Dynamical Response of a Beam in a Centrifugal Field …
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Fig. 5 Domain of instability for D, ω, L variable
Fig. 6 Domain of instability for D, ω, L variable
of determining the admissible values for geometric and mass elements. Because
a theoretical approach is less useful in practical applications, only the numerical
approach can provide useful results. In the paper, the motion equations obtained by
other authors have been used, in a particular form, for the rotation of a beam around
an axis. On the basis of these equations obtained via FEA, it is analyzed for some
cases, the domain of values that the geometric and mass parameters can have. The
results are presented in graphical form and the method used to determine areas of
instability uses the calculation of the positivity of the stiffness matrix, a much easier
operation than the calculation of its eigenvalues. Our application is inspired from
the practical case of the rotor blade of helicopters, where the use of one-dimensional
111
Fig. 5 Domain of instability for D, ω, L variable
Fig. 6 Domain of instability for D, ω, L variable
of determining the admissible values for geometric and mass elements. Because
a theoretical approach is less useful in practical applications, only the numerical
approach can provide useful results. In the paper, the motion equations obtained by
other authors have been used, in a particular form, for the rotation of a beam around
an axis. On the basis of these equations obtained via FEA, it is analyzed for some
cases, the domain of values that the geometric and mass parameters can have. The
results are presented in graphical form and the method used to determine areas of
instability uses the calculation of the positivity of the stiffness matrix, a much easier
operation than the calculation of its eigenvalues. Our application is inspired from
the practical case of the rotor blade of helicopters, where the use of one-dimensional