An accurate frequency-domain model of water interaction with cylinders of arbitrary shape during earthquakes

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.

Stable parameters identification for rational approximation of Single degree of freedom frequency response function of semi‐infinite medium

“…First, in order to assess the effectiveness of the proposed method in constraining the stability of the rational function, a CRA and DRA was used to fit the hydrodynamic pressure frequency response function of the rigid cylinder shown in Figure 4 of Reference 49. The density, Young's modulus and damping ratio of the cylinder is 2500 kg/m 3 , 30,000 MPa and 0.05, respectively.…”