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16 Computer Programs in Vibration Analysis
Table 16.1 Outline of computer program for program RESPONSE
Forced vibration
10
Input
From low speed memory
Natural frequencies and mode shapes
Mass matrix
Geometric and material properties
Input
From user
Damping coefficient
Time step, duration
Pressure function
Initial displacements and velocities
Displacement and stress output points
Call
ORTHO (* to orthonormalise the eigenvectors
[] T [M] []∗)
Call
NEWMARK (*to determine the constants of
Newmark’s scheme of integration*)
Call
FORCE (*to find out nodal forces from pressure
function*)
Call
TRANS (*to calculate [] T {F (t)}∗)
Cal I
INTIG (*to evaluate displacements, velocities and
accelerations at the next time step*)
Write
(displacement, velocity and acceleration)
If
(stress is required)
Then Call
STRESS (*to generate element stress from nodal
displacement*)
Write (stresses)
End
If
NSTEP: =
NSTEP + 1
If
(End of time function is reached) RETURN
Go to 10
End
16.3 Computer Program for Random Vibration Analysis
The computer program for determining response under stochastic loading is much
more involved than the deterministic approach. It has been shown in the previous
chapter that the mode superposition method can be applied to the solution of the
random vibration problems. The analysis in this case has to be carried out in the
frequency domain. This system admittance matrix and the cross-spectral density
matrix of the generalised forces are populated square matrices of the order of total
number of equations of the problem, If they are stored in the computer memory, they