Design and Stress Analysis of Extraterrestrial ... - The Black Vault

Determining the frequencies of inherent (free)
vibrations of blades
In the vibrational analysis of blades let us use the following
assumption.
1. The blade is a rod one end of which is tightly sealed and
the other is free. The axis of the unbent blade (in free position)
is rectilinear and is directed strictly along the z-axis (Fig. 3.23).
2
a) a) L(b)(c
Fig. 3.22. Types of vibration Fig. 3.23. Calculation diagram of
cracks in turbine blades.
a blade (for vibrati.onal analysis).
2. We shall examine blade vibrations only in the smallest
rigidity plane, i.e., relative to the principal side axis.
3. We assume the blade is not twisted but is turned a certain
angle 0 = const (there is no rotational inertia of the section).
I. There is no rotation, i.e., theie are no longitudinal forces
being caused by centrifugal forces (the effect of centrifugal forces
on vibration frequency in a blade will be discussed later).
The natural frequencies of blade vibration will be determined
by the method of the direct compilation of a freqiency equation
using the familiar D'Alambert principle.
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