A Study of Damping Effect on Elasto-dynamics and Buckling of Column and String Musical Instrument based on Hybrid Finite Element Method

摘要

First of all, the motion equation with velocity damping effect in elasto-dynamics will be discussed. Unlike the conventional displacement FEM, the higher-order time derivatives ought to be considered in the Hybrid FEM formulation. When the motion equation is transformed to the formulation of complete variation, the difference between the conventional displacement FEM and Hybrid FEM becomes quite clear from the view-point of meaning of interpretation and the transformation to a kind of telegraph equation is quite effective primarily because of complete variational formulation. Furthermore the strain rate damping effect will be discussed, where hε ~* △ method is quite effective.As the second part, buckling of column and string musical instrument issues will be explored based on structure mechanics. For the unified formulation of Hybrid FEM, the mysterious string musical instrument issue (Chinese-Japanese Harp string ≈ Heart) clarified that the Hybrid FEM formulation with 4th higher order time derivative ought to be natural. For Beck column problem, the unified formulation for Hybrid FEM gives rise to worse solution compared to the case of M-K system. It is however concluded that the phenomenon can be interpreted as "bad". The unified formulation can be employed in general for elasto-dynamics and structure mechanics.