Dynamic and static performance of the new type of offshore wind turbine blade based on equivalence of BFRP beetle elytron plate

Abstract

In order to avoid the damage of the new type of offshore wind turbine blade (beetle elytron plate blade), it is of great significance to study its dynamic and static stability for the safe operation of the beetle elytron plate blade (BEP blade). In this study, the equivalent model of the beetle elytron plate was proposed to simplify the calculation model of the BEP blade. The static performance of BEP blade under four representative working conditions and its advantages over FRP blades were studied by ANSYS Workbench, and the influence of material type, rotational speed, thickness of skin and web on the dynamic performance of BEP blade was discussed by parametric analysis. The results show that the equivalent plate theory adjusted by dichotomy method is suitable for the equivalence of the cantilevered beetle elytron plate. The first-order natural frequency of BEP blade is more than 1.25 times that of GFRP blade, which is about 43% higher than that of BFRP blade. The natural frequency of the BEP blade generally increases with the increase of the thickness of the skin and web, and the rotational speed and pitch angle has little effect on it. In addition, the pitch and shutdown can significantly reduce the surface stress level of the BEP blade by exerting the bending resistance of the web when the BEP blade under shutdown failure condition. This study provides a reference for engineering design and promotes the application of BEP blade in the field of wind power.

Keywords

basalt fiber reinforced polymer dynamic and static performance wind turbine blade beetle elytron plate equivalent model

Introduction

The bionic integrated honeycomb plate made of basalt fiber reinforced polymer (BFRP) is composed of small column-honeycomb core layer and plates and prepared by integration molding technology (To prevent local fiber deficiency, a suitable amount of fiber is pre-placed above each small column. The chopped basalt fibers and basalt twistless yarns are uniformly laid within the plate space, the integrated molding technique is shown in Figure 1.) (Chen et al., 2012a; 2012b, 2021a). Compared with traditional honeycomb plate, the core layer of beetle elytron plate has circular hollow columns, which makes it have better mechanical properties (Tuo et al., 2021; Zhang et al., 2019). As a green inorganic material, BFRP has excellent properties such as corrosion resistance, high temperature resistance, light weight and high strength (Chikhradze et al., 2015; Wu, 2018). The application of BFRP beetle elytron plate in the skin and web of offshore wind turbine blade can make the wind turbine blade a box-type thin-walled spatial shell structure (The ribs are primarily connected to other parts of the blade using adhesive bonding (Figure 2)) (Zheng et al., 2022, 2024) with high strength and high rigidity. The cost of basalt fiber blades is about 1.5 to 2 times that of glass fiber blades, while the cost of carbon fiber blades is 5 to 10 times that of glass fiber blades. With a balanced profile of moderate cost and high performance, basalt fiber is a promising alternative—particularly for large, high-capacity offshore wind turbine blades. The novel type of blades proposed in this study is based basalt fiber reinforced polymer (BFRP) and honeycomb bionic plate structure, offering a combination of light weight, high strength, corrosion resistance, and excellent fatigue performance. These attributes make it well-suited to meet the growing demands for longer and higher-performance offshore wind turbine blades.

Figure 1.

The preparation process of basalt fiber bionic plate by integrated molding technique (Chen et al., 2021a).

Figure 2.

The offshore wind turbine blade with basalt fiber bionic plate (Zheng et al., 2022, 2024).

When the bionic plate is applied to large-span spatial structures, the establishment of refined model of bionic plate will consume huge time and cost, which requires the establishment of a reasonable and reliable equivalent model of bionic plate. Many scholars have studied the equivalent model (Dong et al., 2014; Li et al., 2015; Sorohan et al., 2016) of honeycomb plate mainly including honeycomb plate theory, equivalent plate theory and sandwich plate theory. Beetle elytron plate and honeycomb plate have similar mechanical properties (Zhao et al., 2023), but it is still unknown whether the equivalent theory of honeycomb plate can be applied to the beetle elytron plate. Therefore, it is necessary to study the difference in mechanical properties between the beetle elytron plate and the honeycomb plate, which is the basis for establishing an equivalent model suitable for the beetle elytron plate.

The offshore wind turbine blade is prone to vibration and deformation under the action of strong wind on the sea surface, followed by the resonance risk. Many scholars studied the static and dynamic performance of offshore wind turbine blades. Zhao et al. (2023) proposed a modeling-based dataset augmentation method to monitor the dynamic characteristics of wind turbine blades and verified its reliability. Chen et al. (2021b) proposed a new analysis method for the structural parameters and natural frequency of wind turbine blade by finite element analysis. In order to avoid the damage of FRP blade under strong wind, it is of great importance to study its static and dynamic stability for the safe operation of BEP blade.

In order to investigate the dynamic and static performance of new type of offshore wind turbine blade, this paper explored the static response advantages of the BEP blade compared with several traditional FRP blades and the influence factors of dynamic performance of BEP blade by parametric analysis. Due to the limited technology, the production of wind turbine blades with BFRP beetle elytron plate is still in the exploratory stage. As an exploratory work, this paper attempts to explore the dynamic and static performance of the BEP blade and the numerical analysis model was established based on existing literature (Jonkman et al., 2009; Zhao et al., 2022, 2023, 2023, 2024). In summary, this study provides a reference for engineering design and promotes the application of BEP blade in the field of wind power.

Equivalent model of cantilevered beetle elytron plate

The force mechanism of offshore wind turbine blades during operation is similar to the bending of the cantilevered beam because its longitudinal length is much larger than the chord length of airfoil, as shown in Figure 3. In this paper, the cantilevered honeycomb plate and beetle elytron plate were taken as the research object to explore a suitable equivalent method for the cantilevered beetle elytron plate.

Figure 3.

The force mechanism of offshore wind turbine blade during operation.

Difference in mechanical properties between two types of cantilevered bionic plates (BEP and HP)

Relevant research results (Zhao et al., 2022, 2023; Zheng et al., 2022, 2023, 2024) shown that the equivalent plate theory (Fu et al., 2015) is applicable to the honeycomb plate of large-span spatial structure. However, its applicability to beetle elytron plates remains uncertain and requires further investigation. Therefore, this study examines the mechanical differences between cantilevered beetle elytron plates and honeycomb plates, providing a basis for developing an equivalent model tailored to the cantilevered beetle elytron plate.

To verify the reliability of the cantilevered beetle elytron plate model, a finite element analysis (FEA) model (Figure 4(a)) was established based on the experimental study by Chen et al. (2021) (Figure 1) and compression simulations were conducted (Figure 4(b)). The finite element model employed C3D8R solid elements, with overall dimensions of 300 mm × 150 mm × 150 mm. A comparison between the FEA results and the experimental data shows a load–displacement curve error of only 1.8% (Figure 4(c)), indicating that the finite element model is accurate and reliable for subsequent analyses.

Figure 4.

The finite element analysis (FEA) model of beetle elytron plate and comparison between the FEA results and the experimental data.

According to the bending mechanism of cantilevered beam (Figure 3), when the length of the cantilevered beam is much larger than the width, the flexural stress in the beam plays a leading role, and the shear stress can be almost ignored. In order to better simulate two types of cantilevered bionic plates, the ratio of longitudinal length to transverse width of the cantilevered beam was set to 5:1. Combined with the size (Figure 5) and force mechanism of the cantilevered beam (Figure 3), a uniform load of 250 N/m² is applied to the reference (Zheng et al., 2022).

Figure 5.

Two types of cantilevered bionic plate model (L = 5B).

The details of cantilevered honeycomb plate and beetle elytron plate models are shown in Figure 5. In order to facilitate the establishment of the equivalent model of BFRP bionic plate, it is assumed that the material is an ideal isotropic material, and the results of static tensile test of BFRP specimens in Zheng et al. (2022, 2024) are referenced as shown in Table 1. The element type of the finite element model adopts the solid element C3D8R, and the convergence analysis is carried out with reference to the relevant literature (Zheng et al., 2024). In order to explore whether the equivalent plate theory can be applied to beetle elytron plate, the mechanical performance (load–displacement behavior) of the cantilevered beetle elytron plate and the conventional honeycomb plate was analyzed using nonlinear finite element analysis under static loading conditions. To evaluate dynamic characteristics, a modal analysis was conducted to extract the natural frequencies of the first six vibration modes. All simulations were performed using ANSYS Workbench, with appropriate material properties and boundary conditions applied to represent cantilevered configurations.

Table 1.

The material characteristics of the three different FRP types and the equivalent plate.

Types	Elastic modulus (GPa)	Tensile strength (GPa)	Equivalent Poisson’s ratio	Density (kg/m³)
Grass fiber reinforced polymer	20	0.7	0.28	2.1
Carbon fiber reinforced polymer	160	3.8	0.17	1.8
Basalt fiber reinforced polymer	52.3	0.718	0.28	2.1
Equivalent plate	5.956	0.718	0.28	0.326

Figure 6(a) shows the load-displacement curves of two types of cantilevered bionic plates. The bearing capacity of beetle elytron plate is 20 kN, and the flexural stiffness is 119.8 kN/m, which are 3.4% and 10.2% higher than those of cantilevered honeycomb plate with the same scale, respectively. Figure 6(b) shows the first six-order natural frequencies and first three-order vibration modes of two types of cantilevered bionic plates, respectively. The natural frequencies of cantilevered beetle elytron plate are generally slightly lower than that of cantilevered honeycomb plate and the low-order vibration mode of the cantilevered beetle elytron plate is very similar to that of the cantilevered honeycomb plate. With the increase of modal order, the difference in of vibration mode between the two types of bionic plates caused by flexural stiffness is becoming smaller, which shows that there is no difference in vibration mode between the cantilevered beetle elytron plate and honeycomb plate with the same scale when facing complex vibration.

Figure 6.

Load-displacement curve, first six-order natural frequencies and first three-order vibration modes of two types of cantilevered bionic plates.

The stress nephograms of two types of cantilevered bionic plates are shown in Figure 7. The stress concentration occurred at fixed end of the cantilevered bionic plates, and the stress concentration area of cantilevered beetle elytron plate is about half of that of the beetle elytron plate. The stress concentration area of cantilevered honeycomb plate is a regular hexagon, while the stress concentration area of cantilevered beetle elytron plate is a regular twelve-angle. The above shows that the column-honeycomb core layer of beetle elytron plate can reduce the stress concentration of the honeycomb wall and the plate and reduce the occurrence of weak areas.

Figure 7.

Stress nephograms of two types of cantilevered bionic plates (150 mm × 100 mm).

Through the dynamic and static performance analysis of two types of cantilevered bionic plates, found that the mechanical properties of cantilevered beetle elytron plate under bending load are very similar to those of cantilevered honeycomb plate with the same scale.

Equivalent model of cantilevered beetle elytron plate

Hoff equivalent theory is that the honeycomb plate is equivalent to isotropic plate, and the equivalent elastic modulus and shear modulus can be obtained. According to equivalent plate theory, the equivalent analysis process of the cantilevered beetle elytron plate is similar to that of the honeycomb plate, which has been verified and expanded (Zheng et al., 2022). The flexural performance of cantilevered beetle elytron plate is primarily determined by its elastic modulus. In order to achieve the same flexural stiffness as the cantilevered beetle elytron plate, the equivalent parameters of the cantilevered honeycomb plate were adjusted using the dichotomy method. This allowed for the establishment of an equivalent model for the cantilevered beetle elytron plate based on equivalent plate theory (Zheng et al., 2022).

The equivalent parameters of the equivalent plate such as elastic modulus, shear modulus, relative density and Poisson’s ratio are as follows.

\begin{array}{l} E_{e q} = \frac{2 E_{f} h_{f}}{\sqrt{t_{f}^{2} + 3 {(h_{c} + h_{f})}^{2}}} \\ G_{x e q} = \frac{G_{c x} {(h_{c} + h_{f})}^{2}}{h_{c} t_{e q}}, G_{y e q} = \frac{G_{c y z} {(h_{c} + h_{f})}^{2}}{h_{c} t_{e q}} \\ t_{e q} = \sqrt{h_{f}^{2} + 3 {(h_{c} + h_{f})}^{2}} \\ ρ_{e q} = \frac{2 ρ_{f} h_{f} + ρ_{c} (H - 2 h_{f})}{t_{e q}}, μ_{c q} = μ_{f} \end{array}}

(1)

Where

h_{c}

and

h_{f}

are the thickness of core layer and thickness of plate, respectively.

ρ_{c}

is the density of honeycomb plate,

μ_{f}

is the Poisson’s ratio of honeycomb plate.

t_{f}

is the thickness of honeycomb plate and

t_{e q}

is thickness of equivalent plate.

According to previous studies on cantilevered beetle elytron plate (Section 2.1), the maximum displacement of cantilevered beetle elytron plate under a uniform load of 250 N/m² is 0.5125 mm, and the flexural stiffness is 3.811 N·m². Firstly, the elastic modulus was adjusted in advance to make the flexural stiffness of the equivalent model approximate that of the beetle elytron plate, and it is known that the elastic modulus of the model is between 5900 MPa and 6000 MPa. Then, the elastic modulus was divided into 10 equal parts twice from 5900 MPa to 6000 MPa. The accurate elastic modulus of the beetle elytron plate can be obtained, which is 5956 MPa. At this time, the error of the flexural stiffness between the beetle elytron plate and the equivalent model is close to 0. Finally, the accurate elastic modulus of beetle elytron plate was introduced into equation (1) to obtain the equivalent elastic parameters of cantilevered beetle elytron plate based on the equivalent plate theory, as shown in Table 2.

Table 2.

The equivalent elastic parameters of cantilevered beetle elytron plate based on equivalent plate theory.

Equivalent elastic modulus (MPa)	Equivalent shear modulus (MPa)	Equivalent Poisson’s ratio	Density (kg/m³)	Equivalent thickness (m)
5956	2326.6	0.28	326.05	0.019

To confirm the validity of the equivalent model, a modal analysis of the cantilevered beetle elytron plate and the equivalent model was conducted based on a dependable static analysis. Figure 8 shows the first six-order natural frequencies and first three-order vibration modes of cantilevered beetle elytron plate and equivalent model. The errors of the first three-order natural frequencies of cantilevered beetle elytron plate and the equivalent model are 5.4%, 1.5% and 7.1%, respectively, which are within a reasonable range, indicating that the equivalent model has certain reliability at low order vibration. The growth potential of equivalent model and the cantilevered beetle elytron plate is essentially the same as the modal order increases. The mechanical properties analysis of cantilevered beetle elytron plate can thus benefit from using the equivalent elastic parameters derived from the equivalent plate theory.

Figure 8.

The first six-order natural frequencies and first three-order vibration modes of cantilevered beetle elytron plate and equivalent model.

Structure selection and model establishment of BEP blade

The finite element analysis of the subsequent chapters is based on the equivalent theory. The beetle elytron plate with complex geometric structure is equivalent to a uniform equivalent plate with the same mechanical behavior by equivalent analysis method, which significantly simplifies the subsequent modeling and calculation process.

Structure selection of BEP blade

The structure selection of BEP blade refers to the NREL-5 MW wind turbine blade (Jonkman et al., 2009), and the parameters are shown in Table 3. The blade tip is NACA64-618 airfoil, the main component is DU airfoil, and blade root and hub are connected by cylindrical shell. Except that the aerodynamic center at the blade root is 50% of the chord length, the aerodynamic center at other places is 25% of the chord length.

Table 3.

The parameters of NREL-5 MW wind turbine blade.

Project	Parameter	Project	Parameter
Rated power	5 MW	Height of hub	87.6 m
Control strategy	Variable speed pitch	Diameter of blade	126 m
Number of blades	3	Rated wind speed	11.4 m/s
Weight of blades	110000 kg	Rated rotational speed	12.1 rpm
Prebending angle of blade	2.5°	Cut-in wind speed	3 m/s
Diameter of hub	3 m	Cut-out wind speed	25 m/s

Establishment of BEP blade

The finite element analysis model of BEP blade was established by Rhino + Grasshopper. The battery program was written by Grasshopper, and the coordinate points were imported into the program to draw the shape curve of a single leaf element, the airfoil distribution numerical analysis model of BEP blade are shown in Figure 9(a) and Figure 9(b). The thickness of wind turbine blade gradually decreases from the root to the tip, as shown in Figure 9(c). The material characteristics of the three different FRP types and the equivalent plate is shown in Table 4.

Figure 9.

Establishment of finite element analysis model of BEP blade.

Table 4.

Four representative working conditions.

Working conditions	Wind speed (m/s)	Rotational speed (rpm)	P ( $N / m^{2}$ )	Centrifugal angle speed (rad/s)	Pitch angle (°)
Rated condition	11.4	12.1	83.83	1.267	0
Extreme gust condition	13.794	12.1	122.73	1.267	8.7
Cutting wind speed condition	25	12.1	403.13	1.267	23.47
Shutdown failure condition	25	0	403.13	0	90

Static performance of BEP blade

The offshore turbine blades will encounter different wind speed conditions during operation. In this paper, four representative working conditions was selected for static performance analysis of BEP blade, as shown in Table 4. Normal operating conditions including rated condition, extreme gust condition, and shutdown failure condition.

In order to facilitate the application of aerodynamic load, only the normal force of aerodynamic load is considered in the strength analysis of new type of offshore wind turbine blade. The skin surface (path 1) and the web surface (path 2) of BEP blade were selected as the research objects of the static response in the strength analysis.

Displacement response and stress response

The displacement response directly determines whether the offshore wind turbine blade can work normally during operation. The stress response reflects the micro-stress change of the offshore wind turbine blade and directly determines whether the blade will undergo strength failure. In order to study the displacement response and stress response of BEP blade under four representative working conditions, the displacement curves and equivalent stress curves of path one and path two were selected for comparison, and the results are shown in Figure 10.

Figure 10.

The displacement curves and equivalent stress curves of path 1 and path 2.

As shown in Figure 10(a) and Figure 10(b), the displacement curves of the path 1 and the path 2 are basically the same. The displacement response of the BEP blade under cutting wind speed condition is the largest, about 0.128 m, which is lower than 50% gap between the blade and the tower, indicating that the BEP blade will not collide with the tower due to excessive displacement during operation. The displacement response of the BEP blade under the shutdown failure condition is the smallest, which is about 42% of the BEP blade under cutting wind speed condition. This is because the blade stops rotating and the pitch angle is adjusted to 90° under the shutdown failure condition, and the decrease of the windward area leads to the decrease of the aerodynamic load, which ensures the safety of the blade.

As shown in Figure 10(c) and Figure 10(d), the high stress of the BEP blade under four representative working conditions is primarily concentrated on the skin surface near the tip of the blade, which has a span of 50 m ∼ 60 m, and on the edge of the blade root. However, the equivalent stress of blade under cutting wind speed condition is the largest, and the peak value is about 4.646 MPa. The stress level on the web surface is low, and the maximum equivalent stress of BEP blade is concentrated near 10 m from the fixed end. The stress response trend of the skin and the web surface under normal operating conditions is basically similar. The maximum equivalent stress of skin surface under the shutdown failure condition is 0.862 MPa, which is 18.6% of the equivalent stress of skin surface under the cutting wind speed condition. This demonstrates that the pitch and shutdown can effectively reduce the stress level on the skin surface by exerting the bending resistance of the web when the BEP blade under shutdown failure condition to ensure the safety of the blade in extreme weather.

Comparison of static response of different FRP wind turbine blades

In order to study the strength characteristics of BEP blade, the GFRP, BFRP and CFRP were applied to the web and skin of wind turbine blades and compared with BEP blade. The displacement response and stress response of skin and web surface of different FRP blades under rated condition is shown in Figure 11.

Figure 11.

The displacement response of skin and web surface of different FRP blades under rated condition.

The displacement response of the BEP blade is between GFRP blade and CFRP blade, which is equivalent to BFRP blade. The maximum displacements of GFRP blade, BFRP blade and CFRP blade are 0.320 m, 0.122 m and 0.033 m, respectively. CFRP blade and BFRP blade show great advantages over GFRP blade due to their high elastic modulus and strong flexural stiffness. The maximum displacement of the BEP blade is 0.118 m. The equivalent elastic modulus of the beetle elytron plate is less than 1/3 of that of the GFRP, but the maximum displacement of BEP blade is higher than 63% of GFRP blade. This fully shows that the economy of BEP blade is better than that of CFRP blade, and the structural performance is better than that of BFRP blade and GFRP blade.

The stress response of BEP blade is much smaller than that of the three FRP blades. The maximum equivalent stress of GFRP blade, BFRP blade and CFRP blade is 44.8 MPa, 44.8 MPa and 39.2 MPa, respectively. The CFRP blade shows only a slight advantage over the first two FRP blades, and the maximum equivalent stress of BEP blade is 6.72 MPa, which is only 17% of the extreme stress of the CFRP blade. The stress level of the skin and web surface of BEP blade is generally smaller than that of the three FRP blades, which reflects the advantages of BEP blade in stress redistribution. The beetle elytron plate structure can protect the blade structure by reducing its surface stress level when the BEP blade under extreme gust condition.

Dynamic performance of the BEP blade

Modal analysis

Only the first 10 order modes of the BEP blade under the rated condition were extracted because the vibration energy is mostly concentrated in the low order. These vibrations can basically include all possible vibration forms during operation. The maximum vibration displacement, first ten-order natural frequencies and first six-order vibration modes of the BEP blade are shown in Figure 12.

Figure 12.

The maximum vibration displacement, first ten-order natural frequencies and first six-order vibration modes of BEP blade.

As shown in Figure 12, the natural frequency of the BEP blade gradually increases as the modal order increases. However, the overall trend of the maximum vibration displacement is to rise first and then fall, and the maximum vibration displacement of the eighth order reaches the peak value of 0.090 m. At this time, the vibration form of BEP blade is the flapping vibration, shimmy vibration and torsional vibration, and the coupling of the three. In general, the vibration form of the wind turbine blade is mainly low-order vibration, only the first six order vibrations were discussed. The vibration mode of BEP blade more violently with increasing order. In general, the high-order vibration mode is complex while the low-order vibration mode is simple. Vibration modes occurred in six different orders: flapping vibration (first order), shimmy vibration (second order), high-order flapping vibration (third and fourth order), and flapping-shimmy coupling vibration (fifth and sixth order) with torsion phenomenon. According to the design requirements of the wind turbine blade, the low-order natural frequency of the 5 MW wind turbine blade should avoid 0.18 Hz ∼ 0.22 Hz and 0.54 Hz ∼ 0.66 Hz, while the first three-order natural frequencies of BEP blade are 2.3058 Hz, 2.7745 Hz and 6.8858 Hz, respectively, avoiding the resonance region and meeting the design requirements.

Parametric analysis of vibration characteristics of BEP blade

Influence of material type

The modal analysis of GFRP blade, BFRP blade, CFRP blade, and BEP blade under rated condition was carried out to examine the impact of material type on the vibration characteristics of the wind turbine blade. The natural frequencies and maximum vibration displacements of first ten-order modes of wind turbine blade with different material types are shown in Figure 13.

Figure 13.

The natural frequencies and maximum vibration displacements of first ten-order modes of wind turbine blade with different material types.

Natural frequencies of FRP blades and BEP blades gradually increase with increasing modal order. The natural frequency of the CFRP blade is the highest under the same modal order, followed by the BEP blade, the BFRP blade, the GFRP blade, and the smallest. This suggests that the BEP blade has substantially better vibration characteristics than the BFRP and GFRP blades. The beetle elytron plate structure changes the vibration mode of maximum vibration displacement peak and valley of wind turbine blade, which means that the maximum vibration displacement can be adjusted to the higher order mode in the future design of BEP blade. The variation in natural frequency brought about by the characteristics of the materials will become increasingly apparent as the modal order increases. The tenth-order natural frequency of BEP blade is about 3/5 of that of CFRP blade. The advantages of the BEP blade blades in vibration characteristics are the result of the double superposition of BFRP and beetle elytron plate structure.

Influence of rotational speed

In order to investigate the impact of rotational speed on the vibration characteristics of the wind turbine blade, five rotational speeds—0, 5, 10, 15, and 20 rpm—are used to conduct the modal analysis of BEP blade under rated. The variation trend in the first-order natural frequency of BEP blade at various rotational speeds are shown in Figure 14(a). The rate of change of first 10 order natural frequencies of BEP blade is shown in Figure 14(b).

Figure 14.

The impact of rotational speed on the vibration characteristics of the BEP blade at various rotational speeds.

The same order mode of the BEP blade at pitch angles of 0° and 90° has a natural frequency that gradually increases with increasing rotational speed. In order to increase the natural frequency of the BEP blade during operation, the centrifugal force produced by the blade during rotation creates an extra bending moment. This bending moment increases stiffness and creates a dynamic stiffening effect. On the first-order natural frequency of the BEP blade, however, the impact of a 90° pitch angle is significantly larger than that of a 0° pitch angle. The rotational speed has the most effect on the second-order natural frequency at a pitch angle of 0° (up 0.87%) and the least effect on the first-order natural frequency (up only 0.17%) when the BEP blade is at this angle. On the contrary, the rotational speed has the least impact on the second-order natural frequency, increasing it by only 0.18%, and the largest impact on the first-order natural frequency, increasing it by 1.17%, when the BEP blade is at a pitch angle of 90°. The natural frequency of the BEP blade will be somewhat enhanced when the rotation speed and pitch angle are adjusted, but the change range is much smaller than 5%. Based on the aforementioned analysis, it is possible to disregard the impact of pitch angle and rotational speed on the vibration characteristics of the BEP blade. Additionally, the dynamic frequency in modal analysis can be roughly replaced with the static frequency.

Influence of thickness of skin and web

The skin and web are the key components of the wind turbine blade that can effectively transmit the wind load. They directly determine the windward area and flexural stiffness of the wind turbine blade during operation. The modal analysis of BEP blades with five kinds of thickness between 20 mm and 60 mm under rated condition is carried out. The first 10 order natural frequencies of the BEP blade with different thicknesses of skin and web are shown in Figure 15.

Figure 15.

The first 10 order natural frequencies of the BEP blade with different thicknesses of skin and web.

The natural frequency of each BEP blade order generally increases as the thickness of the skin and web increases. The difference in natural frequency caused by the thickness of the web and the skin becomes more obvious at higher order vibrations. Increasing the thickness of the web results in a more significant increase in the natural frequency of the BEP blade, which is due to the larger contribution of the web to the overall flexural stiffness of the BEP blade.

In the low-order modes, the natural frequency of the BEP blade increases linearly with the increase in the thickness of web. The first-order natural frequency of BEP blade increases by approximately 0.1 Hz for every 10 mm increase in thickness. However, the first-order natural frequency of the BEP blade increases initially and then decreases as thickness of skin increases. The peak and valley values are 1.80 Hz and 1.78 Hz, respectively, with a difference of only 0.02 Hz, which is far less than the influence of the web thickness. With an increase in the thickness of the skin and web, the natural frequency of the BEP blade in high-order modes first rises and subsequently falls. The tenth-order natural frequency of the skin and web with a thickness of 50 mm reaches its maximum simultaneously, while the skin and web with a thickness of 20 mm have the lowest tenth-order natural frequency. The difference between the peak and valley values affected by the thickness of the skin is 4.918 Hz, which is about 64.8% of the influence amplitude of the thickness of web.

Conclusions

In this paper, static and dynamic performance of BEP blade was studied based on the equivalence of BFRP beetle elytron plate. The conclusions are as follows:

(1) The mechanical properties of the beetle elytron plate and honeycomb plate under bending load are similar, and the equivalent model for the cantilevered beetle elytron plate can be established using the equivalent plate theory adjusted by dichotomy method.

(2) Under four typical operating conditions, the high stress of the BEP blade is primarily concentrated on the skin surface near the tip of the blade with a span of 50m ∼ 60 m and on the edge of the blade root. The pitch and shutdown can significantly reduce the stress level on the skin surface by exerting the bending resistance of the web when the BEP blade under shutdown failure condition to ensure the safety of the blade in extreme weather.

(3) When the BEP blade is subjected to high wind speeds, the beetle elytron plate structure can strengthen its natural frequency and lower surface stress levels, protecting the blade structure. The first-order natural frequency of BEP blade is approximately 43% higher than that of BFRP blade, at more than 1.25 times that of GFRP blade.

(4) The natural frequency of the BEP blade generally increases with the thickness of the skin and web, while the effects of rotational speed and pitch angle on this frequency can be considered disregarded. Increasing the thickness of web has a more significant increase in the low-order natural frequency, which is about 10 times that of the skin.

Footnotes

ORCID iDs

Tengteng Zheng

Caiqi Zhao

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was financially supported by the Postgraduate Research & Practice Innovation Program of Jiangsu Province under grant NO. KYCX22_0219, China Scholarship Council under grant NO. 202306090255, and the Natural Science Foundation of China under grant NO. 51578136 and 51875102.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

References

Chen

Xie

Zhu

, et al. (2012a) Integrated honeycomb structure of a beetle forewing and its imitation. Materials Science and Engineering: C 32(3): 613–618.

Chen

Guo

, et al. (2012b) Integrated honeycomb technology motivated by the structure of beetle forewings. Materials Science and Engineering: C 32(7): 1813–1817.

Chen

Pan

, et al. (2021a) The compressive property of a fiber-reinforced resin beetle elytron plate and its influence mechanism. Journal of Applied Polymer Science 138: e50692.

Chen

Fan

(2021b) New method for correlation analysis of natural frequency of wind turbine blade. Renewable Energy Resources 29: 15–19, (In Chinese).

Chikhradze

Marquis

FDS

Abashidze

(2015) Hybrid fiber and nanopowder reinforced composites for wind turbine blades. Journal of Materials Research and Technology 4(1): 60–67.

Dong

Zhang

Fei

, et al. (2014) An approach on identification of equivalent properties of honeycomb core using experimental modal data. Finite Elements in Analysis and Design 90(1): 84–92.

Chen

(2015) An overview of equivalent parameters of honeycomb cores. Materials Review 29: 127–134, (In Chinese).

Jonkman

Butterfield

Musial

, et al. (2009) Definition of a 5MW Reference Wind Turbine for Offshore System Development. Office of Scientific & Technical Information Technical Reports, 16–75.

Hoang

Abbes

, et al. (2015) Analytical homogenization for in-plane shear and torsion of honeycomb sandwich plates with skin and height effects. Applied Mechanics and Materials 752-753: 804–811.

10.

Sorohan

Sandu

, et al. (2016) Finite element models used to determine the equivalent in-plane properties of honeycombs. Materials Today: Proceedings 3(4): 1161–1166.

11.

Tuo

Yan

Chen

, et al. (2021) Effect of the length of basalt fibers on the shear mechanical properties of the core structure of biomimetic fully integrated honeycomb plates. Journal of Sandwich Structures & Materials 23(5): 1527–1540.

12.

(2018) Innovative application of basalt fiber and its composite materials as construction materials. Jiangsu Building Materials 4: 15–22, (In Chinese).

13.

Zhang

Chen

Okabe

, et al. (2019) Compression properties of metal beetle elytron plates and the elementary unit of the trabecular-honeycomb core structure. Journal of Sandwich Structures & Materials 21(6): 2031–2041.

14.

Zhao

Zheng

Zhao

, et al. (2022) Research on bearing capacity of honeycomb plate box-type hollow roof structure. Construction and Building Materials 347: 128596.

15.

Zhao

Zheng

Shang

, et al. (2023) Research and optimization of lateral compressive performance of the 3-D printed beetle elytron plate. KSCE Journal of Civil Engineering 27(8): 3517–3527.

16.

Zheng

Zhao

(2022) Research on fatigue performance of offshore wind turbine blade with basalt fiber bionic plate. Structures 47: 466–481.

17.

Zheng

Yan

Zhao

, et al. (2023) Research on seismic performance of honeycomb plate cylindrical reticulated shell structure. Case Studies in Construction Materials 18: e0189710.

18.

Zheng

Zhao

Shang

(2024) Aerodynamic performance of BFRP bionic plate wind turbine blade based on fluid-structure interaction analysis. Wind and Structures 39(4): 243–258.