3414 質量と剛性の分布を保存するシステム同定(S83 モード解析とダイナミックス)

Abstract

This paper proposes a method to identify mass and stiffness matrices of structures. The mass and stiffness matrices of finite-elements have mass and stiffness distributions. Therefore, the proposed method identifies mass and stiffness matrices to improve the mass and stiffness distributions of the original model to approach those of the real structures. The mass and stiffness matrices of finite-elements are divided into several groups considering vibration modes of structures. A group is represented by a sparse matrix (grouped matrix) with non-zero values at only degrees of freedom in the group. Mass and stiffness matrices are modified group by group. The objective function to be minimized is the sum of each norm of difference between analytical and identified group matrices. A numerical example is given to show the effectiveness of the method. Nomenclature A : Area of cross section [E ] : Unit matrix g : Gravity acceleration IX, IY, IZ : Measured moment of inertia IXY, IYZ, IZX : Product of inertia [kA i] : Original stiffness matrix of element i [k A i, j ] : Element stiffness matrix of finite element i in group j [k i ] : Identified stiffness matrix of finite element [K ] : Identified stiffness matrix of structure l : Length of beam element m : Measured mass [m A i ] : Original mass matrix of element i [m A i, j ] : Element mass matrix of finite element i in group j [m i ] : Identified mass matrix of structure [ ] M : Identified mass matrix of structure [M 0 ] : Rigid-body mass matrix with measured mass properties n : Number of element nT : Number of measured modes p : Number of group in element mass and stiffness matrices r : Torsional rigidity {R} : Rigid-body displacement vector [T ] : Transformation matrix X G , Y G , Z G : Measured center of gravity α, β, γ : Lagrange multiplier λ, ν : Modification coefficient {φ } : Measured mode Ω : Measured angular frequency IIM II : Norm of matrix [M] {1} : Vector with all elements 1