Forced
vibration of a damped SDOF system requires us to determine both transient and
steady-state structural responses. The transient response is obtained from the
complementary function of the solution of the full form equilibrium equation.
Steady-state response on the other hand, is the particular integral which is
only dependent of the loading frequency and time. Over long period of time, the
transient response diminishes, and the structural response is mainly governed
by the steady-state response.
The following shows the example of forced vibration of an undamped SDOF system. Watch the video above for full details.
System overview
Derivation 1
Derivation 2
Derivation 3
Derivation 4
Derivation 5
Derivation 6
Derivation 7
Derivation 8
Derivation 9
Derivation 10
Derivation 11
Derivation 12
Derivation 13
Derivation 14
Derivation 15
Complementary function
Comparison of transient and steady-state responses
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