FREQUENCY RESPONSE
In direct frequency response analysis, structural response is computed at discrete excitation frequencies by solving a set of coupled matrix equations using complex algebra.
The load is introduced as a complex vector. Which is convenient for the mathematical solution of the problem.
For harmonic motion (basis of frequency response), assume a harmonic solution. U(ω) is the complex displacement vector.
Differentiating and substituting, and simplifying e(iωt) the final equation is obtained.
If damping is present or the applied loads have phase angles, the coefficients of the equations are complex.
This set of equations is solved in a manner similar to a static problem using complex arithmetic.