Following simple theory of bending one can write
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(11.1) |
where  = bending moment amplitude at the section,  =
depth of the beam,  = maximum bending stress amplitude at the section  (i.e., in the fibre at a distance  from the neutral axis), and  = bending stress
amplitude in the fibre at a distance  from the neutral axis where the width of
the beam is  . The maximum elastic energy stored in the beam for a complete cycle of vibration may be expressed as
 |
(11.2) |
where l = length of the beam and  = Young's modulus. Substituting eqn.
(11.1) in eqn. (11.2), we obtain
Using the damping-stress amplitude relationship, we get the energy dissipated
per cycle from the entire beam as
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