User`s guide
46
The altitude is equivalent to maximum deflection at vibration peaks. The amplitude can
be given by:
Therefore, the maximum velocity and maximum acceleration can be expressed as:
Damping Ratio
A common method for analyzing the damping of an underdamped oscillation is the
logarithmic decrement method, for which the following relationships apply.
where
is the amplitude of peak i (i is an integer counting each peak), n is the number of
cycles being considered, is the log decrement,
is the undamped natural frequency, and
is the damped natural frequency. Both frequencies are in radiance per second. Note, it is assumed
that object oscillates about zero. If there is an offset in y, the
amplitude must be defined
relative to that offset.
Elastic Modulus
From the expression for natural frequency, the expression for elastic modulus can be
derived as:
where
is
natural frequency, is density, L is effective length, T is thickness, and
values for cantilever beams are
=1.8751,
=4.6941,
=7.8548,
,
,
.