| V.2 No 1 | 91 |
| Bend effect on vibration pattern | |
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Fig. 3. The vibration patterns in a homogeneous
semi-finite elastic line having a bend with the angle
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As was supposed, the difference between the x-
and y-components is only the value of projections of external force amplitude,
and the solutions before and after the bend do not differ. None the less, the vibration
patterns within the indicated regions will differ. In Fig. 3 the typical pattern is shown
dependently on the external force inclination angle  at the positive angles  , and in Fig. 4 – at the
negative . |
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Fig. 4. The vibration patterns in a homogeneous
semi-finite elastic line having a bend with the angle |
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In Fig. 5 the diagrams of typical vibrations in the lines
with positive and negative bend angles are shown dependently on the external force
momentary phase  =  t +  0 . As we can see from the construction, in the region
before the bend in all the diagrams the inclined waves propagate. The inclination value
equals to the angle of an external force inclination to the axis x. During the
vibration process all elements move elliptically, in full correspondence with the multiple
experimental facts (see, e.g., [13, pp. 300–301]). In the after-bend region, with
positive we
see the decreasing amplitude of a longitudinal component, and vice versa with negative . At the same
time, with the positive the slop of wave front grows with growing , and with the negative it diminishes
with growing . |
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at the 17th line element, with
respect to the external force momentary phase = t + 0 at the external force inclination angle = 40o
to the axis x. The line parameters: s = 100 N/m; m = 0,01 kg; F0
= 1 N; = 110
sec-1 |
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