ABSTRACT
The response (acceleration, velocity, and displacement) estimation for the vibration load is important to understand the dynamic behavior of structures, machines, etc. The dynamic equation of a system is given by
( ) ( ) ( ) ( )+ + = t t t tMr Cr Kr F (4.1)
where M, C, and K are the system mass, damping, and stiffness matrices, respectively. If the number of DOFs at a node is six and the total number of nodes is equal to n, then the system matrices size will be 6n × 6n. The response vectors, r(t), and the force vectors, F(t), at time t can be written as
(4.2)
If the time increment is Δt and the total number of time steps is q, then the time data are t = [ 0 Δt 2Δt ⋯ (q − 1)Δt ]T and the corresponding force and response vectors are F(t) = Ft = [ F0 FΔt F2Δt ⋯ F(q − 1)Δt ]T and r(t) = rt = [ r0 rΔt r2Δt ⋯ r(q − 1)Δt ]T, respectively. The responses can be calculated either by the direct integration method or the mode superposition method. Both methods are discussed here.
