at the hub and the wind-wave misalignment of 90°, the FA stroke of the BBNES with a small mass ratio (i.e., 0.01∼0.035) is significantly smaller than that of the BTMD with the same mass ratio by more than 1.1 m, and even up to about 4 m. The SS stroke of the BBNES is slightly greater than that of the BTMD, and in most cases, the difference between both is less than 0.52 m. Therefore, the BBNES is superior to the BTMD in this regard. When the 1st mode natural frequency of the OWT decreases, the BTMD can lose its tuning efficacy and makes the tower more susceptible to resonance caused by 1p and wave loadings, while the BBNES is not affected by the 1st mode natural frequency variation of the OWT, demonstrating its stronger robustness.

Effect of scour on the fatigue life of offshore wind turbines and its prevention through passive structural control

Abstract. Offshore wind turbine (OWT) support structures are exposed to the risk of fatigue damage and scour, and this risk can be effectively mitigated by installing structural control devices such as tuned mass dampers (TMDs). However, time-varying scour altering OWTs' dynamic characteristics has an impact on the TMD design and fatigue life, which has rarely been studied before. In this paper, a simplified modal model is used to investigate the influence of scour and a TMD on the fatigue life evaluation of a 5 MW OWT's support structure, and a traditional method and a newly developed optimization technique are both presented to obtain TMD parameters. This optimization technique aims at finding optimal parameters of the TMD which maximize the fatigue life of a hotspot at the mudline, and the effect of time-varying scour can be considered. This study assumes that the TMD operates in the fore–aft (FA) direction, while the vibration in the side–side (SS) direction is uncontrolled. Results show that scour can decrease the fatigue life by about 24.1 % and that the TMD can effectively suppress vibration and increase the fatigue life. When the scour depth reaches 1.3 times the pile diameter, the TMD with a mass ratio of 1 % can increase the fatigue life of an OWT's support structure by about 64.6 %. Further, it is found that the fatigue life can be extended by 25 % with the TMD optimized by the proposed optimization technique rather than using a traditional design method which does not take the change in dynamic characteristics into account.

OC6 project Phase IV: validation of numerical models for novel floating offshore wind support structures

Abstract. This paper provides a summary of the work done within Phase IV of the Offshore Code Comparison Collaboration, Continued with Correlation and unCertainty (OC6) project, under International Energy Agency Wind Technology Collaboration Programme Task 30. This phase focused on validating the loading on and motion of a novel floating offshore wind system. Numerical models of a 3.6 MW horizontal-axis wind turbine atop the TetraSpar floating support structure were compared using measurement data from a 1:43-Froude-scale test performed in the University of Maine's Alfond Wind–Wave (W2) Ocean Engineering Laboratory. Participants in the project ran a series of simulations, including system equilibrium, surge offsets, free-decay tests, wind-only conditions, wave-only conditions, and a combination of wind and wave conditions. Validation of the models was performed by comparing the aerodynamic loading, floating support structure motion, tower base loading, mooring line tensions, and keel line tensions. The results show a relatively good estimation of the aerodynamic loading and a reasonable estimation of the platform motion and tower base fore–aft bending moment. However, there is a significant dispersion in the dynamic loading for the upwind mooring line. Very good agreement was observed between most of the numerical models and the experiment for the keel line tensions.

Optimized design of multiple tuned mass dampers for vibration control of offshore wind turbines

Offshore wind turbines (OWTs) are dynamically sensitive structures to low-frequency wind-wave loadings due to their low damping and high flexibility. This makes them vulnerable to unwanted vibrations in ocean environments. Therefore, there is a need to implement innovative vibration control devices to suppress undesired vibration and ensure their structural safety. A tuned mass damper (TMD) has been a promising solution to control excessive vibrations recently in OWTs due to higher efficiency and low installation cost. However, TMD performance in vibration mitigation of OWTs when placed at a nacelle is still challenging to investigate because the generator torque and pitch control may affect the dynamics of the overall system. In this paper, an optimal multiple TMD system is designed by placing TMDs at optimal locations along the tower, which are defined using the maximum amplitude of the displacements for the first three natural frequencies of the tower. In addition, extensive simulations are carried out with integrated OWT-TMD systems to find the optimal mass ratio values and quantity of the TMDs. The TMD system is also tuned for several scenarios, including operating, parked, and idling conditions under the combined wind-wave loadings. A numerical model of the 5 MW NREL OWT developed in OpenFAST is considered as the baseline in this study. The results show a root mean square (RMS) response reduction of 10.2% and 42% in fore-aft (FA) and side-side (SS) tower displacement with optimally designed multiple TMDs. Moreover, improved mitigation effects on tower base moment of RMS 43.6% and 20.8% are observed in orthogonal directions, respectively. The findings of this paper may have the potential for designing passive TMD systems for vibration reductions in OWT.

Enhanced recovery caused by nonlinear dynamics in the wake of a floating offshore wind turbine

An experimental study in a wind tunnel is presented to explore the wake of a floating wind turbine subjected to harmonic side-to-side and fore–aft motions under laminar inflow conditions. The wake recovery is analysed as a function of the frequency of motion $f_p$ , expressed by the rotor-based Strouhal number, $St = f_p D / U_{\infty }$ ( $D$ is the rotor diameter, $U_{\infty }$ the inflow wind speed). Our findings indicate that both directions of motion accelerate the transition to the far-wake compared with the fixed turbine. The experimental outcomes confirm the computational fluid dynamics results of Li et al. (J. Fluid Mech., vol. 934, 2022, p. A29) showing that sideways motions lead to faster wake recovery, especially for $St \in [0.2, 0.6]$ . Additionally, we find that fore–aft motions also lead to better recovery for $St \in [0.3, 0.9]$ . The recovery is closely linked to nonlinear spatiotemporal dynamics found in the shear layer region of the wake. For both directions of motion and $St \in [0.2, 0.55]$ , the noisy wake dynamics lock in to the frequency of the motion. In this synchronised-like state, sideways motions result in large coherent structures of meandering, and fore–aft movements induce coherent pulsing of the wake. For fore–aft motion and $St \in [0.55, 0.9]$ , the wake shows a more complex quasiperiodic dynamic, namely, a self-generated meandering mode emerges, which interacts nonlinearly with the excitation frequency $St$ , as evidenced by the occurrence of mixing components. The coherent structures grow nonlinearly, enhance wake mixing and accelerate the transition to the far-wake, which, once reached, exhibits universal behaviour.

Sensitivity of fatigue reliability in wind turbines: effects of design turbulence and the Wöhler exponent

Abstract. Fatigue assessment of wind turbines involves three main sources of uncertainty: material resistance, load, and the damage accumulation model. Many studies focus on increasing the accuracy of fatigue load assessment to improve the fatigue reliability. Probabilistic modeling of the wind's turbulence standard deviation is an example of an approach used for this purpose. Editions 3 and 4 of the IEC standard for the design of wind energy generation systems (IEC 61400-1) suggest different probability distributions as alternatives for the representative turbulence in the normal turbulence model (NTM) of edition 1. There are debates on whether the suggested distributions provide conservative reliability levels, as the established design safety factors are calibrated based on the representative turbulence approach. The current study addresses the debate by comparing annual reliability based on different scenarios of NTM using a probabilistic approach. More importantly, it elaborates on the relative importance of load assessment accuracy in defining the fatigue reliability. Using the DTU 10 MW reference wind turbine and the first-order reliability method (FORM), we study the changes in the annual reliability level and its sensitivity to the three main random inputs. We perform the study considering the blade root flapwise and the tower base fore–aft moments, assuming different fatigue exponents in each load channel. The results show that integration over distributions of turbulence in each mean wind speed results in less conservative annual reliability levels than representative turbulence. The difference in the reliability levels varies according to turbulence distribution and the fatigue exponent. In the case of the tower base, the difference in the annual reliability index after 20 years can be up to 50 %. However, the model and material uncertainty have much higher effects on the reliability levels compared to load uncertainty. Knowledge about such differences in the reliability levels due to the choice of turbulence distribution is especially important, as it impacts the extent of lifetime extension through reliability reassessments.

Compliant liquid dampers-inerter for mitigating wind-, wave-, and earthquake-induced vibrations of monopile offshore wind turbines

This work explores the possibility of installing compliant liquid dampers-inerter (CLDI) on monopile offshore wind turbines (OWTs) for controlling combined vibrations from wind, wave, and earthquakes. For numerical demonstration, the 5-MW NREL monopile OWT is taken up. Seven different wind speeds and a set of 20 earthquakes are considered. Hence, the means of structural response quantities are chosen. The peak and root mean square (RMS) values of displacement and acceleration responses of tower-top are monitored. A genetic algorithm-based multi-objective optimization is performed, and the optimum CLDI parameters are estimated for different ranges of inertance ratio and inerter topology. The optimization comprises four cases: firstly, minimizing the mean of peak responses and second, minimizing the mean of RMS responses in fore-aft (FA) as well as in side-side (SS) directions. Hence, each case has four objective functions, covering two loading scenarios, wind & wave, and earthquake. With the obtained optimum parameters, considering all these cases, the control effectiveness of CLDI is further investigated in time and frequency domains. The time domain results reveal that the CLDI controls the SS vibrations effectively, whereas, in FA direction, the efficiency is marginally less. Additionally, the frequency domain plots indicate the multi-mode control capability of CLDI.

Spontaneous locomotion of a symmetric squirmer

The squirmer is a popular model to analyse the fluid mechanics of a self-propelled object, such as a micro-organism. We demonstrate that some fore–aft symmetric squirmers can spontaneously self-propel above a critical Reynolds number. Specifically, we numerically study the effects of inertia on spherical squirmers characterised by an axially and fore–aft symmetric ‘quadrupolar’ distribution of surface-slip velocity; under creeping-flow conditions, such squirmers generate a pure stresslet flow, the stresslet sign classifying the squirmer as either a ‘pusher’ or ‘puller’. Assuming axial symmetry, and over the examined range of the Reynolds number $Re$ (defined based upon the magnitude of the quadrupolar squirming), we find that spontaneous symmetry breaking occurs in the puller case above $Re \approx 14.3$ , with steady swimming emerging from that threshold consistently with a supercritical pitchfork bifurcation and with the swimming speed growing monotonically with $Re$ .

Historical trends of floating wind turbine fatigue loads (Ireland 1920–2010)

We present a new method for analysing the fatigue loads of offshore floating wind turbines over the long term. In this method, bias-corrected wind and wave data from the 20th century (ERA20C versus ERA5 reanalysis) is used for an energetic sea location in western Ireland. To reduce the computational cost and theoretical complexity, the sea states were clustered into categories to indicate how these categories evolve over three climate periods during a period of 30 years (1921–1950, 1951–1980, and 1981–2010). OpenFAST aeroelastic code simulation in floating mode was then conducted at each sea state for spar-type 5-MW and semi-submersible 15-MW wind turbines. This shows the damage loads and fatigue increments over the century, with some relevant cases (rotor torque, blade pitch and flapping, and tower side–side and fore–aft moments) showing fatigue increments of 5%–8%. Thus, in the new method, historical data are used to create a model to represent the evolution of sea states and corresponding fatigue over the long term, which can be applied globally to future projections.

A Novel Composite Pitch Control Scheme for Floating Offshore Wind Turbines with Actuator Fault Consideration

It is of great importance to simultaneously stabilize output power and suppress platform motion and fatigue loads in floating offshore wind turbine control systems. In this paper, a novel composite blade pitch control scheme considering actuator fault is proposed based on an augmented linear quadratic regulator (LQR), a fuzzy proportional integral (PI) and an adaptive second-order sliding-mode observer. Collective pitch control was achieved via the fuzzy PI, while individual pitch control was based on the augmented LQR. In the case of actuator fault, an adaptive second-order sliding-mode observer was constructed to effectively eliminate the need for the upper bound of unknown fault derivatives and suppress the chattering effect. This paper conducted co-simulations based on FAST (Fatigue, Aerodynamics, Structures, and Turbulence) and MATLAB/Simulink to verify the effectiveness and superiority of the proposed scheme under different environmental conditions. It is shown that platform roll was reduced by approximately 54% compared to that under PI control. For the tower fore–aft moment, load reductions of 45% or more were achievable. The proposed scheme can greatly reduce the pitch and roll of the floating platform and loads in the windward direction of the wind turbine.

Variable cross-sectional effect on bi-directional blades–tower–soil–structure dynamic interaction on offshore wind turbine subject to wind–wave loads

BackgroundThis study introduces a numerical model designed to simulate interactions occurring between a wind turbine's tower and the surrounding soil, as well as between the nacelle, blades, and the surrounding environment. This simulation accounts for both fore–aft and side-to-side movements. To describe these interactions, the model leverages the Euler–Lagrange equations. It calculates wave loads utilizing the Morison equation, with wave data generated based on the JONSWAP spectrum. Furthermore, aerodynamic loads are determined using the blade element moment theory, and the wind spectrum is generated using the Von Karman turbulence model. The tower is represented as a variable cross-sectional beam, employing a two-noded Euler beam element with two degrees of freedom: transverse displacement and rotation, and utilizing Hermite polynomial shape functions.ResultsIn a comparative analysis against experimental data, this modified model demonstrates significant enhancements in accurately reproducing the dynamic behavior of wind turbines with variable cross-sectional towers, outperforming models that approximate the tower with a constant cross section. Our findings reveal that the modified model achieves a remarkable improvement of 15% in replicating the tower's dynamic response when compared to the constant cross-sectional models. As a case study, a 5 MW monopile wind turbine with a flexible foundation, specifically the one provided by the National Renewable Energy Laboratory (NREL), is employed to simulate its dynamic response.ConclusionsThis research presents a robust numerical model for simulating wind turbine behavior in various environmental conditions. The incorporation of variable cross-sectional tower representation significantly improves the model's accuracy, making it a valuable tool for assessing wind turbine dynamics. The study's findings highlight the importance of considering tower flexibility in wind turbine simulations to enhance their real-world applicability.

Sensitivity Analysis of Modal Parameters of a Jacket Offshore Wind Turbine to Operational Conditions

Accurate estimation of offshore wind turbine (OWT) modal parameters has a prominent effect on the design loads, lifetime prediction, and dynamic response of the system. Modal parameters can vary during the operation of OWTs. This paper studies the variation and sensitivity analysis of an OWT’s modal parameters with respect to operational and environmental conditions. Three finite element models of a jacket-supported OWT at the Block Island Wind Farm are created within the OpenSees, SAP2000, and OpenFAST platforms and validated using experimental measurements. The OpenFAST model is used to simulate the modal parameters of the turbine under various wind speed, rotor speed, power, yaw angle, mean sea level, blade pitch angle, and soil spring values. The model-predicted modal parameters of the first fore–aft (FA) and side–side (SS) modes are compared to those identified from experimental measurements. Results from the simulations show that the first FA natural frequency and damping ratio mostly depend on the rotor speed and wind speed, respectively, while yaw angle and mean sea level do not have a visible effect. It is observed that there is about 8% stiffening in the first FA frequency and an aerodynamic damping of 7.5% during the operation of the OWT.

Study on a three-dimensional variable-stiffness TMD for mitigating bi-directional vibration of monopile offshore wind turbines

Bi-directional vibrations of offshore wind turbine (OWT) exist due to the misalignment of wind and wave loadings, which induces the structural fatigue failure. At present, monopile offshore wind turbine (MOWT) is widest utilized in worldwide, which is adopted as the research objective in this study. A novel semi-active three-dimensional magnetorheological elastomer (MRE) based tuned mass damper is proposed to suppress a MOWT bi-directional vibration under misaligned wind, wave, seismic loadings. The proposed MRE-based TMD is installed in the nacelle, which presents dual-directional controllable stiffness properties. Its nonlinear behavior is depicted by bi-lateral Bouc-Wen model. A semi-active control framework is developed, in which current-dependent stiffness of MRE-based TMD is tuned for tracing real-time dominant frequency of the MOWT. The numerical results reveal that MRE-based TMD can effectively attenuate the bi-directional dynamic responses of MOWT under various operation conditions. Additionally, the semi-active MRE-based TMD outperforms passive TMD in reducing the peak and RMS displacement of the tower top in both fore-aft (FA) and side-side (SS) directions, especially in operational state. MRE-based TMD also presents strong robustness under the condition of structural stiffness degradation.

Quantification and correction of motion influence for nacelle-based lidar systems on floating wind turbines

Abstract. Inflow wind field measurements from nacelle-based lidar systems offer great potential for different applications including turbine control, load validation, and power performance measurements. On floating wind turbines nacelle-based lidar measurements are affected by the dynamic behavior of the floating foundations. Therefore, the effects on lidar wind speed measurements induced by floater dynamics must be understood. In this work, we investigate the influence of floater motions on wind speed measurements from forward-looking nacelle-based lidar systems mounted on floating offshore wind turbines (FOWTs) and suggest approaches for correcting motion-induced effects. We use an analytical model, employing the guide for the expression of uncertainty in measurements (GUM) methodology and a numerical lidar simulation for the quantification of uncertainties. It is found that the uncertainty of lidar wind speed estimates is mainly caused by the fore–aft motion of the lidar, resulting from the pitch displacement of the floater. Therefore, the uncertainty is heavily dependent on the amplitude and the frequency of the pitch motion. The bias of 10 min mean wind speed estimates is mainly influenced by the mean pitch angle of the floater and the pitch amplitude. We correct motion-induced biases in time-averaged lidar wind speed measurements with a model-based approach, employing the developed analytical model for uncertainty and bias quantification. Testing of the approach with simulated dynamics from two different FOWT concepts shows good results with remaining mean errors below 0.1 m s−1. For the correction of motion-induced fluctuation in instantaneous measurements, we use a frequency filter to correct fluctuations caused by floater pitch motions for instantaneous measurements. The correction approach's performance depends on the pitch period and amplitude of the FOWT design.

Obstructed free-surface viscoplastic flow on an inclined plane

The interaction of steady free-surface flows of viscoplastic material with a surface-piercing obstruction of square cross-section on an inclined plane is investigated theoretically. The flow thickness increases upstream of the obstruction and decreases in its lee. The flow depends on two dimensionless parameters: an aspect ratio that relates the flow thickness, the obstruction width and the plane inclination; and a Bingham number that quantifies the magnitude of the yield stress relative to the gravitationally induced stresses. Flows with a non-vanishing yield stress always form a static ‘dead’ zone in a neighbourhood of the upstream and downstream stagnation points. For relatively wide obstructions, a deep ‘ponded’ region develops upstream with a small dead zone, while the deflected flow reconnects over relatively long distances downstream. The depth of the upstream pond increases with both the dimensionless yield stress and width of the obstruction, while the unyielded dead zone varies primarily with the yield stress. Both are predicted asymptotically by balancing the volume flux of fluid into and out of the ponded region. When the obstruction is narrow, the perturbation to the depth of the oncoming flow is reduced. It exhibits fore–aft antisymmetry, while the dead zone is symmetric to leading order. Increasing the yield stress leads to larger dead zones that eventually encompass all of the upstream- and downstream-facing boundaries of the obstruction and fully divert the flow. Results for obstructions with circular and rhomboidal cross-sections are also presented and illustrate the effects of boundary shape on the properties of the steady flow.

Closed-form derivation of aerodynamic damping matrix and pitch vector of an aero-servo-elastic wind turbine system

This paper develops closed-form expressions of aerodynamic damping matrix and pitch controller of an aero-servo-elastic wind turbine (WT) system. This facilitates establishing a linearized WT model completely analytically at an arbitrary operational point, without resorting to extensive numerical linearizations or fittings. The rotor blade flexibility and pitch controller are included in the model development, thus unfolding a full understanding of the aerodynamic coupling effects. The linearized WT model is verified by good agreement with results from the original nonlinear WT model. Based on the verified linearized model, it is seen that aerodynamic coupling between tower fore–aft and side–side vibrations is solely due to the tower top rotations, and the top rotations also significantly enlarge the diagonal aerodynamic damping coefficients. Both tower top rotations and flexible blade–tower interaction play important roles in tower aerodynamic damping ratios. The developed formulas of load coefficients are also readily applicable to a FE modeling framework of the tower–foundation system.

Dynamics of horizontal walking and vertical climbing in the Australian green tree frog (Ranoidea caerulea).

Despite the high mechanical demands associated with climbing, the ability to ascend vertically has evolved independently in most major animal lineages. However, little is known about the kinetics, mechanical energy profiles or spatiotemporal gait characteristics of this locomotor mode. In this study, we explored the dynamics of horizontal locomotion and vertical climbing on both flat substrates and narrow poles in five Australian green tree frogs (Ranoidea caerulea). Vertical climbing is associated with slow, deliberate movements (i.e. reduced speed and stride frequency and increased duty factors) and propulsive fore-aft impulses in both the forelimb and hindlimb. By comparison, horizontal walking was characterized by a braking forelimb and a propulsive hindlimb. In the normal plane, tree frogs mirrored other taxa in exhibiting a net pulling forelimb and a net pushing hindlimb during vertical climbing. In terms of mechanical energy, tree frogs matched theoretical predictions of climbing dynamics (i.e. the total mechanical energetic cost of vertical climbing was predominantly driven by potential energy, with negligible kinetic contributions). Utilizing power as a means of estimating efficiency, we also demonstrate that Australian green tree frogs show total mechanical power costs only slightly above the minimum mechanical power necessary to climb, highlighting their highly effective locomotor mechanics. This study provides new data on climbing dynamics in a slow-moving arboreal tetrapod and raises new testable hypotheses about how natural selection can act upon a locomotor behavior that is notably constrained by external physical forces.

Dynamic modeling and vibration control of barge offshore wind turbine using tuned liquid column damper in floating platform

This study investigated the vibration suppression of a barge-type floating offshore wind turbine (FOWT) using a passive tuned liquid damper (TLCD) in the floating platform. The fully coupled aero-hydro–servo-elastic model was established using OpenFAST, and it was used to evaluate the suppression performance of the TLCD in the time and frequency domains. To optimally design the TLCD parameters, a 3-degree of freedom (DOF) model was proposed based on the Lagrange equation for a barge-type FOWT with a platform TLCD, which accounts for the DOF of platform pitching, tower bending in the fore–aft direction, and vertical-liquid column motion of TLCD. The unknown parameters of the 3-DOF model were estimated and validated to ensure result accuracy. The exhaustive search method was implemented to obtain the optimized TLCD parameters of the barge-type FOWT, and the simulation results showed that TLCD can effectively mitigate the structural vibration of barge-type FOWT. When applying a large TLCD mass to the barge platform for structural vibration control, replacing part of the ballast with a TLCD of equal mass to maintain the overall mass of the barge-type FOWT was prioritized.