Single degree-of-freedom systems, 55–56, 68–335,
590–592, 602–625
acceleration measurements of, 235–238
attached to beams, 590–592, 602–625
damping factor of, 83, 85–88, 95–96, 98, 100–101,
157–158
energy dissipation of, 244–255
force-balance methods for, 70–76
forced responses of, 180–283
free responses of, 126–179
frequency-response functions for, 204–218, 291–292
governing equations for, 68–125
Lagrange’s equations for, 93–116
moment-balance methods for, 76–79
natural frequency of, 79–83, 84, 85–86, 95–96, 98,
100–101
nonlinear elements of, 168–173, 269–277
periodic excitations of, 180–283
rotating machines, 218–225
stability of, 161–164
transient excitations of, 284–335
vibration isolation of, 238–244
vibration modeling and, 54–56
Skew-symmetric matrix, 348, 675–676
Ski model, 58
Slider mechanisms, 28, 109–111, 265–269, 510–513
bar-, 510–513
base excitation of, 265–269
crank-, 265–269
equation of motion for, 109–111
rotary inertia for, 28
vibration absorber, 510–513
Softening springs, 42
Spectral energy of responses, 316–317
Spring constants, 31–45
table of, 35–36
Spring systems, 29–34, 42–45, 82–83, 84, 103–105,
168–170, 380–381, 584–586
beam attachments, 584–586, 589–590, 592
combinations of, 32–34
cubic, 44–45, 168
governing equations for, 103–105
hardening, 42, 168
linear, 31–34, 168–170
mode shapes of, 380–381
multiple degree-of-freedom, 380–381
natural frequency of, 82–83, 84, 104–105, 380–381
nonlinear, 42–45, 82–83, 84
piecewise linear, 168–170
single degree-of-freedom, 103–105, 168–170
softening, 42
torsion, 31
translation, 31, 103–105, 584–586, 589–590, 592
Square matrix, 675, 677–678
Stability of systems, 161–164, 419–422
asymptotic, 163–164
gyroscopic forces and, 419–420
multiple degree-of-freedom, 419–422
root locus diagrams for, 162–163
single degree-of-freedom, 161–164
wind-induced vibrations and, 420–422
State vector, 459
State-space formulation, 436–437, 458–471, 669–671,
673–674
arbitrarily damped systems, 469–471
complex harmonic excitation and, 673–674
constant modal damping model and, 468–471
differential equations and, 669–671, 673–674
eigenvalue problem and, 464–467
proportionally damped systems, 464–467
State-space matrix, 466–467
State-space plots, 138–139, 154–155, 159–161
Static displacement, 71–72
Static-equilibrium positions, 72–76, 78–79, 345–348,
360
linear systems governing small oscillations about, 79,
345–348
multiple degree-of-freedom systems, 345–348,
360
single degree-of-freedom systems, 72–76, 78–79
Steady-state response, 184–185
Step input responses, 300–310, 474–475
Laplace transform for, 474–475
percentage overshoot, 303–304, 305
rise time, 302–303, 305
settling time, 304–305
Stiffness elements, 28–49, 165–173, 269–277, 395–396,
588–613
beam interiors, effects of, 588–613
compressed gas, 46–47
cutting, 165–167
fluids, 45–46
force of magnitude (F), 29–30
gravity loading, 45–49
machine tool chatter and, 165–167
modal, 395–396
multiple degree-of-freedom systems, 395–396
nonlinear systems, 168–173, 269–277
nonlinear springs, 42–45, 165–170
potential energy and, 29–30, 45–49
single degree-of freedom systems, 165–173,
269–277
710 Index