Page 75 - Dynamic Loading and Design of Structures

Page 54

Figure 2.20 Comparison between various commonly used time integration methods for a two DOF
system.

t
We first focus on the free vibration problem, with f (t)=sin ω, so that eqns (2.69) assume the
form

(2.70)

The eigenfrequencies, natural periods as well as the corresponding eigenvectors which result
from solving the above homogeneous system of equations are given in Table 2.2. Also, a
sketch of the three eigenvectors appears in Figure 2.22. Next, we continue with modal
analysis along the lines developed in the previous section; Table 2.3 presents all intermediate
computations plus the final static values of the three modal displacements A , n=1, 2,3 from
nst
eqn (2.64). The values for the DLF corresponding to each modal equation depend on the rise
time t of the applied load (see Figure 2.8) and on the natural periods T ; they in turn are given
n
r
in Table 2.4.
Maximum values for the three modal components of the horizontal dynamic dis-