Page 5 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)
P. 5
Cantilever beam with end load 3EI
k eq =
l 3
Simply supported beam with load 48EI
at the middle k eq = l 3
...
... Springs in series 1 1 1 1
= + + g +
k eq k 1 k 2 k n
Springs in parallel k eq = k 1 + k 2 + g + k n
u
Hollow shaft under torsion k eq = pG 1D - d 2
4
4
(l = length, D = outer diameter, 32l
d = inner diameter,
Equivalent viscous dampers
h Relative motion between parallel mA
surfaces c eq = h
1A = area of smaller plate2
Fluid, viscosity m
Dashpot (axial motion of a 3pD l 2d
3
piston in a cylinder) c eq = m 3 a1 + b
4d D
l
d D d
Torsional damper pmD 1l - h2 pmD 3
2
c eq = +
2d 32h
l
d D d
h
Dry friction (Coulomb damping) 4fN
( fN = friction force, c eq = pvX
v = frequency,
X = amplitude of vibration)
