W-1-1-4 INTRODUCTION OF DAMPING MATRIX INTO ABSOLUTE NODAL COORDINATE FORMULATION

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概要

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• Accurate seismic analysis of large deformable moving structures is still unsolved problems in the field of earthquake engineering. In order to analyze the problems, the dynamics of flexible beam undergoing large deformation has been studied by the authors. Generally this type problem is tackled by the finite element method. There are three basic finite element formulations which are used in the dynamics of flexible beams. There are the floating frame of reference approach [1,2,3], the finite segment method [4,5], and the large rotation vector approach [6] Recently, the absolute nodal coordinata (ANC) formulation for beam elements was proposed by A. A. Shabana [7,8]. In this procedure, there is no need to transform the element matrices into the global ones because the equations of motion are already defined in terms of the absolute nodal coordinates defined in the global reference frame. Consequently, the mass matrix becomes constant with time, whereas the stiffness matrix becomes nonlinear function of time, even in case of linear elastic deformation. One possible method to avoid such cumbersome of the absolute nodal coordinate formulation in calculating elastic forces is to assume the infinitesimal deformation theory for beams undergoing large rotation. A new time independent formulation for bending motion in calculating elastic forces of the beam, and consequently the constant stiffness matrix were derived by the authors [9]. In this formulation, the elastic force for axial deformation is still time dependent. When we calculate the dynamic problems of a flexible moving structure such as a crane during earthquakes, application of large deformation theory for the structures composing of the beam elements is unavoidable to obtain accurate results. Respose calculation, in this case, requires the damping property as well as mass and stiffness properties of the structures. This paper firstly summarizes the former researches done by the authors and then considers the introduction of damping property into the flexible system described by the absolute nodal coodinates. In the practical linear theory of structural dynamics, Rayleigh damping is often used to describe the system damping because of its simplicity and practicality. It may be attractive in the response calculation if we introduce Rayleigh type damping into nonlinear equations of motion described by ANC formulation. We have tried to develop a procedure of introduction of Rayleigh type and other type damping matrices into ANC formulation. Reasonable assumptions lead to practical damping matrices for calculating structual seismic responses. Our former formulation for ANC plays an important role for our present study.

• 一般社団法人日本機械学会の論文

著者

• Shimizu Nobuyuki

  Dep. Of Mechanical Engineering Iwaki Meisei University

• Takahashi Yoshitaka

  Dep. Of Mechanical Engineering Iwaki Meisei University

• Suzuki Kohei

  Dep. of Mechanical Engineering Tokyo Metropolitan University

関連論文

• W-1-1-4 INTRODUCTION OF DAMPING MATRIX INTO ABSOLUTE NODAL COORDINATE FORMULATION

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