Index
153
time domain analysis
amplitude phase representation, 15–17
arbitrary forcing, 20–25
damping estimation, 17
harmonic force, damped system, 28–32
harmonic force, undamped system,
25–27
homogeneous solution, 12–14
simple forcing functions, 17–20
standard form, 14–15
Standard form, 14–15
State-space representation, 98
Steady-state solution, 36–39, 103, 108–110
Symmetric matrices, 59–63
T
Taylor series, 133–134
Time domain, 9
Time domain analysis
amplitude phase representation, 15–17
arbitrary forcing, 20–25
damping estimation, 17
harmonic force, damped system, 28–32
harmonic force, undamped system, 25–27
homogeneous solution, 12–14
non-proportional damping (see Nonproportional damping)
simple forcing functions, 17–20
standard form, 14–15
Torsional vibration
equation of motion, 96–97
mass matrix, 95
single story structure, 94
structural and mechanical systems, 93
structural stiffness, 94–96
Transition matrix, 110–111
U
Undamped system, harmonic force
beating phenomenon, 27–28
resonance phenomenon, 26–27
Undamped systems
forced vibration, 84–86
free vibration, 86–88
Unit impulse response function, 22
V
Vector spaces, 141–145
Vector-valued forcing functions, 107
W
Work-energy (WE), 5, 6