dispersive and nondispersive results!

Hi dear friends 

I am working about wave propagation modeling in solids. in FEM for 1D beam model when governed differential equation of motion is solving by central difference method the output results of displacement are nondispersive but by using MATLAB "lsim" command for simulation of LTI system for arbitrary inputs, the outputs are dispersive which we expect this phenomenon will be happen in beam like models!

in bar models both methods leads to nondispersive results which is resonable.

could you help me?