Shuang Zhao’s research while affiliated with Chongqing University of Science and Technology and other places

The nonlinear effects exhibited by structures under the action of wind loads have gradually stepped into the vision of wind-resistant researchers. By summarizing the prominent wind-induced nonlinear problems of four types of wind-sensitive structures, namely tall buildings, high-rise structures, flexible bridges, and transmission lines, the occurrence mechanism of their nonlinear effects is revealed, providing cutting-edge research progress in theoretical studies, experimental methods and vibration control. Aerodynamic admittance provides insights into the aerodynamic nonlinearity (AN) between the wind pressure spectrum and wind speed spectrum of tall building surfaces. The equivalent nonlinear equation method is used to solve nonlinear vibration equations with generalized van-der-Pol-type aerodynamic damping terms. The elastic–plastic finite element method and multiscale modeling method are widely employed to analyze the effects of geometric nonlinearity (GN) and material nonlinearity (MN) at local nodes on the wind-induced response of latticed tall structures. The AN in blunt sections of bridges arises from the amplitude dependence of the aerodynamic derivative and the higher-order term of the self-excited force. Volterra series aerodynamic models are more suitable for the nonlinear aerodynamic modeling of bridges than the polynomial models studied more in the past. The improved Lindstedt–Poincare perturbation method, which considers the strong GN in the response of ice-covered transmission lines, offers high accuracy. The complex numerical calculations and nonlinear analyses involved in wind-induced nonlinear effects continue to consume significant computational resources and time, especially for complex wind field conditions and flexible and variable structural forms. It is necessary to further develop analytical, modeling and identification tools to facilitate the modeling of nonlinear features in the future.

The displacement and comfort of the tower top are important reference indexes for wind resistance design of the curved torsional column spiral beam landscape tower (LT). The dynamic response of tower top and platform is analyzed and discussed through wind tunnel test of aeroelastic model, and the influence of the tower itself on wind response and comfort of pedestrian is studied. The conclusion shows that the wind Angle has a great influence on the displacement of the top of the landscape tower, and the 150° wind Angle is the most unfavorable wind Angle of LT displacement. In addition, the peak acceleration of the platform reaches its maximum value at 90° wind Angle, resulting in poor lateral pedestrian comfort at high wind speed. It is suggested to restrict pedestrians from climbing the tower at high wind speed or to carry out vibration reduction research on such structures at high wind speed.

Existing studies have found that curved beam unilateral stayed bridges (CBUSB) have a risk of cable breakage under the design wind velocity. To ensure structural wind-induced vibration security, it is necessary to study the wind-induced vibration characteristics of CBUSBs considering the influence of the impact load due to the cable breakage. Based on the aerodynamic coefficients determined by a wind tunnel test and the established impact load model, parametric analyses of important CBUSBs’ characteristics (beam curvature and cable arrangement scheme) and the location of the cable breakage are carried out to assess the influence of cable breakage on the time-domain statistical values and frequency-domain distribution characteristics of wind-induced vibration response. The DAF, considering the influence of cable breakages on the wind-induced vibration peak value of CBUSBs, is proposed through dynamic analysis. Study results show that, with increasing curvature, under the two-modes action of wind loads and impact loads, the fluctuation component of the CBUSB is changed, resulting in a smaller proportion of resonant response. For CBUSBs with unilateral or bilateral cable arrangements, their wind-induced vibration behavior is significantly different. The former have dynamic characteristics and the latter have quasi-static characteristics. The breakage of the shortest cable at 7/33 to 7/22 of the curved beam length and its symmetry part significantly increases the wind-induced peak response of CBUSBs. The DAF recommended values can consider the amplification effect of wind-induced vibration due to the cable breakage.

Sectional model wind tunnel tests and numerical simulation are general methods for studying a curved beam unilateral stayed bridge (CBUSB) to clarify the influence law of the bridge curve linear distribution on wind-induced vibration characteristics of stayed bridges. Aerodynamic force and wind-induced displacement responses are obtained using aerodynamic force and sectional model vibration tests, respectively. Based on experimental results, the finite element model is used to analyze effects of five curvature parameters on the displacement, acceleration, and cable tension of CBUSB. Results show that the displacement and acceleration of wind-induced vibration are restrained as the curvature increases, and the high-order modal vibration of the bridge is stimulated, which shows that the high-frequency vibration reduction should be considered for pedestrian comfort control at high wind speed, and a broadband vibration reduction method can be used.

Wind-induced vibration coefficient β is an essential parameter for the structural wind-resistant design. In order to provide accurate design wind loads, β of a landscape tower with curved and twisted columns and spiral beams (short for LT) is studied by wind tunnel test and numerical simulation. The results show that the displacement wind-induced vibration coefficient is greatly affected by wind yaw angle. Moreover, the inertial load wind-induced vibration coefficients increase along the height and increase sharply at the platform position. Due to the influence of nonuniform shape and mass distribution and wind yaw angle, β calculated by the Chinese and American load code does not apply to LT structures. In addition, this article puts forward some suggestions for the shortcoming in the use of code to calculate β of LTs and made some prospects for future research on wind-resistant design of LTs, hoping to provide theoretical guidance and thinking inspiration for future research.

The linear curve distribution of the beam and the asymmetrical layout of the stay cables may have beneficial or adverse influences on cable-stayed bridges. Sectional model wind tunnel tests and numerical simulations were used to analyze the influence of these two factors on the wind-induced vibration characteristics of a curved beam unilateral stayed bridges (CBUSB) and the interaction between its stay cables and curved beams. According to the basic similarity law, the sectional models of a CBUSB example were designed and manufactured. The aerodynamic force and wind-induced vibration of the models were measured in an atmospheric boundary wind tunnel laboratory to obtain the aerodynamic coefficient and displacement, respectively. Based on the wind tunnel test results, the verified finite element model was used to determine the displacement, acceleration, and cable tension of the CBUSB excited by the buffeting force under 5 curvature cases and 4 cable layout cases. Then, band-pass filter technology and fast Fourier transform technology were used to analyze the influence of these two parameters on the wind-induced vibration characteristics of the CBUSB. Results show that the CBUSB had good aerodynamic stability in the wind tunnel at low and high wind speeds. With increasing curvature, the high-order modal vibration and modal coupling vibration of the CBUSB may be generated. The frequency, the proportion of wind-induced vibration response components, and the distribution characteristics of spectrum energy of CBUSB will be affected by 4 cable layout schemes. Cables arranged on both sides of the bridge and near the center of curvature can improve pedestrian comfort and reduce wind-induced vibration, respectively. Affected by the interaction between cable and bridge, the cable and bridge transmit their own vibration to each other, both of which contain the response components of each other.

The complex aerodynamic shape and structural form affect the wind-induced vibration coefficient β of landscape towers with a twisted column and spiral beam (short for LTs). To clarify the β distribution characteristics, evaluate the applicability of existing load codes, and provide accurate design wind loads, wind tunnel tests and numerical simulations were carried out on a LT. The LT’s aerodynamic coefficients and wind-induced responses were measured using rigid sectional and aeroelastic models. Furthermore, the displacement wind-induced vibration coefficient βd and inertial load wind-induced vibration coefficient βi(z) of the LT were calculated from these measured data. Combined with test data and a finite element model, the impacts of the wind speed spectrum type, the structural damping ratio ξ, and the peak factor g on β of the LT are analyzed. The accuracy of β of the LT calculated by Chinese and American load codes was examined and given the correction method. The results showed that the wind yaw angle had a significant impact on βd of the LT, which cannot be neglected in current load codes. The abrupt mass increase at the platform location makes the distribution characteristics of βi(z) of the LT different from conventional high-rise structures. The values of ξ and g have a significant impact on the calculation results of β, which are the key to the accurate design wind loads of LTs. The existing load codes are not suitable for LTs, and the correction method proposed in this paper can be used to improve them.

As one of the most commonly-used simulation methods, the spectral representation method (SRM) has been utilized to generate fully non-stationary spatially varying ground motions. However, this method usually fails to simulate these ground motions at a large number of interesting locations because of the heavy computational cost of the decomposition of spectral matrices and the superposition of harmonic functions, especially for simulations with time-frequency coupled modulation functions. To address this issue, this study develops an efficient SRM-based method based on a simple interpolation strategy and a quadratic regularization projected Barzilai–Borwein assisted non-negative matrix factorization (QRPBB-NMF). Concretely, the distribution of interpolation nodes is predetermined via spectral feature analysis and only the spectral matrix decomposition at these nodes is required. Then, QRPBB-NMF is introduced to decouple the decomposed spectra into the sum of the products of various time and frequency expressions. Finally, a simple spline interpolation is carried out for these expressions, thereby approximately achieving the SRM-required matrix decomposition in a decoupled manner. The developed method can decrease the operand of the matrix decomposition and invoke the Fast Fourier Transform to speed up the harmonic superposition. A case study in which the fully non-stationary spatially varying ground motions of a tunnel are simulated proves the effectiveness of the developed method in terms of accuracy and efficiency.

A simplified calculation method is proposed for determining the peak dynamic windage yaw angle φ ^ of electricity transmission line (TL) tower suspension insulator strings (SISs). According to the rigid-body rule, the geometric stiffness matrix in the calculation of the windage yaw angle φ of SISs is dominated by the average wind loads, while the fluctuating wind loads are the dominant factor in the elastic stiffness. With the average wind state of conductors as the initial calculation condition, the load-response-correlation (LRC) method can be used to determine the fluctuating windage yaw angle φ d and the corresponding equivalent static wind loads (ESWLs). Then, the improved rigid straight rod model, which uses the actual length of conductors rather than the projected length, was used to determine the average windage yaw angle φ ¯ . Through the linear superposition of the horizontal increments of φ ¯ and φ ^ d (the peak value of φ d ), the formulae to calculate the φ ^ of SISs were derived. Additionally, the formulae for the dynamic wind load factor, β c , which is a key factor in designing wind loads for φ , were derived according to the principle of ESWLs, rather than being empirically determined by the Chinese code. Thus, the calculation model regarding the loads and response for the φ of SISs was established, and an actual TL was used to verify the established calculation model. Afterward, the influence of the different engineering design parameters on φ and its β c were analyzed. The parameter analyses show that the wind speed, span, and ground roughness influence the magnitudes of φ ^ and β c , however, the height difference between the two suspension points of the conductors, the nominal height, and the sag-to-span ratio may be neglected in the approximate calculation. Our method offers a new solution to TL design when there are large deformations and small strains.