WAVE-DISPERSION AND OPTIMAL MASS MODELING FOR ONE-DIMENSIONAL PERIODIC STRUCTURES

Discrete analysis methods are frequently used for the study of the str ucture and soil. However, the assumption of the displacement interpola tion function makes the waves dispersive, which means the numerical di spersion. The wave dispersion induced by the discretization depends on the mass modelling. Also, the existence of added lumped masses makes waves dispersive even for the continuum modelling. In order to examine these wave dispersions, a one-dimensional periodic structure is adopt ed as an analysis model and the dynamic transfer matrix method is appl ied. A wave solution and a finite element solution are used for the ev aluation of the transfer matrix. The phase and group velocities in the structure are explicitly represented. These values are compared among the continuum modelling and the discretization modelling in which sev eral consistent mass ratios are adopted. The optimal consistent mass r atio, which makes the wave velocity of the discrete model the same as that of the continuum model, is newly developed here. The validity of this mass modelling technique is presented by examining the frequency response function and impulse response function.