Flexible Blades Research Articles

Effect of Vertical Confinement and Blade Flexibility on Cross-Flow Turbines

Both scientific and industrial communities have a growing interest in marine renewable energies. There is a wide variety of technologies in this domain, with different degrees of maturity. This study focuses on two models of a mast-free vertical axis Darrieus tidal turbine with the objective of characterizing the effect of vertical confinement, rotor configuration, and fluid–structure interactions on their performances in free-surface flows. The first model comprised four straight rigid blades maintained by circular flanges on both ends of the rotor and the second model is equipped with free-ended interchangeable blades attached to a single upper flange. Two configurations of the second model mounted with either rigid or flexible blades were used, first for comparison with the dual-flange turbine, then in order to address the effect of fluid–structure interactions on the turbine performances. While the single-flange models exhibit a significantly lower efficiency at all operating points, it is observed that the use of flexible blades tends to enhance turbine performances at low Reynolds numbers. The flow topology obtained from PIV measurement at selected operating points is discussed with respect to the performance of each turbine model in order to highlight the role of the dynamic stall and blade–vortex interactions.

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.

A study of nonlinear aeroelastic response of a long flexible blade for the horizontal axis wind turbine

As long flexible blades in large wind turbines are prone to excessive bending deformations, there are failures in dynamic analyses under linear (small deflection) conditions. Thus, a large deflection blade model is developed here to study the dynamic response. The updated Lagrangian equation is used to derive the large deflection blade model from the Euler–Bernoulli beam. Then, the nonlinear aeroelastic dynamics equations of the blade are established using blade element momentum (BEM) theory, and time-domain simulations are performed using the nonlinear Newmark and Newton–Raphson methods. The effects of structural vibrations and aerodynamic damping are considered throughout the process. Finally, the nonlinear model is applied to the DTU 10 MW wind turbine. The results show that under steady and below-rated wind speeds, the flapwise deflection of the nonlinear blade is smaller than that of the linear blade. However, this phenomenon is the opposite for above-rated wind speeds. Under a step wind, the model responds quickly to the blade’s flexible deformation. Under turbulence, the linear results are consistent with the DNVGL Bladed 4.3 results, indicating that the nonlinear blade based on the linear Euler–Bernoulli beam is reliable. Meanwhile, the flapwise deflection for both blades fluctuates slightly when turbulent speeds are lower than the rated speed (0–5 s and 41–50 s), which is distinct from the steady-state analysis. In the aeroelastic coupling analysis, responses that consider vibration feedback are significantly smaller than those without feedback, and a nonlinear blade is significantly more affected in the flapping direction than a linear blade. Finally, the aerodynamic performance of large wind turbines is negatively affected by certain turbulent wind speeds.

Dynamic Response of a Flexible Multi-Body in Large Wind Turbines: A Review

Dynamic response of flexible multi-body large wind turbines has been quickly growing in recent years. With the new normal economic policy, the economy of China is developing innovatively and stably. New energy development and utilization is an important strategy for people’s lives and economic development around the world. It is feasible to analyze from a broad perspective. In particular, the development and application of wind power is affecting the economic development of industry to a certain extent. Persistent and significant large wind turbines have cast concern over the prospects of wind power technology, and a comprehensive development potential of wind power technology has been analyzed its potential use in the future. The multi-body dynamics method can better analyze and describe the impact of flexible blade elastic deformation on motion characteristics and provides a practical analysis method for the aeroelastic stability analysis and control system design of wind turbines.

Scaling the thrust and deformations of a rotor with flexible blades

We experimentally investigate the problem of a propulsive rotor submerged in water with flexible blades in both spanwise and chordwise directions. When we rotate the propeller and set an incoming flow, the blades bend and twist. We report measurements of forces and associated blade deformations. We show how the direction and magnitude of the deformation can be understood through simple geometric arguments, and highlight a relationship between the thrust and bending angle.

Numerical investigation of the aerodynamic and wake characteristics of a floating twin-rotor wind turbine under surge motion

To elevate the power capacity of floating wind turbines and cut costs, development towards large-scale systems is underway. However, this requires solving the problem of fatigue loading on large, flexible blades, as well as corresponding improvements to production and installation technology. As an alternative to larger turbines, twin-rotor floating wind turbines have been proposed. The aerodynamic and wake interference characteristics of this twin-rotor are not yet well understood. In this study, we have investigated the power and wake characteristics of a twin-rotor floating wind turbine based on unsteady Reynolds-averaged Navier-Stokes turbulence model for a comprehensive analysis. Specifically, the power and wake recovery of a twin-rotor floating horizontal-axis wind turbine (FHAWT) under surge motion are compared in detail with those of a single floating wind turbine and bottom-fixed case, while both the effects of the three wind directions (β = 0°, 45°, 90°) and spacing ratios (S/D = 1.2, 1.375, 1.5) are considered. The results suggest that the mean power of the twin-rotor is enhanced by a maximum of 13% under surge motion compared to the single rotor, the small spacing ratio promotes the power gain. Surge motion plays a significant role in wake interaction between the twin-rotor and facilitates wake recovery. As compared to the baseline case, both power and wake recovery performance of the twin-rotor are boosted at β = 45°, with an increase in power of 12.7% as opposed to the single rotor. The modified Jensen wake model is proposed for the far-wake region and a modified Gaussian wake model is also suggested for different cases. This study can provide affiliated guidance for the application of the twin-rotor floating wind turbine.

A novel cost-efficient deep learning framework for static fluid–structure interaction analysis of hydrofoil in tidal turbine morphing blade

A tidal turbine can benefit from exquisitely designed morphing blades with a flexible trailing edge by mitigating up to 90% of the load fluctuation in harsh ocean environments, which reduces the overall cost of tidal energy. However, existing fluid–structure interaction (FSI) methods of resolving flow-induced deformation of the blades is computationally expensive, which poses an important challenge to effective morphing blade design. This paper presents a novel static FSI tool based on deep learning to cost-efficiently analyze the fluid–structure coupling of a hydrofoil. Specifically, adopting a convolutional neural network (CNN) to predict the fluid force and finite element method (FEM) to solve the solid structure response, a new CNN-FEM framework with an iterative scheme for solving the FSI problem is developed to achieve equilibrium between the fluid and structural forces. The new framework is used to predict the elastic deformation of the flexible blade section of the hydrofoil to demonstrate its effectiveness in the FSI evaluation. Comparison of the results to those produced by commercially developed software (i.e., Ansys Workbench) shows that this method yields extremely close prediction results of average equivalent stress and an accuracy of more than 92%. Moreover, it is 100 times more computationally efficient than the commercial Ansys Workbench software, requiring less than 3s for one-way FSI calculation. Taking advantage of this cost-effectiveness, the CNN-FEM can be used to achieve the accurate prediction of the deformation characteristics of the flexible hydrofoil under various flow scenarios that lay a foundation for advanced morphing blade design in the future.

A fluid–structure interaction model for large wind turbines based on flexible multibody dynamics and actuator line method

With higher demand of affordable electricity and rapid development of wind turbine technology, scale of wind turbines has been upsizing. As a consequence, blades grow longer and slender. Large geometrically nonlinear deformation and vibration of the blades lead to more challenges in the structural design. In the aerodynamic analysis, traditional blade element momentum theory cannot predict the complicated behavior of these modern blades while fully resolved Navier–Stokes equation methods cost much time modeling and refinement. To overcome these challenges, this paper proposes a new numerical method to analyze turbine aeroelastic performance and fluid–structure interaction based on flexible multibody dynamics and large eddy simulation with anisotropic actuator line method. By comparing the results with various existing numerical methods, we show that the newly proposed method can effectively predict the performance of the wind turbine, such as deformation and power output. We find that blade flexibility poses noticeable impact on the performance of large scale turbines in normal working conditions. The location of nascent vortex is postponed by blade deflection. The max difference between rigid and flexible blades in downstream velocity distributions reaches 10% and occurs at a radial distance around 0.55D. The new method also takes the fluid–structure coupling effect and momentum interaction into consideration and eliminates the non-physical oscillations caused by uncoupled methods. Also, blades deflection and vibration are found to accelerate momentum exchange, which facilitates the wake recovery process. Furthermore,compared to the rigid-blade model, the turbulent kinetic energy obtained by the newly developed flexible-blade model is higher in the low-frequency region, in which large-scale vortices develop and the turbulent mixing effect is strong. This paper is expected to provide a framework for researchers and technology developers to design or estimate the performance of modern large wind turbines.

Stability and dynamical analysis of whirl flutter in a gimballed rotor-nacelle system with a smooth nonlinearity

AbstractWhirl flutter is an aeroelastic instability that affects aircraft with propellers/rotors. With their long and flexible rotor blades, tiltrotor aircraft are particularly susceptible. Whirl flutter is known to have destroyed aircraft and in the best case it constitutes a fatigue hazard. The complexity of whirl flutter analysis increases significantly with the addition of nonlinearities, due to the more complex dynamical behaviours that emerge as a result. Most whirl flutter stability analyses in current literature are grounded in linear theory, preventing the full discovery of the nonlinearities’ effects. Continuation and bifurcation methods (CBM) may instead be used to fully appreciate and analyse the effects of the presence of nonlinearities. Previous CBM-based work on nonlinear gimballed hub rotor-nacelle models, representing those found on tiltrotor aircraft, are capable of whirl flutter in parametric regions declared safe by linear analysis. Furthermore, it was found that they are capable of complex behaviours including limit cycle oscillations, quasi-periodic behaviour and even chaos, though the whirl flutter implications of such behaviours has not been explored. This paper investigates the impact of a smooth structural nonlinearity on the whirl flutter stability of a basic gimballed rotor-nacelle model, compared to its baseline linear stiffness version. A 9-DoF model with quasi-steady aerodynamics, a flexible wing and blades that can move both cyclically and collectively in both flapping and lead-lag motions, producing gimbal flap-like behaviour, was adopted from existing literature. A smooth stiffness nonlinearity was introduced in the blade flapping stiffness and CBM was used to find the new whirl flutter behaviours created by the presence of the nonlinearity. Time simulations, Poincaré sections and spectral analysis were then used to investigate the various behaviours found. This in turn allowed recommendations to be made concerning preferable and/or hazardous parameter combinations of use to the tiltrotor designer.

Flexible blades to improve Darrieus turbine performance and reduce cost

Low cost “sailwing” aerofoils of flexible nylon mounted between a rigid leading edge of circular cross section and a rigid flat trailing edge were investigated in the 1970s and 1980s. Wind tunnel measurements of lift and drag of these aerofoils over the full range of angles of attack were published, but no predictions were made for a complete wind turbine incorporating them. Another paper stated that a sailwing turbine with aerofoils incorporating pivoting aerodynamic profile leading edges was found to exert considerable starting torque. In the present paper, published lift and drag data have been used to predict the performance of a small Darrieus hydrokinetic or wind turbine with sailwing aerofoils, using a standard multiple streamtube model over the full range of tip-speed ratios (TSRs) from 0.5 to 3. To provide a fair comparison, this method is also used to predict the performance of the turbine with symmetrical NACA0018 and cambered Gö420 blade profiles. At all examined TSRs, average torque and power of the turbine with flexible blades are higher than the turbines with rigid blades. For instance, at TSR of 2.5, the flexible blade turbine achieved 55 % and 165 % higher average torque than the turbines with symmetrical and cambered blades, respectively. This finding is attributed to the fact that the flexible blade camber reverses with reversing incidence, producing high lift coefficients at low incidence. Drag is higher for the flexible aerofoil, probably due to separation at the circular cross section leading edge, and measures are suggested to improve this. The flexible aerofoils are very cheap and simple to fabricate, making them an attractive option for affordable hydrokinetic turbines.

Actuator fault tolerant offshore wind turbine load mitigation control

Offshore wind turbine (OWT) rotors have large diameters with flexible blade structures which are subject to asymmetrical loads caused by blade flapping and turbulent or unsteady wind flow. Rotor imbalance inevitably leads to enhanced fatigue of blade rotor hub and tower structures. Hence, to enhance the life of the OWT and maintain good power conversion the unbalanced loading requires a reliable mitigation strategy, typically using a combination of Individual Pitch Control (IPC) and Collective Pitch Control (CPC). Increased pitch motion resulting from IPC activity can increase the possibility of pitch actuator faults and the resulting load imbalance results in loss of power and enhanced fatigue. This has accelerated the emergence of new research areas combining IPC with the fault tolerant control (FTC)-based fault compensation, a so-called FTC and IPC “co-design” system. A related research challenge is the clear need to enhance the robustness of the FTC IPC “co-design” to some dynamic uncertainty and unwanted disturbance. In this work a Bayesian optimization-based pitch controller using Proportional–Integral (PI) control is proposed to improve pitch control robustness. This is achieved using a systematic search for optimal controller coefficients by evaluating a Gaussian process model between the designed objective function and the coefficients. The pitch actuator faults are estimated and compensated using a robust unknown input observer (UIO)-based FTC scheme. The robustness and effectiveness of this “co-design” scheme are verified using Monte Carlo simulations applied to the 5MW NREL FAST WT benchmark system. The results show clearly (a) the effectiveness of the load mitigation control for a wide range of wind loading conditions, (b) the effect of actuator faults on the load mitigation performance and (c) the recovery to normal load mitigation, subject to FTC action.

Study on the Rotation Effect on the Modal Performance of Wind Turbine Blades

With the large-scale development of wind turbines, large flexible blades bear heavier loads. In the actual rotating work of blades, the coupling of structural deformation and motion produces a dynamic stiffening effect and spin softening effect, which affects the dynamic characteristics of blades. In this study, the finite element method is used to model the NREL 5MW blade, and the dynamic stiffening and spin softening effects are investigated using the modal analysis. The influence of rotating effects on the blade’s natural frequency is revealed. It is concluded that the effect of dynamic stiffening is more significant than that of spin softening, and the comprehensive result of the two effects is not simply the superposition of them but presents obvious nonlinearity.

Influences of blade crack on the coupling characteristics in a bladed disk with elastic support

In aero-engines, the blades are exposed to severe environments and subjected to complex conditions, which can cause damage and cracks. Existing analytical models focus primarily on the blade crack in a single blade. Even in the cracked-bladed disk system, most theoretical models are based on the rigid disk assumption, and few studies pay attention to the boundary conditions of the disk. A new model is proposed in this paper to compensate for deficiencies in existing theoretical models. The flexible disk and blade are deduced based on Kirchhoff plate and Timoshenko beam theories. The crack-caused stiffness loss is calculated through the released strain energy. In addition, the elastic support on the disk's inner edge is simulated by the linear spring stiffness and torsional stiffness. The accuracy of the developed model is verified by comparing it with the finite element method and experimental test. After that, the influences of the crack depth and crack location on the coupling characteristics of the system are systematically investigated. The results indicate that blade crack mainly affects the blade-predominated modes, leading to the mistuned disk mode shapes, which are symmetrically distributed along the line between the cracked blade and the disk center. Moreover, as the blade crack becomes severe or approaches the blade root, the first natural frequency of the paired orthogonal modes decreases; the first mode shape of the paired tuned high nodal diameter degenerates into mistuned low nodal diameter; the new coupling characteristics between the mistuned disk and elastic support become more stronger. The proposed methodology can serve as a theoretical basis for diagnosing faults and monitoring safety in the bladed disk coupling system.

FLUID DYNAMIC PERFORMANCE AND PERFORMANCE ANALYSIS OF A NOVEL FLEXIBLE OSCILLATING WIND TURBINE

While the variable pitch angle design has been proven to significantly enhance the performance of vertical axis wind turbines, its implementation requires the addition of extra mechanical devices, such as a chain-and-sprocket system. These additional mechanisms not only increase system friction and produce extra vibrations but also cause vertical axis wind turbines to lose their omnidirectional characteristics. To address this issue, this study proposed a novel flexible oscillating wind turbine, wherein the function of changing the pitch angle is accomplished through the deformation of flexible blades. To reveal the internal flow field mechanism of this novel turbine, particle image velocimetry experiments were conducted. The results indicate that the flexible blade can alter its posture to form a suitable angle of attack under different azimuth angles. In the downstream region, the blades spread out to generate a substantial positive torque. In contrast, in the upstream region, the blades are in a diversion state, always maintaining a small angle of attack to avoid generating excessive negative torque. Wind tunnel experiments were carried out on the flexible oscillating wind turbine to explore the effects of wind speed and key geometric parameters on the turbine’s performance. The results show that the novel flexible oscillating wind Turbine maintains high efficiency even under low wind speed conditions.

The Behavior of Vertical Axis Water Turbine With Flexible Blades: Self-Start, Ventilation, and Cavitation

Abstract Three-bladed Darrieus-type vertical axis water turbine is a promising solution for producing electricity with minimal impact on the environment. Although considered a viable option, straight-bladed Darriues-type turbines have not been used commonly due to various operational issues; self-start and stall at low water speeds while ventilation and cavitation are limiting at high water speeds. In this study, the use of flexible blades with an aspect ratio of 2.21 is investigated at water velocities of 0.34, 0.51, 0.68, and 0.85 m/s experimentally. A stiffer turbine that has an 85–95 Shore A hardness blade starts to rotate at 0.51 m/s flow velocity. The more flexible turbine that has a 75–85 Shore A hardness blade starts to rotate at lower water velocities and experiences low rotational speeds resulting in an improved self-start. However, low rotation speed will cause a reduction in the coefficient of performance (Cp). High-speed imaging of the flow field also shows that a low tip speed ratio (TSR) helps to prevent the occurrence of ventilation and cavitation for the turbine with 75–85 Shore A hardness blades.

FLUID DYNAMIC PERFORMANCE AND PERFORMANCE ANALYSIS OF A NOVEL FLEXIBLE OSCILLATING WIND TURBINE

While the variable pitch angle design has been proven to significantly enhance the performance of vertical axis wind turbines, its implementation requires the addition of extra mechanical devices, such as a chain-and-sprocket system. These additional mechanisms not only increase system friction and produce extra vibrations but also cause vertical axis wind turbines to lose their omnidirectional characteristics. To address this issue, this study proposed a novel flexible oscillating wind turbine, wherein the function of changing the pitch angle is accomplished through the deformation of flexible blades. To reveal the internal flow field mechanism of this novel turbine, particle image velocimetry experiments were conducted. The results indicate that the flexible blade can alter its posture to form a suitable angle of attack under different azimuth angles. In the downstream region, the blades spread out to generate a substantial positive torque. In contrast, in the upstream region, the blades are in a diversion state, always maintaining a small angle of attack to avoid generating excessive negative torque. Wind tunnel experiments were carried out on the flexible oscillating wind turbine to explore the effects of wind speed and key geometric parameters on the turbine’s performance. The results show that the novel flexible oscillating wind Turbine maintains high efficiency even under low wind speed conditions.

Simplified complex-valued modal model for operating wind turbines through aerodynamic decoupling and multi-blade coordinate transformation

An efficient modelling methodology for steady-state operating wind turbines is proposed, combining aerodynamic decoupling, multi-blade coordinate transformation, and modal reduction. This leads to a complex-valued, reduced-order modal model for prediction of dynamic responses of the tower-rotor-blade wind turbine system, considering rotor rotation, blade flexibility, and vibration coupling between rotor and tower. A fully coupled finite element model was first developed, with aerodynamic forces linearised and expressed as a viscous aerodynamic damping matrix. A time-invariant state space model is formed using multi-blade coordinate transformation, allowing standard modal analysis. The complex-valued eigenvalues and mode shapes were obtained, and it is shown that the operating wind turbine modes exhibit a combination of tower and blade vibrations. Various degrees of modal reduction are applied to the state space model to obtain a modal model with fewer degrees of freedom, whose performance was evaluated in the time and frequency domain for operating wind turbines in normal condition. The displacement and stress responses are in close agreement with those of the fully coupled model with the first 21 modes included. The model already performs well with 8 modes considered to capture relevant fundamental frequency peaks. This allows significantly reduced computational effort and can be particularly beneficial for fatigue prediction, reliability analysis, and structural identification.

Parked aeroelastic field rotor response for a 20% scaled demonstrator of a 13‐MW downwind turbine

AbstractAeroelastic parked testing of a unique downwind two‐bladed subscale rotor was completed to characterize the response of an extreme‐scale 13‐MW turbine in high‐wind parked conditions. A 20% geometric scaling was used resulting in scaled 20‐m‐long blades, whose structural and stiffness properties were designed using aeroelastic scaling to replicate the nondimensional structural aeroelastic deflections and dynamics that would occur for a lightweight, downwind 13‐MW rotor. The subscale rotor was mounted and field tested on the two‐bladed Controls Advanced Research Turbine (CART2) at the National Renewable Energy Laboratory's Flatiron Campus (NREL FC). The parked testing of these highly flexible blades included both pitch‐to‐run and pitch‐to‐feather configurations with the blades in the horizontal braked orientation. The collected experimental data includes the unsteady flapwise root bending moments and tip deflections as a function of inflow wind conditions. The bending moments are based on strain gauges located in the root section, whereas the tip deflections are captured by a video camera on the hub of the turbine pointed toward the tip of the blade. The experimental results are compared against computational predictions generated by FAST, a wind turbine simulation software, for the subscale and full‐scale models with consistent unsteady wind fields. FAST reasonably predicted the bending moments and deflections of the experimental data in terms of both the mean and standard deviations. These results demonstrate the efficacy of the first such aeroelastically scaled turbine test and demonstrate that a highly flexible lightweight downwind coned rotor can be designed to withstand extreme loads in parked conditions.

A novel forecasting method of flutter critical wind speed for the 15 MW wind turbine blade based on aeroelastic wind tunnel test

Flutter is one of the primary challenge that has to be overcome for the development of super-large wind turbine blade. Although the vibration wind tunnel test based on an aeroelastic scale model is the most effective solution, similarity ratio and measuring accuracy of the model cannot be solved accurately by traditional methods. In this study, a novel aerodynamic-stiffness mapping integrated three-dimensional complete aeroelastic scale model design method of super-long flexible blades based on the principle of equivalent stiffness of main beam was proposed for the first time. Later, synchronous full-wind angle wind tunnel tests of vibration and force measurement were carried out using the high-speed photography technology and a high-frequency six-component balance. The nonlinear dynamic response spectral characteristics of NREL-15MW super-long flexible blades were discussed systematically. A comparative analysis of flutter performances and critical instability state of wind turbine blades based on blade tip deflection and blade root reaction force was carried out, which proved the feasibility of forecasting flutter performances according to blade root reaction force. Finally, the blade root reaction force method for flutter instability forecasting of super-long flexible blades was put forward. Results show that the proposed aeroelastic scale model design and experimental method can simulate dynamic performances and flutter behaviors of wind turbine blades accurately and effectively. In the test, it finds that the super-long flexible blades flutter in pitch angle ranges of 93°–96° and 284°–287°. In the flutter ranges, the flutter critical wind speed decreases firstly and then increases with the increase of pitch angle, reaching the valley (5.4 m/s) at 94°. The blade root reaction force and blade tip deflection have consistent divergence and strong correlation. It is suggested that the wind turbine blade enters into the flutter critical state when the flutter index of blade root reaction force is δ ≥ 2%.

Theoretical and experimental investigations on steady-state responses of rotor-blade systems with varying rotating speeds based on a new nonlinear dynamic model

Rotor-blade systems are major units in turbine structures, whose dynamic responses will affect structural safety, energy conversion efficiency, overall durability and service performance. During high-speed rotation, periodic disturbances near resonant regions may lead to a large deflection of flexible blades and an unstable rotation of rotor-blade systems. Due to the coupling effect of rotation and vibration, the distributions of mass/inertia, damping and stiffness are related with varying rotation speed and local deformation in rotor-blade systems, which has not been concerned in conventional harmonic balance methods. In this paper, a modified harmonic balance method is proposed to obtain dynamic responses of rotor-blade systems with a comprehensive model in incremental form, which considers geometric nonlinearity, centrifugal and gyroscopic effects of flexible blades and nonlinear constraints between rotor and multiple blades. Based on Reddy’s high order shear deformation plate theory, dynamic equations for a rotating composite blade with a pre-setting angle is established with consideration of von Kármán type geometrical nonlinearity, varying rotating speeds and equivalent aerodynamic loads. A coupling motion equation for rotor-blade systems is derived out by assembling corresponding elemental equilibrium and joint nonlinear constraints. Steady-state responses are obtained by using a modified harmonic balance method which accounts nonlinearities of mass, damping and stiffness. Numerical and experimental studies for rotor-blade systems are carried out to validate the effectiveness of the proposed model. Results show that a higher rotating speed leads to larger natural frequencies of rotor-blade systems, and a more evidently coupling effect between motion and vibration. Meanwhile, joint constraints, damping effect and load distributions have evident influences on vibration amplitudes and resonant points of system’s steady-state responses.