Machine Design Databook, Second Edition

Chapter 22: Mechanical Vibrations

SYMBOLS

a

coefficients with subscripts flexibility acceleration, m/s 2 (ft/s 2)

A

area of cross section, m (in 2) constant

B

constant

C

coefficient of viscous damping, Ns/m or N/v (lbfs/in or lbf/v) constant

C c

critical viscous damping, Ns/m (lbfs/in)

C t

coefficient of torsional viscous damping, N m s/rad (lbf in s/rad)

C 1, C 2

coefficients constants

d

diameter of shaft, m (in)

D

flexural rigidity [= Eh 3/12(1 ? v 2)]

e

displacement of the center of mass of the disk from the shaft axis, m (in)

E

modulus of elasticity, GPa (Mpsi)

f

frequency, Hz

F

exciting force, kN (lbf)

F o

maximum exciting force, kN (lbf)

F T

transmitted force, kN (lbf)

g

acceleration due to gravity, 9.8066 m/s 2 (32.2 ft/s 2 or 386.6 in/s 2)

G

modulus of rigidity, GPa (Mpsi)

h

thickness of plate, m (in)

i

integer (=0, 1,2,3, )

I

mass moment of inertia of rotating disk or rotor, N s m (lbf s 2 in)

J

polar second moment of inertia, m 4 or cm 4 (in 4)

k

spring stiffness or constant, kN/m (lbf/in)

k e

equivalent spring constant, kN/m (lbf/in)

k t

torsional or spring stiffness of shaft, J/rad or N m/rad (lbf in/rad)

K

kinetic energy,...

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