Results of different time steps analyzed by the damped Newmark's
algorithm with δ¼0.6, α¼0.5 are obtained and plotted in
Fig. 14. It can be found that very good results have been obtained
when a time step Δt is less than 0.01. However, when the time
step Δt is equal to 0.02, the results already show a serious decrease
of amplitude and decrease of frequency. Thus a proper
choice of the time step Δt plays an important role in the forced
vibration analysis. An indicator for a proper choice of the time step
is the value of the dimensionless parameter β = c t Δ
L , where
c E = /ρ L
1
2
. c is the (longitudinal) wave velocity and L is a characteristic
length of the discretization, that is the length of the
element, and L2 is the height of the beam. Therefore, β describes
the number of elements through which the elastic wave passes