任意境界を持つ弾性体の拡張低次元化物理モデル設計法

第1報, 設計法の提案とモデリング精度の検証

抄録

This paper proposes a modeling method of an Extended Reduced-Order Physical Model (Extended Model) with arbitrary boundary condition. The Extended Model is proposed to apply to the simultaneous motion and vibration control of elastic structures. The Extended Model consists of some rigid bodies which are called as rigid body elements and stiffness elements. To design rigid body elements, four dynamical conditions are used ; (1) Total mass and Total moments of inertia, (2) Position of center of gravity, (3) Modal mass and Orthogonality, (4) Modal momentum and Modal angular momentum. The (1) - (4) values of a modeling object are needed to identify masses and moments of inertia of rigid body elements. In the case of that an elastic body has free boundary conditions, the values of the Modal momentum and the Modal angular momentum are zero. On the other hand, in the case of that an elastic body has general boundary conditions, these values are not zero and needed to be identified by any means. However, it is not always any to identify these values. Therefore, a novel formulation to identify mass and inertia matrices is presented that utilizes dynamical conditions for the original object subjected to free boundary conditions. The effectiveness of the presented formulation is examined by using a simple beam. Numerical analysis is carried out and the effectiveness of the presented modeling procedure is verified.