Aeroelastic Experimental Investigation of Hyperbolic Paraboloid Membrane Structures in Normal and Typhoon Winds

Abstract

The lightweight and flexible membrane structure of roofs are susceptible to wind loads with the risk of damage and failure. Compared with uniform and low-level turbulence flow cases (i.e., normal winds) that have been well investigated, the wind-induced vibration problem of membrane structures in high-level turbulence flows such as typhoons has been paid little attention. To address the gap, this paper aimed at investigating the aerodynamic behavior of hyperbolic paraboloid membrane structures in normal and typhoon winds by a series of wind tunnel tests. Some distinct wind characteristics of upcoming normal and typhoon flows in terms of vertical profiles of wind velocity, turbulence intensity, and power spectrum density of fluctuating winds were well simulated in an automatically controlled wind tunnel. The aeroelastic behavior of a scaled model was analyzed and discussed in terms of displacement time-history responses, probability distribution characteristics, and dynamic characteristics including the natural frequency, mode shape, and damping ratio. Results show that the increasing suction in a typhoon leads to significant growth in maximum deformations and more risks to suffer from aeroelastic instability. Non-Gaussian characteristics appear more remarkable with skewness and kurtosis increasing almost two-fold in typhoons. Structural modal parameters are influenced by both turbulence intensity and wind velocity. This study provides basic insights into the deficiency of dynamic response of membrane structures in typhoons, and promotes the applications of membrane structures in green buildings.

1. Introduction

Hyperbolic paraboloid membrane structures have been used worldwide for large-span roofs in public facilities and green buildings, e.g., the Denver Union Station roof in Denver, USA, the London Olympic Velodrome in London, UK, and the Bailu Stadium roof in Xiamen, China. The lightweight and flexible characteristics of the membrane structure render them to be susceptible to wind loads, leading to many undesirable aerodynamic behaviors such as dynamic buffeting, galloping and flutter, and even damage and failure [1,2,3]. For example, the membrane dome structure in Japan was damaged by Typhoon Songda [4], and the membrane roofing in the USA was blown off by Hurricane Katrina [5]. Therefore, a deeper understanding of the dynamic behavior of membrane structures in wind loads is necessary, especially in typhoon-prone coastal regions.

In general, the wind-induced vibration of a flexible membrane structure can be classified as the following excitation mechanism: movement-induced vibration (MIV), extraneously induced vibration (EIV), and coupled MIV-EIV [6,7]. The mechanism of MIV involves the self-excited vibration of a membrane structure in a uniform flow. The mechanism of EIV is concerned with the linear or weak nonlinear vibration of a membrane structure with a small displacement response in a non-uniform flow (i.e., low-level turbulence flow) [8]. In the case of high-level turbulence flow, a membrane structure experiences a strong nonlinear vibration with a large displacement response, which is associated with the coupled MIV-EIV mechanism [9]. A systematic study of the complex vibration problem including MIV, EIV, and coupled MIV-EIV mechanisms of a hyperbolic parabolic membrane structure is highly desirable, especially the more complex coupled MIV-EIV mechanism existing in extreme wind events with high-level turbulences.

The MIV and EIV problems have been studied extensively and addressed by means of experiments and finite element model (FEM) simulations. Schwarze [10] overviewed the new applications of experimental and numerical flow models in different cases, such as railway tunnels after a train fire accident [11], isolated cubical buildings in a warm Mediterranean climate [12], parabolic trough solar collectors [13], flexible flaps in a laminar glycerin flow [14], and boiling model for rod bundle flows [15]. Ciappi et al. [16] proposed the reliable analytical computational fluid dynamics models of wells turbines for oscillating water column systems, exploring the most straightforward and reliable solution for utilizing sea wave energy. Uematsu and Uchiyama [17] investigated the response of a hyperbolic-parabolic-shaped roof in uniform flows, and found that the oscillation of an aeroelastic model was quite similar to the vortex-excited oscillation with the strong FSI phenomena. Wu et al. [18] performed a series of wind tunnel tests of a hyperbolic paraboloid membrane structure in uniform flows, and evaluated the FSI effects quantitatively with the aerodynamic damping and added mass. Zorrilla et al. [19] applied the numerical method to a hyperbolic paraboloid membrane tent in uniform flows, and found the mechanism between the pressure distribution and displacement response. Yang et al. [20] demonstrated that the structural natural frequency in a low-level turbulence flow is remarkably decreased and the frequency band is significantly broadened. Daw et al. [21] identified the aerodynamic damping of a semi-circular roof in a low-level turbulence flow. It is concluded that the aerodynamic damping arising from the FSI is significantly larger than the structural damping, which must be taken into account in dynamic analysis. Colliers et al. [22] used computational fluid dynamics (CFD) simulation techniques to study the wind load distribution over hyperbolic paraboloid roofs in turbulence flows. It is indicated that the suction and pressure increase for higher surface curvature, but with similar geometrical patterns.

Different from MIV and EIV mechanisms that have been well investigated mentioned above, the coupled MIV-EIV mechanism of a hyperbolic paraboloid membrane structure in extreme wind events, such as typhoons, has been paid little attention. In tropical regions, typhoons have a typically complex vortex structure, which would increase mean wind velocity, gust factor, and turbulence intensity [23,24,25]. These increases lead to the decrease of the reattachment length over the membrane surface and the increase of the peak suction in the separation region [26]. Compared with uniform and low-level turbulence flows, the risks of damage to membrane structures would be enlarged in typhoons, and the wind-resistant design for the flexible structure in typhoon-prone regions requires an additional independent examination.

To address the deficiency in dynamic responses of membrane structures in typhoons, this paper aims at investigating the aerodynamic behavior of hyperbolic paraboloid membrane structures in normal and typhoon winds through a comparative experimental study, and providing more insights via data analysis and discussion. The paper is structured as follows: In Section 2, the model of hyperbolic paraboloid membrane structures is introduced first. In Section 3, a series of aeroelastic tests on the scaled model under normal and typhoon winds with respect to different wind velocities and turbulence intensities are then conducted in the wind tunnel and described. In Section 4, aeroelastic responses of the membrane structure in these two wind fields are analyzed and discussed in terms of displacement time-history response, non-Gaussian characteristics, natural frequencies, modal shapes, and damping ratios. The conclusion is finally provided in Section 5.

2. Introduction of Hyperbolic Paraboloid Membrane Structure Models

The model is designed and scaled based on the scaling requirements including geometrical similarities, aerodynamic similarities, and stiffness similarities investigated by literature [27,28,29]. As is shown in Figure 1a, the geometry of the hyperbolic paraboloid membrane structure model is the 700 mm × 900 mm rectangular plane (i.e., L₁ = 700, L₂ = 900) with 30 mm sag/80 mm rise (i.e., f₁ = 30, f₂ = 80). It shows that C1 is the direction connecting the two lowest points, and C2 is the direction connecting the two highest points. Correspondingly, the sag–span ratio f₁/L₂ is 1/30, and the rise–span ratio f₂/L₁ is 4/35. The equation to describe the hyperbolic paraboloid surface is z₀ = 4f₁x²/L₂ − 4f₂y²/L₁. Following this, the curvature along the x and y axis can be obtained as k_x0 = ∂²z₀/∂x² = 4/15 and k_y0 = ∂²z₀/∂y² = −32/35, respectively. The Gaussian curvature is K = k_x0 k_y0 = −0.24. The mathematical boundary conditions of displacements w are expressed as:

$$w(x,L_1/2)=0, w(x,-L_1/2)=0$$

(1)

$$w(L_2/2,y)=0, w(-L_2/2,y)=0$$

(2)

The membrane structure is commonly covered with prestressed fabric material and fixed on the steelwork. The pre-stress in membrane structures is provided as 1.12 kN/m after the form-finding analysis. Then, the membrane surface is fixed along the boundary of the steelwork illustrated in Figure 1b. The polyvinyl chloride (PVC) membrane material commonly used in engineering was selected, i.e., XYD brand made in China. The mechanical characteristics can be identified based on the strip method recommended in the European code (i.e., EN ISO 13934-1). The strip specimen with a length of 200 mm and a width of 50 mm was tensioned by the universal testing machine at the loading rate of 100 mm/min. The material parameters identified are listed in

Table 1. Technical parameters of PVC materials.

Technical Parameter	Value
Titer of yarn (dtex)	1300
Yarn count (warp/weft) (yarn/cm)	12/12
Weight of base fabric (g/m2)	360
Total weight (g/m2)	950
Total thickness (mm)	0.8
Elastic modulus (warp/weft) (MPa)	1720/1490
Tensile strength (warp/weft) (N/5 cm)	4400/4200/5
Tear strength (warp/weft) (N)	800/700

.

3. Aeroelastic Wind Tunnel Tests

3.1. Simulation of Wind Fields

The aerodynamic model experiments were carried out in a Boundary Layer Wind Tunnel of the Xiamen University of Technology. The wind tunnel is a closed-circuit tunnel with a low-velocity test section of 6 m in width and 3.6 m in height, and an upstream fetch of 25 m. Consequently, the blockage ratio of the membrane structure model is only 1.67%, within the range of 5% required by Chinese Standards (GB 50009-2012) [30]. The maximum wind velocity in the wind tunnel is 32 m/s. The wind tunnel floor is lined with roughness elements, which are electronically driven and controlled. The roughness elements, strips, and spires are used to generate the desired wind profiles.

Due to its simplicity and efficiency, the empirical power law has been widely adopted to express the wind velocity profile in Chinese Load Design Standards (GB 50009-2012) as:

$$U=U_1{\left(\frac{z}{z_1}\right)}^{\alpha }$$

(3)

where U is the wind velocity at height z, U₁ is the wind velocity at reference height z₁, and α is the power law coefficient, which is the key parameter to describe the terrain roughness and atmospheric stability.

For membrane structure generally established in suburban regions, the coefficient α = 0.15 is recommended for normal winds with category B (suburban terrain) in Chinese Standards (GB 50009-2012), and α = 0.19 is selected for typhoons based on the in-field observation and investigation by He et al. [31]. The normal wind defined in this study refers to the turbulence flow with low-level turbulence density in the atmospheric boundary layer. For both normal and typhoon winds, the wind velocity profiles in the wind tunnel can be measured by cobra probes located at different heights, and further validated as shown in Figure 2a. The reference height z₁ is 1.0 m and the corresponding wind velocity is U₁.

Furthermore, the turbulence profile is expressed with the general form of power function in GB 50009-2012:

$$I_{\mathrm{u}}=c{\left(\frac{z}{z_1}\right)}^d$$

(4)

where I_u is the turbulence intensity, c is the turbulence intensity at reference height z₁, and d is the power coefficient affecting the shape of the profile. It is suggested that d = −0.15 for normal winds in GB 50009-2012. The turbulence intensity in typhoon I_uT is suggested as I_uT = 1.48 I_u by Sharma and Richards [32]. The wind turbulence intensities in the wind tunnel are compared with the theoretical curve in Figure 2b. The turbulence intensities at the top height of the membrane structure (z₁ = 1.0 m) are 14% for normal winds, and 20.7% for typhoons. It can be viewed that the wind velocity and turbulence intensity profiles match well with the reference theoretical profiles.

The power spectral density (PSD) of wind generally represents the energy distribution in the wind flow. In general, the normal wind spectrum can be described by the Kaimal spectrum [30] as follows:

$$S_{\mathrm{u}}=\frac{200u_0^{2}z/U_{\mathrm{z}}}{{\left(1+50nz/U_{\mathrm{z}}\right)}^{5/3}}$$

(5)

where S_u is the power spectral density of longitudinal wind velocity, n is frequency, u₀ is the friction velocity, and U_z is wind velocity at the height z.

However, the PSD in typhoons generally followed the von Karman spectrum [31] expressed as:

$$S_{\mathrm{u}}=\frac{4{\sigma }_{\mathrm{u}}^2{L}_{\mathrm{u}}^{\mathrm{x}}/U}{{[1+70.8{\left(L_{\mathrm{u}}^{\mathrm{x}}n/U\right)}^2]}^{5/6}}$$

(6)

where $L_u^x$ is turbulence integral scale, and U is the mean value of wind velocity. Figure 3 shows that the simulated spectra in the wind tunnel were consistent with the expected theoretical curves.

3.2. Arrangement of Measurement Points

The displacement response was measured by the laser sensors. The largest sampling rate is 50 kHz, and the measurement error is 0.05%. According to the symmetry of the membrane, seven measurement points over the membrane surface were scheduled in Figure 4a and shown in Figure 4b. Points 1–5 were distributed equidistantly along the direction C1. Points 6 and 7 were located 3/4 through direction C2.

3.3. Test Cases

Three levels of mean wind velocity are set as 11 m/s, 15 m/s, and 19 m/s, and two levels of turbulence intensities including 14% and 20.7% were scheduled in wind tunnel experiments. The photograph of the fabricated model in the wind tunnel is shown in Figure 5. The spires and roughness elements are set reasonably to simulate the desired normal and typhoon winds. For each wind field case, seven wind directions including 0°, 30°, 60°, 90°, 120°, 150°, and 180° were tested with consideration of the model symmetry. A total of 42 test cases were employed as listed in

Table 2. Summary of test case IDs.

Attack Angle (°)	Wind Type	Wind Velocity (m/s)
		11	15	19
0	Normal	N-11-0	N-15-0	N-19-0
	Typhoon	T-11-0	T-15-0	T-19-0
30	Normal	N-11-30	N-15-30	N-19-30
	Typhoon	T-11-30	T-15-30	T-19-30
60	Normal	N-11-60	N-15-60	N-19-60
	Typhoon	T-11-60	T-15-60	T-19-60
90	Normal	N-11-90	N-15-90	N-19-90
	Typhoon	T-11-90	T-15-90	T-19-90
120	Normal	N-11-120	N-15-120	N-19-120
	Typhoon	T-11-120	T-15-120	T-19-120
150	Normal	N-11-150	N-15-150	N-19-150
	Typhoon	T-11-150	T-15-150	T-19-150
180	Normal	N-11-180	N-15-180	N-19-180
	Typhoon	T-11-180	T-15-180	T-19-180

. Each test case was measured for 180 s after the steady wind field was formulated. The test cases were identified using the wind type, the wind velocity, and the wind direction. For example, the test case T-11-30 means: (i) the wind type is typhoon, (ii) the wind velocity is 11 m/s, and (iii) the wind direction is 30°.

4. Test Result and Analysis

4.1. Displacement Time-History Response

As shown in Figure 6, the time-history analysis of displacement at Point 4 and Point 7 was performed quantitatively to identify some significant parameters when the wind velocity is 19 m/s and the wind direction is 0°. It is noted that the positive value of displacement means that the membrane structure experiences downward deformation under wind pressure. The displacement time-history results can be analyzed by using some significant parameters, i.e., mean deformation $\overline{d}$, RMS deformation d_RMS, maximum deformation d_max, minimum deformation d_min, and peak-to-peak deformation Δd. The mean deformation $\overline{d}$ represents the new equilibrium position during vibration, and the RMS deformation d_RMS describes the average amplitude above the mean deformation, representing the kinetic energy level of membrane structures. The peak-to-peak value Δd reveals the gap between downward maximum deformation d_max and upward maximum deformation d_min.

In this study, the result analysis was performed by comparing the results in typhoons with those in normal winds, in order to identify their dynamic response features in typhoons. It can be found that the mean deformations $\overline{d}$ at Point 4 and Point 7 in normal winds are −0.75 and 0.40 mm, respectively. However, the corresponding values for typhoons reduce to −0.41 and 0.15 mm, with reductions of 45.33% and 62.50%, respectively. A similar decreasing trend occurs in the RMS deformation d_RMS, maximum deformation d_max, and peak-to-peak deformation Δd as follows: (i) The RMS deformations at Point 4 and Point 7 in normal winds are 0.82 and 0.44 mm, respectively, while the corresponding results in typhoons decrease sharply almost in half, reducing to 0.50 and 0.20 mm, respectively. (ii) Compared with the 0.88 and 1.47 mm in normal winds, the maximum deformations at Point 4 and Point 7 in typhoons drops to 0.68 and 1.16 mm, with a reduction of 22.73% and 21.09%, respectively. (iii) The peak-to-peak deformations at Point 4/Point 7 in typhoons show a slight reduction up to 11.73%, decreasing from 3.89/1.96 mm to 3.76/1.73 mm.

However, it should be mentioned that the minimum deformation d_min attributed to the suction in typhoons is generally larger than that in normal winds. Specifically, the upward maximum deformations at Point 4 and Point 7 in normal winds are only −3.01 and −0.49 mm, respectively, while the corresponding results in typhoons can reach −3.08 and −0.57 mm, with the growth of 2.33% and 16.33%, respectively. This can be explained by the fact that the larger turbulence intensity in typhoons contributes to a decrease in the reattachment length scale, and the small-scale turbulence is responsible for an increased roll-up of separated shear layers and larger suction effects [33]. These phenomena reveal that the high-level turbulence intensity in typhoons leads to a decrease in mean, RMS, minimum and peak-to-peak deformation, and an increase in negative peak deformation. Hence, a more significant suction response of membrane structure in typhoons should be considered in the wind-resistance design.

4.2. Statistical Characteristics of Displacement

4.2.1. Probability Distribution Characteristics of Displacement

The probability density function (PDF) distributions of displacement at Point 4 and Point 7 for normal and typhoon winds are shown in Figure 7. The test results are expressed in the histogram and fitted by Gaussian distribution and stable distribution. It can be found that the displacement responses in normal and typhoon winds follow the non-Gaussian distribution with significant tail characteristics (i.e., skewed left/right tail characterized by negative/positive skewness value). Both skewness and kurtosis in typhoons are much larger than those in normal winds. Specifically, the values of skewness at Point 4 and Point 7 in normal winds are −0.31 and 0.38, respectively, while the corresponding results in typhoons increase almost in half, up to −0.69 and 0.71, respectively. Similarly, the values of kurtosis at Point 4 and Point 7 in normal winds are only 3.71 and 3.49, respectively, while the corresponding results in typhoons can reach up to 4.91 and 4.55, respectively. The phenomenon observed herein may result from the nonlinear motion-induced force and the decrease of structural damping, which is consistent with the probabilistic features of VIV of slender structures [34]. Therefore, the strong non-Gaussian characteristics of wind-induced response in typhoons should be mentioned in the reliability-based design of membrane structures.

4.2.2. Mean and RMS Results

Test results of the mean deformation varying with the wind directions in the case of 19 m/s wind flow are shown in Figure 8. It can be found that the mean deformation decreases with the wind direction increasing from 0° to 90°. The areas of wind pressure and suction are different between normal and typhoon winds. In detail, the wind suction in normal winds is distributed at the central section (i.e., Points 3 and 4) with their negative mean deformation. However, the suction action in typhoons occurs near the ridge section (i.e., Points 6 and 7). In the wind direction of 90°, the mean deformations at all points become negative in these two types of wind, representing almost the entire membrane surface to be lifted off under strong suction. As the wind direction increases from 90° to 180°, the mean deformation becomes positive and the membrane surface is experiencing wind pressure. For the extreme response, the mean deformation in normal winds can reach up to 0.71 mm in maximum at Point 6 with the wind direction of 30°, and −0.78 mm in minimum at Point 4 with the wind direction of 0°. However, the extreme mean deformation in typhoons obviously reduces to 0.21 mm in maximum at Point 3 with the wind direction of 0°, and −0.49 mm in minimum at Point 6 with the wind direction of 90°. It is indicated that the suction effects of wind on the membrane structure prove more significant, especially in typhoon cases where the upward deformation is several times the downward deformation in magnitude.

In addition to mean deformation, the RMS deformation varying with the wind direction is shown in Figure 9. Similarly, the RMS deformations reduce initially ranging from 0° to 90°, and increase continuously from 90° to 180°. The maximum results in normal and typhoon winds appear in the wind direction of 0°, namely 0.82 mm at Point 4 (normal winds) and 0.51 mm at Point 7 (typhoons). Furthermore, it can be found that the larger RMS deformations in normal winds are distributed in the central section (i.e., Point 4), while the larger RMS deformations in typhoons are centered in the ridge section (i.e., Points 6 and 7).

Figure 10 compares the mean and RMS deformations at Point 4 in normal and typhoon winds varying with wind velocities when the wind direction is 0°. It can be found that both mean and RMS deformations increase almost linearly with the increasing wind velocity, but have large differences between normal and typhoon winds. Generally, the mean and RMS deformations in typhoons reduce almost in half compared with those in normal winds, which indicates the dominant role of wind velocity in determining the structural dynamic response, rather than the turbulence intensity. It is demonstrated that the increases in turbulence intensity may lead to the increase of the damping, and the depression effects of mean and RMS deformations in typhoons.

4.2.3. Skewness and Kurtosis Results

The results of skewness and kurtosis distributed over the membrane surface are plotted in Figure 11. The skewness and kurtosis show different patterns in space distribution (i.e., either symmetrical or anti-symmetrical along the x axis) between normal and typhoon winds. For skewness, the spatial distribution in normal winds shows symmetrical, and the larger values are more scattered in the central section. However, the spatial distribution in typhoons becomes anti-symmetrical, and the larger results are located in the ridge section. The kurtosis in typhoons shows similar symmetrical distributions to that in normal winds. It can be seen that the skewness and kurtosis results in typhoons are almost two-fold than those in normal winds, which demonstrates that the larger turbulence intensity introduces the stronger non-Gaussian characteristics.

The largest results of skewness and kurtosis exist in the wind direction of 30° when the wind flow increases from 11 m/s to 19 m/s, as plotted in Figure 12. It can be found that both skewness and kurtosis results remain stable with increasing wind velocity. It is proved that these non-Gaussian characteristics are not sensitive to wind velocity. The skewness and kurtosis in typhoons are almost twice those in normal winds, which proves that the skewness and kurtosis are basically governed by the turbulence intensity, rather than the wind velocity.

4.3. Structural Dynamic Characteristics

Based on the measured displacement response, the structural modal parameters (e.g., frequencies, mode shapes, and damping ratios) are presented in this section. More specifically, the Bayesian FFT method is applied in this study [35,36]. Taking advantage of the narrow-band behavior of the vibration of membrane structures, the Bayesian FFT method fits a modal model within a narrow frequency band. Following the Bayesian principle, fast algorithms have been proposed to calculate the most probable value of modal parameters and quantify their estimation uncertainty.

4.3.1. Frequency

The root singular value (SV) spectrum, i.e., eigenvalues of PSD matrix, of displacement is shown in Figure 13. The modal frequencies can be directly identified from the peaks of the largest eigenvalue curve. Due to the flexible and symmetric characteristics of membrane structure, the closely spaced frequencies are observed in both normal and typhoon winds. Specifically, the first six frequencies of the membrane structure in typhoons are spaced closely within narrow bands (i.e., 39.02 Hz–66.41 Hz). Similar phenomena occur in normal winds but with a slight reduction (i.e., 38.31 Hz–65.50 Hz), which is associated with the stronger external force acting on the membrane surface and a larger mean deformation response.

4.3.2. Mode Shape

In the modal analysis, the first six mode shapes have been identified as shown in

Table 3. The first six orders of identified mode shapes and corresponding frequencies.

No.	Normal Wind	Typhoon
1	f1 = 38.31	f1 = 39.02
2	f2 = 43.02	f2 = 43.06
3	f3 = 48.51	f3 = 49.49
4	f4 = 54.31	f4 = 55.75
5	f5 = 61.38	f5 = 62.01
6	f6 = 65.50	f6 = 66.41

. It can be found that the recognized mode shapes show as representative and basically symmetrical or anti-symmetrical. These mode shapes become more complex with the increasing frequency order. The multiple mode shapes in typhoons are mostly consistent with those in normal winds with a slight difference in amplitude. The amplitude ratios of higher mode shapes (i.e., 4th–6th) in typhoons are larger than those in normal winds. This reveals more flexible behaviors and local characteristics of membrane structures in typhoons, probably due to the increasing turbulence intensity and more FSI effects.

4.3.3. Damping Ratio

As shown in Figure 14, the damping ratios in normal and typhoon winds are extracted for the first six modes. It can be found there exist obvious differences in the damping ratios between normal and typhoon winds. In the case of 11 m/s, all the damping ratios of the membrane structure excited by typhoons are significantly higher than those excited by normal winds. In particular, the damping ratios corresponding to the first three orders in typhoons are 2.37% (1st-order), 2.52% (2nd-order), and 1.97% (3rd-order), which are about twice those in normal winds, namely 1.65% (1st-order), 1.12% (2nd-order), and 0.91% (3rd-order). The phenomena indicate that the damping force in typhoons would increase with low-level wind velocities, and, consequently, reduce the overall response of structures. For both 15 m/s and 19 m/s, however, the damping ratios in typhoons are basically smaller than those in normal winds, except for the damping ratios in the 2nd-order (15 m/s) and 3rd-order (19 m/s). It suggests that the damping force in typhoons would reduce with the high-level wind velocities, and the membrane structures are more likely to suffer from aeroelastic instability.

5. Conclusions

Experimental investigations on the aerodynamic characteristics of hyperbolic paraboloid membrane structures under normal and typhoon winds have been conducted to identify the influences of large wind velocities and high-level turbulence intensities on the dynamic responses of structure. The main conclusions can be summarized as follows.

• The increase of turbulence intensity leads to an obvious reduction of mean, RMS, maximum, and peak-to-peak deformations, within the range of 11.73–62.50%. However, there is a rapid growth in maximum deformations, up to a 16.33% increase. The suction influence of typhoons on the membrane structure should be emphasized in the wind-resistance design. Both mean and RMS deformations exhibit a roughly linear increasing trend varying with the increasing wind velocity.
• The non-Gaussian characteristics of displacement are determined mostly by the turbulence intensity, rather than the wind velocity. The skewness and kurtosis distributed over the membrane surface in typhoons are almost twice those in normal winds, which should be considered in the reliability-based design of membrane structure in typhoons.
• The increasing turbulence intensity results in larger amplitude ratios in higher mode shapes, and a two-fold increase of damping ratios at low-level wind velocity cases. However, there is an obvious reduction of damping ratios at high-level wind velocity in typhoons, which is consistent with the decrease of overall vibration amplitude and reveals the amplitude-dependent characteristics of damping ratios.