Dynamical Response of a Beam in a Centrifugal Field …
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Fig. 1 Eigen pulsations for
a beam with L = 0.55 m (D
variable and ω variable)
Fig. 2 Eigen pulsations for
a beam with L = 0.55 m and
L = 1 m (D variable and ω
variable). The first
eigenvalue
be complex, without a real part (the Coriolis matrix doesn’t introduce damping in
the system) (Figs. 3 and 4).
The problem arising in calculating a beam in a centrifugal field is the loss of
stability, which happens from a mathematical point of view, when the stiffness matrix
becomes negatively defined.
It is virtually impossible to determine analytical expressions to determine the
geometric and mass field that ensures the stability of the beam in the centrifugal
field. In this case, a numerical analysis can be made to determine the nature of the
values.
The numerical calculus of eigenvalues and eigenvectors for a matrix is a difficult
operation that consumes time resources. A simpler method is to determine whether
the stiffened matrix is positively defined. For a set of defining values for the beam,