Study on dynamic characteristics of high-rise steel chimneys based on Adomian decomposition method and regression analysis (II): Modal shape

Modal shape is one of the key factors for analyzing wind induced responses, and hence in this work the modal shape of high-rise steel chimneys is studied. Firstly, after the boundary conditions and continuity conditions being introduced, the modal shape is solved via Adomian Decomposition Method (ADM). Secondly, the sample data of modal shape are obtained using random sampling method based on the statistical distributions of the parameters of high steel chimneys, as investigated in previous studies of the authors. Lastly, the expressions of dimensionless modal shape, which contain the Eurocode function, polynomial, summation of exponential function, summation of Sine function and Fourier series, are fitted by introducing regression analysis method. Then the expressions of first four modal shapes are presented, and the fitting precision, complexity and applicability of all expressions are also discussed. The results show that the expression in the form of Polynomial or Fourier series is more suitable for the further investigation of unified wind vibration theory. This work may offer some reference for the design of high-rise steel chimneys and the revision of relevant codes.