Abstract
An accurate frequency domain model is proposed to analyze the seismic response of uniform vertical cylinders with arbitrary cross section surrounded by water. According to the boundary conditions and using the variables separation method, the vertical modes of the hydrodynamic pressure are firstly obtained. Secondly, the three-dimensional wave equation can be simplified to a two-dimensional Helmholtz equation. Introducing the scaled boundary coordinate, a scaled boundary finite element (SBFE) equation which is a linear non-homogeneous second-order ordinary equation is derived by weighted residual method. The dynamic-stiffness matrix equation for the problem is furtherly derived. The continued fraction is acted as the solution of the dynamic-stiffness matrix for cylinder dynamic interaction of cylinder with infinite water. The coefficient matrices of the continued fraction are derived recursively from the SBFE equation of dynamic-stiffness. The accuracy of the present method is verified by comparing the hydrodynamic force on circular, elliptical and rectangle cylinders with the analytical or numerical solutions. Finally, the proposed model is used to analyze the natural frequency and seismic response of cylinders.
Highlights
With the development of the economy and transportation, more and more offshore and coastal structures, such as bridge piers and offshore wind turbines, have been constructed in China in recent years
Wang et al (2019b) present an accurate and efficient numerical model to calculate the earthquakeinduced hydrodynamic pressure on uniform vertical cylinders with an arbitrary cross section surrounded by water and the simplified formulas for the hydrodynamic pressure on round-ended and rectangular cylinder were given
3.1 Scaled boundary finite element transformation SBFEM defines the domain V by scaling a defining curve Si relative to a scaling center (x0 y0), which is chosen at the center of the cylinder in this study
Summary
With the development of the economy and transportation, more and more offshore and coastal structures, such as bridge piers and offshore wind turbines, have been constructed in China in recent years. The simplified formulas of the added mass for the earthquake induced hydrodynamic pressure on circular cylinder and elliptical cylinders were given by Jiang et al (2017), Li and Yang (2013), and Wang et al (2018a). Considering the flexible of the circular cylinder, an accurate and efficient time-domain model was proposed to analyze water-cylinder interaction during earthquake (Wang et al 2018c). Wang et al (2019b) present an accurate and efficient numerical model to calculate the earthquakeinduced hydrodynamic pressure on uniform vertical cylinders with an arbitrary cross section surrounded by water and the simplified formulas for the hydrodynamic pressure on round-ended and rectangular cylinder were given. The problem of three-dimensional water-cylinder interaction is reduced to solve a two-dimensional Helmholtz equation with the boundary conditions (Liaw and Chopra 1974) as follows
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