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Volume 25, Number 5, November 2017

he nonlinear aerodynamic instability of a tensioned plane orthotropic membrane structure is theoretically investigated in this paper. The interaction governing equation of wind-structure coupling is established by the Von Kármán\'s large amplitude theory and the D\'Alembert\'s principle. The aerodynamic force is determined by the potential flow theory of fluid mechanics and the thin airfoil theory of aerodynamics. Then the interaction governing equation is transformed into a second order nonlinear differential equation with constant coefficients by the Bubnov-Galerkin method. The critical wind velocity is obtained by judging the stability of the second order nonlinear differential equation. From the analysis of examples, we can conclude that it\'s of great significance to consider the orthotropy and geometrical nonlinearity to prevent the aerodynamic instability of plane membrane structures; we should comprehensively consider the effects of various factors on the design of plane membrane structures; and the formula of critical wind velocity obtained in this paper provides a more accurate theoretical solution for the aerodynamic stability of the plane membrane structures than the previous studies.

Key Words
membrane structures; orthotropy; nonlinearity; wind-induced instability; critical wind velocity

Changjiang Liu: State Key Laboratory of Geohazard Prevention and Geoenvironment Protection,
Chengdu University of Technology, Chengdu, 610059, China;
Department of Structural Engineering, University of California, San Diego, La Jolla, CA 92093, USA
Feng Ji: State Key Laboratory of Geohazard Prevention and Geoenvironment Protection,
Chengdu University of Technology, Chengdu, 610059, China
Zhoulian Zheng: College of Civil Engineering, Chongqing University, Chongqing, 400045, China
Yuyou Wu: Department of Buildings, Shenzhen Institute of Urban Safety, Shenzhen, Guangdong, 518000, China
Jianjun Guo: Chongqing Water Resources and Electric Engineering College, Yongchuan, Chongqing, 402160, China

As a novel typical wind-sensitive structure, the wind load and wind-induced structural behaviors of super-large straight-cone cooling towers are in an urgent need to be addressed and studied. A super large straight-cone steel cooling tower (189 m high, the highest in Asia) that is under construction in Shanxi Power Plant in China was taken as an example, for which four finite element models corresponding to four structural types: the main drum; main drum + stiffening rings; main drum + stiffening rings + auxiliary rings (auxiliary rings are hinged with the main drum and the ground respectively); and main drum + stiffening rings + auxiliary rings (auxiliary rings are fixed onto the main drum and the ground respectively), were established to compare and analyze the dynamic properties and force transferring paths of different models. After that, CFD method was used to conduct numerical simulation of flow field and mean wind load around the cooling tower. Through field measurements and wind tunnel tests at home and abroad, the reliability of using CFD method for numerical simulation was confirmed. On the basis of this, the surface flow and trail characteristics of the tower at different heights were derived and the wind pressure distribution curves for the internal and external surfaces at different heights of the tower were studied. Finally, based on the calculation results of wind-induced responses of the four models, the effects of stiffening rings, auxiliary rings, and different connecting modes on the dynamic properties and wind-induced responses of the tower structure were derived and analyzed; meanwhile, the effect mechanism of internal suction on such kind of cooling tower was discussed. The study results could provide references to the structure selection and wind resistance design of such type of steel cooling towers.

Key Words
steel cooling tower; straight-cone type; numerical simulation; mean wind load; wind-induced response; internal pressure effect

S.T. Ke: Department of Civil Engineering, Nanjing University of Aeronautics and Astronautics, 29 Yudao Road,
Nanjing 210016, China;
State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China
L.Y. Du: Department of Civil Engineering, Nanjing University of Aeronautics and Astronautics, 29 Yudao Road,
Nanjing 210016, China
Y.J. Ge and L. Zhao: State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China
Y. Tamura: Center of Wind Engineering Research, Tokyo Polytechnic University, 1583 Iiyama, Atsugi, Kanagawa 243-0297, Japan

In this study an analytical expression is derived for the natural frequency of the wind turbine towers supported on flexible foundation. The derivation is based on a Euler-Bernoulli beam model where the foundation is represented by a stiffness matrix. Previously the natural frequency of such a model is obtained from numerical or empirical method. The new expression is based on pure physical parameters and thus can be used for a quick assessment of the natural frequencies of both the real turbines and the small-scale models. Furthermore, a relationship between the diagonal and non-diagonal element in the stiffness matrix is introduced, so that the foundation stiffness can be obtained from either the p-y analysis or the loading test. The results of the proposed expression are compared with the measured frequencies of six real or model turbines reported in the literature. The comparison shows that the proposed analytical expression predicts the natural frequency with reasonable accuracy. For two of the model turbines, some errors were observed which might be attributed to the difference between the dynamic and static modulus of saturated soils. The proposed analytical solution is quite simple to use, and it is shown to be more reasonable than the analytical and the empirical formulas available in the literature.

Key Words
natural frequency; wind turbine tower; soil-structure interaction; beam theory; stiffness matrix

Xue-Ning Rong: School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
Ri-Qing Xu and Su-Yang Feng: Research center of coastal and urban geotechnical engineering, Zhejiang University,
Hangzhou 310058, China
Heng-Yu Wang: Ningbo institute of technology, Zhejiang University, Ningbo 315100, China

nclined and yawed circular cylinder is an essential element in the widespread range of structures. As one of the applications, cables on bridges were reported to have the possibility of suffering a kind of large amplitude vibration called dry galloping. In order to have a detailed understanding of the aerodynamics related to dry galloping, this study carried out a set of wind tunnel tests for the inclined and yawed circular cylinders. The aerodynamic coefficients of circular cylinders with three surface configurations, including smooth, dimpled pattern and helical fillet are tested using the force balance under a wide range of inclination and yaw angles in the wind tunnel. The Reynolds number ranges from 2 X105 to 7X105 during the test. The influence of turbulence intensity on the drag and lift coefficients is corrected. The effects of inclination angle yaw angle and surface configurations on the aerodynamic coefficients are discussed. Adopting the existed the quasi-steady model, the nondimensional aerodynamic damping parameters for the cylinders with three kinds of surface configurations are evaluated. It is found that surface with helical fillet or dimpled pattern have the potential to suppress the dry galloping, while the latter one is more effective.

Key Words
inclined and yawed circular cylinder; surface configuration; Reynolds number; drag coefficient; lift coefficient; nondimensional aerodynamic damping parameter

Siyuan Lin, Mingshui Li and Haili Liao: Research Centre for Wind Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, China;
Key Laboratory for Wind Engineering of Sichuan Province, Chengdu, Sichuan 610031, China

Wind-induced response behavior of long-span roof structures is very complicated, showing significant contributions of multiple vibration modes. The largest load effects in a huge number of members should be considered for the sake of the equivalent static wind loads (ESWLs). Studies on essential matters and necessary conditions of the universal ESWLs are discussed. An efficient method for universal ESWLs on long-span roof structures is proposed. The generalized resuming forces including both the external wind loads and inertial forces are defined. Then, the universal ESWLs are given by a combination of eigenmodes calculated by proper orthogonal decomposition (POD) analysis. Firstly, the least squares method is applied to a matrix of eigenmodes by using the influence function. Then, the universal ESWLs distribution is obtained which reproduces the largest load effects simultaneously. Secondly, by choosing the eigenmodes of generalized resuming forces as the basic loading distribution vectors, this method becomes efficient. Meanwhile, by using the constraint equations, the universal ESWLs becomes reasonable. Finally, reproduced largest load effects by load-response-correlation (LRC) ESWLs and universal ESWLs are compared with the actual largest load effects obtained by the time domain response analysis for a long-span roof structure. The results demonstrate the feasibility and usefulness of the proposed universal ESWLs method.

Key Words
universal equivalent static wind loads; long-span roof structures; generalized resuming forces; POD analysis; constraint equations

Nan Luo, Haili Liao and Mingshui Li: Research Center for Wind Engineering, School of Civil Engineering,
Southwest Jiaotong University, Chengdu, Sichuan, 610031, China

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