Edgewise Direction Research Articles

Aerodynamic characteristics of wind turbines considering the inhomogeneity and periodic incentive of wake effects

In wind farms, the wake can lead to a loss of output power, and the uneven characteristics of wake can also exacerbate the fatigue load of downstream wind turbine (WT), affecting their operating life. To explore the impact of wake effects on downstream WT, this article proposes a new method for calculating the load of WT wake wind conditions and verifies it. Establishing a 3DJG wake model coupled with improved BEM for wind turbine aerodynamic performance calculation method. The influence of downstream WT operation phase angle and positions of 3D wake on the time-varying aerodynamic characteristics of downstream WTs was discussed from three perspectives: Blade elements on the spanwise, single blade and wind rotor. Results shown that: (1) For the blade element, calculated the shear force in the flapwise direction and the edgewise direction on each blade segment. The overall shear force of blade element in the vertical upward direction of WT blades is significantly greater than that in other directions. The non-uniformity of the wake is not sufficient to change the position of the maximum shear force on the blade. The position of the maximum shear force at each wake position is in the rear segments of the blade; (2) For the single blade, the most severe load fluctuation occurs when it is in the partial wake condition. The period of this fluctuation is 360°. When in full wake condition, the load fluctuation is relatively small, and due to the symmetry of the wake, the load fluctuation period is only 180°. The load standard deviation (SD) of the partial wake condition increases by 51 % compared to the full wake condition. (3) For the wind rotor, different wake positions have a weighty impact on the power loss of the WT rotor. Compared to the incoming shear wind, the power loss at the wake center can reach up to 54.22 %. At the wake boundary, the power loss of the WT is only 5.6 %. The non-uniformity of wake also has a periodic impact on the power output of the entire WT rotor, with the fluctuation period is 120°, and the fluctuation amplitude of no more than 2 %. This article provides a more intuitive quantitative analysis of the impact of wake on the time-varying aerodynamic characteristics of downstream WTs. It has certain reference value for the design strength verification of WTs, as well as the yaw strategy and layout design of wind farms.

Numerical Simulation Method for the Aeroelasticity of Flexible Wind Turbine Blades under Standstill Conditions

With the trend towards larger and lighter designs of wind turbines, blades are progressively being developed to have longer and more flexible configurations. Under standstill conditions, the separated flow induced by a wide range of incident flow angles can cause complex aerodynamic elastic phenomena on blades. However, classical momentum blade element theory methods show limited applicability at high angles of attack, leading to significant inaccuracies in wind turbine performance prediction. In this paper, the geometrically accurate beam theory and high-fidelity CFD method are combined to establish a bidirectional fluid–structure coupling model, which can be used for the prediction of the aeroelastic response of wind turbine blades and the analysis of fluid–structure coupling. Aeroelastic calculations are carried out for a single blade under different working conditions to analyze the influence of turbulence, gravity and other parameters on the aeroelastic response of the blade. The results show that the dominant frequency of the vibration deformation response in the edgewise direction is always the same as the first-order edgewise frequency of the blade when the incoming flow condition is changed. The loading of gravity will make the aeroelastic destabilization of the blade more significant, which indicates that the influence of gravity should be taken into account in the design of the aeroelasticity of the wind turbine. Increasing the turbulence intensity will change the dominant frequency of the vibration response in the edgewise direction, and at the same time, it will be beneficial to the stabilization of the aeroelasticity response.

In-situ monitoring of an offshore wind turbine blade using acceleration and strain measurements

One of the most critical components of wind turbines is the blades. As blades are constantly exposed to weather and high loads, they can wear and become damaged. Performing in-situ continuous monitoring can help detect sudden damages and prevent further degradation, which is imperative to avoid economic losses and fatal accidents. However, monitoring a rotating rotor blade presents some challenges. One challenge is the consideration of lightning protection. Hence, a non-conductor measurement system must be used. Another challenge is system identification and modal tracking considering environmental and operational conditions (EOCs). Furthermore, vibration-based monitoring results from actual and operational rotor blades are scarce in the existing literature. This study centres on operational modal analysis (OMA) using covariance- driven stochastic subspace identification (SSI-COV) of an offshore wind turbine blade in operation employing eight months of data from fibre optic accelerometers (FOA) and fibre Bragg grating (FBG) strain gauges. The identification focuses on the first two bending modes in flapwise and edgewise directions and the first torsional mode. The study aims to determine which fibre optic sensor delivers better results. Furthermore, it addresses the effect of EOCs on the modal parameters, where system identification and modal tracking are discussed. It was found that tracked modes showed similar trends with respect to time, and a high connection was observed between wind speed, rotor speed, and pitch angle with frequency and damping. Additionally, acceleration and strain measurements deliver the same frequency and damping values. FBG better identified the first flapwise mode. On the other hand, FOA was superior in almost all other modes. This study points towards employing FOA for vibration-based monitoring of wind turbine blades using modal parameters.

Alterations to the bending mechanical properties of Pinus sylvestris timber according to flatwise and edgewise directions and knot position in the cross-section

Given the heterogeneity of the material, the behaviour of a timber beam may differ depending on which of its sides is subjected to tension and which one is subjected to compression. An analysis is undertaken in the present work of the behaviour in non-destructive bending tests on the four sides of 57 samples of Pinus sylvestris (scots pine) of structural size (2000 × 100 × 70 mm3). A study is additionally performed of the influence of the size and position of knots in the cross-section. The modulus of elasticity in flatwise direction was found to be 3 % higher than in edgewise direction. This difference could be attributable to the shear effect. While the introduction of knottiness variables did not improve modulus of elasticity prediction, it did decrease the error in the prediction of the modulus of rupture. The margin knot area ratio corresponding to the outer eighth of the cross-section’s width occupied by knots was the knottiness variable with the lowest error in modulus of rupture prediction.

Control of edgewise vibration of a pre-twisted rotating beam with shunted piezoelectric tuned mass damper

The edgewise vibration control of a pre-twisted beam, rotating in the vertical plane, is considered in this study. A piezoelectric tuned mass damper (PTMD) comprising a spring–mass–damper system and a piezoelectric transducer with its associated shunt circuit is considered the control device. A finite element formulation of the pre-twisted rotating beam with the attached PTMD is developed while considering the effect of centrifugal stiffening due to rotation and the effect of gravity force. The natural frequencies of the beam (without PTMD) obtained using the present formulation are corroborated by comparing them with the results derived from Ansys. A single PTMD attached at the tip end of the beam can effectively suppress the response of the beam subjected to a distributed load in the edgewise direction. The best values of resistance and inductance of the shunt circuit are obtained through a parametric study on the peak and root mean square value of the beam tip response. A qualitative difference in the uncontrolled as well as in the controlled responses can be noticed while considering the effect of the gravity load component in the edgewise direction. Further, it has been observed that the conventional Tuned Mass Damper (TMD) provides better control than the PTMD system for ideally tuned conditions, however, the control performance of TMD degrades rapidly as compared to the PTMD in the presence of detuning. This demonstrates the effectiveness of PTMD in a practical implementation where achieving the perfectly tuned condition is seldom realized. The control performance of PTMD marginally degrades when the beam is subjected to multi-directional excitation. Hence, the proposed control system has the potential for application in rotating beam-type structures, such as wind turbine blades.

Impact of rotor blade aerodynamics on tower vortex induced vibration of modern wind turbines

Modern wind turbines in standstill or idling could experience vortex induced vibrations (VIV); the origin of these vibrations is either shedding from the wind turbine blade referred to as blade VIV or shedding from tower termed as tower (or turbine) VIV. When the whole structure of the wind turbine is considered and the blades are pitched out, the dominant 1st order mode for blade deformation in edgewise direction leads to negligible motion of the tower top, while when the whole turbine vibrates with first tower mode, blades also undergo significant periodic translations and deformations. In this study, forced motion is used to study the impact of aerodynamic damping due to rotor moving with 1st tower mode. In the literature no comprehensive work is available to characterize the impact of blades aerodynamics in the turbine mode either using systematic tests or high-fidelity computational fluid dynamics (CFD). In this article high-fidelity numerical simulations are performed to compute the power injections from the rotor blades when the turbine moves in 1st tower mode. Depending on the inflow angle and the azimuthal position, blades can inject significant power. Thus, the estimated damping from tower-only empirical models could severely underestimate the total aerodynamic power if the power injection from the rotor is neglected.

Autonomous Sensor System for Low-Capacity Wind Turbine Blade Vibration Measurement.

This paper presents the design, implementation, and validation of an on-blade sensor system for remote vibration measurement for low-capacity wind turbines. The autonomous sensor system was deployed on three wind turbines, with one of them operating in harsh weather conditions in the far south of Chile. The system recorded the acceleration response of the blades in the flapwise and edgewise directions, data that could be used for extracting the dynamic characteristics of the blades, information useful for damage diagnosis and prognosis. The proposed sensor system demonstrated reliable data acquisition and transmission from wind turbines in remote locations, proving the ability to create a fully autonomous system capable of recording data for monitoring and evaluating the state of health of wind turbine blades for extended periods without human intervention. The data collected by the sensor system presented in this study can serve as a foundation for developing vibration-based strategies for real-time structural health monitoring.

Active Edgewise Blade Damping Control of Large Wind Turbines by Using the Pitch Controller and an Interval Observer

Large wind turbines have typically poorly damped structures. Hence, the absence of damping leads to aeroelastic oscillations, and the operational rotor speed can approach the critical rotor speed. By using damping injection, the control system can actively introduce some additional damping. In the present work, a control approach to reduce oscillations of the rotor blades in the edgewise direction is proposed. The concept is based on the damping injection mechanism, and an additional level of safety is obtained by introducing the Dynamic Safety Margin (DSM) in the control law. The feedback control scheme requires some unmeasurable variables. This aspect is covered by using an interval observer. The control approach is tested by using simulations on a high-definition model implemented in an aeroservoelastic code. Simulation results are very satisfactory and promising for future experiments using hardware-in-the-loop equipment.

Field load testing of wind turbines based on the relational model of strain vs load

Compared to theoretical calculations, field blade load testing can more accurately obtain actual load characteristics. The main challenge is the field relationship correction of strain vs load. The initial state of the strain sensing installation can be divided into two scenarios. One scenario is to install before the blade is lifted and another is to install online during the service of wind turbines. The key analysis is conducted on the field correction of the relationship of strain vs load, and corresponding correction strategies are constructed. A decoupled calculation model for strains in the edgewise direction induced by the aerodynamic moment and the gravity moment is proposed. Ground and online experiments for blade strain testing have been carried out. Through the combination of strain testing data and SCADA data, some new insights have been gained on strain characteristics. For example, the mapping coefficient of strain vs load induced by the aerodynamic moment varies under different operating conditions, while the mapping coefficient of strain vs load induced by gravitational moment is relatively stable. When the power of the wind turbine is 552 kW, 853 kW, and 1379 kW, the coefficients induced by the aerodynamic moment are 2270 N m/μɛ, 2480 N m/μɛ, and 3224 N m/μɛ, respectively.

Load bearing investigations on novel Acrylonitrile butadiene styrene‐carbon quantum dots 3D printed core/bamboo fiber polyester sandwich composite for structural applications

AbstractIn this research, a novel 3D printed core and natural fiber polyester composite skin based thick sandwich panel was developed as structural material for domestic and commercial infrastructure applications. The main objective of this research was to analyze how the carbon quantum dots (C‐dots) from agriculture waste strengthen the softer thermoplastic acrylonitrile butadiene styrene (ABS) core and overall sandwich panel's load bearing properties. The core of sandwich was prepared using additive manufacturing method whereas the skin was developed by hand layup method. According to the results the C‐dots of 20 phr into the ABS improved the compression properties of core in both flatwise and edgewise directions. A highest tensile and flexural strength of skin was observed to be 114 and 146 MPa respectively. The addition of C‐dots improved the load bearing effect and also restricts the deformation against load. This performance improved novel 3D printed core and bamboo fiber skin sandwich could be used as an alternative construction and building material where the commercial plywood and other forms of powder wood face damages via weather and termite issues.Highlights Higher filler volume of up to 20 phr of carbon quantum dots in acrylonitrile butadiene styrene (ABS) were developed Novel 3D printed thin walled core of 1 mm diameter was developed using carbon quantum dots and ABS. Bamboo fiber‐polyester skin with highest tensile strength of 114 MPa was developed. Improved flatwise compression and tensile strength were achieved for ABS core with 20 phr of Carbon quantum dots Flexural strength and edgewise compression properties were improved with 20 phr of Carbon quantum dots in ABS

Smart optimized structural control of onshore wind turbines with MR dampers

This paper presents an effective control approach for structural vibration of onshore wind turbines in the edgewise direction. Huge multi mega-watt wind turbines are currently developed to harvest large amounts of energy from the wind. Such designs require the construction of huge slender blades and towers which consequently lead to undesirable structural deformations that hinder the power production and reduce life span of the wind turbine. Many researchers have worked on structural control of wind turbines. However, these efforts neither have resulted in an effective reliable mitigation for deformation of structural elements, nor they have achieved an economical solution in terms of actuators exploitation. The work presented in this paper, however, introduces a particle swarm optimisation-based semi-active controller which exploits magnetorheological dampers to mitigate edgewise blade displacements. Dampers are modelled using neural networks for they are capable of predicting future forces and eliminating control lag. The developed controller is tested at several configurations of actuators placement on a benchmark 5-MW wind turbine. The proposed approach, indeed, showed a significant reduction of over 80% in the peak responses and about 77% of peak-to-peak response of blades against uncontrolled and passive systems which leads to promoting longevity of wind turbines.

Wind turbine blades load matching method under biaxial fatigue test

In order to improve the fatigue test accuracy and efficiency of full-scale structure of wind turbine blades, an effective load matching method for full-scale structure fatigue test of wind turbine blades under biaxial loading is proposed. The blade biaxial loading fatigue test scheme is designed. The transfer matrix method is used to calculate the test bending moment under biaxial loading. The particle swarm optimization algorithm is designed to optimize the position and mass of the excitation device in the flap-wise and edgewise directions and the position, mass and quantity of the fixed counterweight. Based on this, the calculation model of the test bending moment and the data of the target bending moment are integrated into the particle swarm optimization algorithm to achieve the optimal matching of the biaxial loading fatigue test load, Finally, a numerical example is given to verify it. The results show that this method can make the test load closer to the target load, further accelerate the popularization of biaxial loading fatigue test, and provide a certain theoretical reference and application value for engineering practice.

Vibration Control of Large Wind Turbine Blades with Unidirectional Cable Pendulum Damper

A unidirectional cable pendulum damper is proposed to mitigate vibration responses of large-scale wind turbine blades in the edgewise direction, and the effectiveness of the proposed device for vibration response control is investigated. First, the configuration and working principles of the vibration damper are introduced. Second, the Euler–Lagrange equation of the single blade vibration damping system with the vibration damper is derived based on the Hamilton’s principle. At last, considering the effect of blade rotation, the wind load that applied on the blade was calculated using the rotating sample spectrum. The dynamic responses of blades are also calculated using the MATLAB/Simulink platform. The peak value and standard deviation of blade responses were taken as evaluation indexes to evaluate the vibration control efficiency of the device with varying the parameters such as the mass ball pendulum length, the fixed pulley block installation position, the stiffness and the pre-stress of the flexible cable. The optimal parameters of the vibration damper are investigated and obtained based on the assumption that no pounding happens between the mass ball of the vibration damper and the inner wall of the blade. Results show that the length of the mass ball pendulum and the installation position of the fixed pulley block, the values of which are within a reasonable range, can ensure the optimal performance of the vibration damper. The displacement of the mass sphere can be effectively reduced by increasing the stiffness of the flexible cable, and the pre-stress shows marginal beneficial effect on the damping performance and the displacement control of the mass sphere. Using the optimum parameters, the vibration damper can keep the mass ball within a safe running distance. The reduction of the peak value and the standard deviation of the blade displacement can reach 89.36% and 89.83%, respectively. The proposed device space can effectively reduce the blade tip response of the wind turbine by occupying less space. Moreover, the size of the device installation space can be changed by adjusting the weight ball swing length, which is suitable for the vibration control of the wind turbine blade edgewise direction.

Bending Strain Sensitivity of Critical Current in REBCO Coated Conductor Winding for Coil Application at 77 K

High-temperature superconducting (RE)Ba₂Cu₃ O_7-x (REBCO)-coated conductor (CC) tapes are known for their capacity to tolerate high tensile stress under uniaxial tension, which is typically in the range of 600-700 MPa at 77 K. However, when used in a coil, there is a limit to the allowed strain before degradation of the critical current (<i>I</i>_c) occurs. This is attributed to the combined strain due to bending and axial tension which was caused during fabrication, cool down, and operation of coils and magnets and corresponds to the irreversible strain limit of <i>I</i>_c degradation. Applied strain along the CC tape&#x0027;s edgewise direction (hard bending strain) also affects the irreversible strain limits of <i>I</i>_c considerably. With such conditions, degradation of the REBCO coil performance can be expected. Therefore, the current study aims to systematically investigate the mechanism for such <i>I</i>_c degradation in REBCO coils. Linear superposition of strains induced in different modes of easy and hard bending were studied analytically and experimentally. The <i>I</i>_c degradation behaviors were examined in IBAD&#x002F;REBCO CC tapes in windings with different pitches on mandrels with different diameters. The investigation was done at 77 K and in self-field conditions using an apparatus designed for coil testing. The bend strain parameters in coils were analyzed, including the radius of curvature and pitch between CC tape turns. Through the linear superposition of strains induced in the REBCO coils, an appropriate approach is suggested to effectively handle the <i>I</i>_c degradation under winding including edgewise bending.

Study of Centrifugal Stiffening on the Free Vibrations and Dynamic Response of Offshore Wind Turbine Blades

Due to their large and increasing size and the corrosive nature of salt water and high wind speeds, offshore wind turbines are required to be more robust, more rugged and more reliable than their onshore counterparts. The dynamic characteristics of the blade and its response to applied forces may be influenced dramatically by rotor rotational speed, which may even threaten the stability of the wind turbine. An accurate and computationally efficient structural dynamics model is essential for offshore wind turbines. A comprehensive model that takes the centrifugal stiffening effect into consideration could make rapid and accurate decisions with live data sensed from the structure. Moreover, this can enhance both the performance and reliability of wind turbines. When a rotating blade deflects in its plane of rotation or perpendicular to it, the centrifugal force exerts an inertia force that increases the natural frequencies and changes the mode shapes, leading to changes in the dynamic response of the blade. However, in the previous literature, studies of centrifugal stiffening are rarely found. This study investigates the influence of centrifugal stiffening on the free vibrations and dynamic response of offshore wind turbine blades. The National Renewable Energy Laboratory (NREL) 5 MW blade benchmark was considered to study the effect of angular speed in the flap-wise and edge-wise directions. The results demonstrate that the angular speed directly affects the modal features, which directly impacts the dynamic response. The results also show that the angular velocity effect in the flap-wise direction is more significant than its effect in the edge-wise direction.

Wind Turbine Blade Design Optimization for Reduced LCoE, Focusing on Design-Driving Loads Due to Storm Conditions

Design modifications of the blade inner structure, targeted at reducing design-driving extreme loads due to storm conditions, are assessed in the present paper. Under survival wind speeds, the lack of sufficient aerodynamic damping in the edgewise direction is responsible for excessive stall-induced vibrations that usually drive wind turbine blade design loads. The modifications considered in the work are (i) a non-symmetric increase in the thickness of the uniaxial and tri-axial material on the suction and pressure side of the blade sections, (ii) a shift in the spar caps in opposite directions and (iii) the ply-angle re-orientation of the laminates on the spar caps. The first two design interventions aim at increasing the damping of the low-damped edgewise modes in the idling rotor, while the third aims at reducing the fatigue and ultimate loads in normal operation. The design parameters in the problem are determined on the basis of a multidisciplinary optimization (MDAO) process, which minimizes the levelized cost of energy (LCoE). The in-house integrated optimization tool employed in the present study combines: (i) a servo-aero-elastic analysis tool for calculating ultimate loads and power yield, (ii) a cross-sectional analysis tool for obtaining structural properties and stress distributions in the modified blades and (iii) a cost model of the overall wind turbine to evaluate the LCoE.

A Review and Case Analysis on Biaxial Synchronous Loading Technology and Fast Moment-Matching Methods for Fatigue Tests of Wind Turbine Blades

Wind power utilization is attracting worldwide attention in the renewable energy field, and as wind power develops from land to sea, the size of the blades is becoming incredibly larger. The fatigue test, especially the biaxial synchronous fatigue test for the blades, is becoming an indispensable step to ensure the blade’s quality before mass production, which means the biaxial independent test presently used may have difficulty reproducing the real damage for large-sized blades that oscillate simultaneously in flap-wise and edgewise directions in service conditions. The main point of the fatigue test is to carry out accelerated and reinforced oscillations on blades in the experimental plan. The target moments of critical blade sections are reached or not during the test are treated as one significant evaluation criterion. For independent tests, it is not hard to realize moment matching using additional masses fixed on certain critical blade sections, which may be not easy to put into effect for biaxial synchronous tests, since the mechanical properties and target moments in the flap-wise and edgewise directions are widely varied. To realize the mechanical decoupling for loading force or additional mass inertia force in two directions is becoming one of the key issues for blade biaxial synchronous fatigue testing. For this problem, the present paper proposed one mechanical decoupling design concept after a related literature review. After that, the blade moment design and target matching approach are also proposed, using the Transfer Matrix Method (TMM) for moment quick calculation and Particle Swarm Optimization (PSO) for case optimization.

Assessment of Different Measurement Methods/Techniques in Predicting Modulus of Elasticity of Plantation Eucalyptus nitens Timber for Structural Purposes

The mechanical properties of plantation Eucalyptus Nitens timber are currently assessed by applying visual stress grading (VSG) designed for the sawn timber from the mature plantation and do not represent the actual characteristics of the resource. However, the well-known limitation of VSG application for this resource led to the discovery of other methods to grade the timber to its relevant structural grade. There is potential for hardwood plantations in Australia to supply wood to the timber industry and be used in structural applications. However, it is necessary to employ criteria to evaluate the structural properties of this resource before it could be satisfactorily used for structural purposes. This research aimed to assess the use of non-destructive technique (NDT) through acoustic wave velocity (AWV), machine stress grading (MSG), and multiple linear regression (MLR) model to predict the modulus of elasticity (MOE) as a grade-determining factor. The results showed that there was a strong correlation (R2 = 0.88) between the dynamic MOE (MOEdyn) and static MOE (MOEs) of the boards, proving the NDT as a reliable method for the MOE estimations of E. nitens timber. The results from the MLR model also showed that the density and AWV are effective parameters and their combination can be practical to estimate the MOE. There was a high correlation between the MOE obtained from MSG and MOE obtained from four-point bending, demonstrating that the MSG method through the flat-wise bending can be a suitable method for fast grading. The results also indicated that the measured MOE in the edgewise direction correlates with both the flatwise and longitudinal directions. The results also showed that the E. nitens timber resource has the potential to be used in structural applications with a wide range of MOE from 7 GPa to 21 GPa.

The effects of layers orientation on impact energy evaluation of FDM printed specimens

This paper investigates the effects of layers orientation on impact energy absorbed by acrylonitrile butadiene styrene (ABS) test specimens, obtained by additive manufacturing (AM), having three in-plane deposition directions (0°, 45°, and 90°). The specimens were tested with instrumented Charpy hammer, CEAST 9050 Pendulum Impact System, according to standard ISO179-1. Unnotched specimens were tested in edgewise direction based on measured velocity and impact force; absorbed energy was computed. The average energy obtained during impact tests for specimens with the orientation of the layers at 45° was about 0.39 J. For those with layer orientation at 0° and 90°, respectively, it was 0.63 and 0.81 J. A hinge break failure mode was observed for 0° and 90° specimens, and brittle fracture for 45° specimens.

Internal, primary and combination resonances of a wind turbine blade with coupled flapwise and edgewise motions

In recent decades blades of wind turbines have been designed longer and longer for better performance of energy harvesting. The growth in structural flexibility has strengthened the effect of geometric nonlinearity and led to complicated nonlinear dynamic behavior of vibration response. In this paper, an investigation on internal, primary and multi-mode combination resonances of a flexible wind turbine blade with coupled flapwise and edgewise motions is studied. Through the Hamilton's principle, the dynamical model is established using the Euler-Bernoulli beam considering the actions of gravitational and unsteady aerodynamic force. The displacement of the blade is expanded into four basic modes based on the Galerkin's method, three in flapwise direction and one in edgewise direction. The governing equations of the four modal coordinates are solved using the method of multiple scales in transient and steady-state. For the transient responses, the internal and multi-mode combination resonances are revealed by the transfer of energy between resonant modes. Unlike the case of primary and internal resonances, the quasi-periodic under the multi-mode combination resonance is discovered through phase diagram of the first edgewise mode. For the steady-state responses, amplitude-frequency curves and phase diagrams of resonance modes under the primary and multi-mode combination resonance are derived. Influence of the combination resonance on the primary resonance is discussed for the steady-state responses with different aerodynamic force and geometric nonlinearity. Finally, parametric analyses are presented to show how steady-state motion of flapwise and edgewise modes vary with detuning parameters and design parameters.