Study Of Generalized Van Der Pol Aerodynamic Damping Model And Equivalent Nonlinear Response Analysis Of Wind-excited High-flexibility Structures

High flexible structures with blunt body sections,such as tall buildings,chimneys,masts and so forth,are highly sensitive to wind loads.When wind passes high flexible structures,periodic vortex shedding may induce the crosswind vibration.When the vortex shedding frequency is close to the structural natural frequency,the vortex shedding frequency will be ‘locked’ by the structural natural frequency,triggering vortex-induced vibration(VIV)with large response amplitude.At this point,wind load is a key factor concerning the safety and comfort design of high flexible structures.Since VIV may trigger structural fatigue,damage of structural element and even collapse problem,it is necessary to evaluate the crosswind response of high flexible structures accurately in practical design.The large crosswind response of high flexible structures is due to the nonlinear self-excited wind load induced by the interaction between the structural vibration and the boundary conditions of the surrounding flow field.In this sense,accurate description of the amplitude-dependent self-excited wind load is the basis for reasonable evaluation of the crosswind response of high flexible structures.Considering that aerodynamic damping models have been widely used for describing the crosswind self-excited wind load of high flexible structures,accuracy of the aerodynamic damping models determines whether the crosswind response of high flexible structures can be accurately evaluated or not.As a result in this thesis,establishment of the crosswind aerodynamic damping model,determination of the undetermined parameters of aerodynamic damping model and the equivalent nonlinear crosswind analysis of high flexible structures are studied by using the research methods of the nonlinear random vibration theory,Monte Carlo random numerical simulation and free vibration wind tunnel test.The main research work of this thesis is as follows:(1)In order to describe the crosswind self-excited wind load of high flexible structures,the generalized Van der Pol(GVDP)aerodynamic damping model is proposed.The proposed model is capable of accurately describing the amplitude-dependent nonlinear aerodynamic damping at various wind speeds.In addition,the proposed model has been successfully adopted to capture the self-excited wind loads of some typical high flexible structures such as chimneys,tall buildings and so forth;(2)In order to determine the unknown parameters of the GVDP aerodynamic damping model,mapping relationship between the GVDP aerodynamic damping model and probability density function(PDF)of the crosswind displacement response is established.Then a method for identifying aerodynamic damping by using PDFs of the crosswind displacement response of high flexible structures is proposed.Accuracy of the proposed method is demonstrated by comparing the predicted results with those of the Monte Carlo simulation and free vibration wind tunnel test of crosswind response of high flexible structures;(3)Since accurate analytical solution of the stochastic structural dynamic equation considering nonlinear aerodynamic damping cannot be obtained so far,the widely-used harmonic balance-and statistical linearization technique are used to linearize the nonlinear GVDP aerodynamic damping model,and the crosswind response is then solved based on the linear random vibration theory.By comparing the calculated(predicted)results with those obtained from the Monte Carlo simulation and free vibration wind tunnel test of crosswind response of high flexible structures,it is found that the equivalent aerodynamic damping linearized by the harmonic balance technique can well predict the root-mean-square(RMS)crosswind response while significantly underestimate the peak response of practical concern.With respect to the equivalent aerodynamic damping linearized by the statistical linearization technique,it underestimates the RMS crosswind response significantly while overestimates the peak response.Based on the linearized equivalent aerodynamic damping and linear random vibration theory,applicability and limitations of crosswind response analysis of high flexible structures are systematically analyzed;(4)Based on the nonlinear random vibration theory,the equivalent nonlinear GVDP aerodynamic is introduced,and analytical solutions of PDF of structural displacement(amplitude)response,extreme value distribution,RMS value,kurtosis and peak factor are derived.The calculated(predicted)results obtained from the present method are compared with those obtained from crosswind response Monte Carlo simulation,free vibration wind tunnel test and full-scale measurement,and accuracy of the proposed method concerning the crosswind response analysis is demonstrated.