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Degrees of
Freedom It is important to
appreciate the concept of "degrees of freedom". The
number of "degrees of freedom" that a vibrating
system has will greatly affect how it
vibrates. A simple definition of
"degrees of freedom" is - the number of coordinates
that it takes to uniquely specify the position of a
system. Consider a rigid
block that is free to move in 3
dimensional space. As shown in the diagram
it may move without rotation in each of
the three directions x, y and z. these are
called the three degrees of
translation. The block may
also rotate about each of the axes, these
are called the three degrees of
rotation. Thus to uniquely
define the position of the block in space
we need to define six coordinates, three
translation and three rotation. It should be
noted that each of the coordinates would
be defined with respect to some fixed
reference. The origin of the x. y and z
axes would be a fixed position with
respect to earth and the directions of the
3 axes would also be fixed. It is possible to
reduce the number of degrees of freedom of
such a rigid block by introducing
constraints One
degree of
freedom
In this first
case we have constrained the block to have
only one degree of freedom by, Using a rigid rod
which is fixed to earth (not shown for
clarity) Thus the block may move along the
rod in the y direction only. Also because the
rod has a square section the block cannot
rotate about the axis of the
rod. There is
therefore only one degree of freedom.
Knowing the position of the fixed and
rigid rod we only need one coordinate - in
this case the y coordinate - to uniquely
specify the position of the
block. Two
degrees of
freedom
In this second
case we have allowed the block a second
degree of freedom by giving the rigid rod
a circular section. This means that
the block may rotate about the axis of the
rod. To uniquely define the position of
the block now requires that we specify the
position along the rod (the y coordinate)
and also the rotation of the block about
the rod (the y
coordinate). The block thus
has two degrees of freedom. |
