Bend effect on vibration pattern

V.2 No 1	93
Bend effect on vibration pattern

In the periodical vibration regime ( < ₀ ), within the elastic line, the standing wave will form, since the solutions have the following form: for the x-component
	(21)
and for the y-component
	(22)
In the aperiodical regime ( > ₀ ), we see the antiphase vibrations damping along the line in the region of external force action, because the solutions have the following form: for the x-component
	(23)
and for the y-component
	(24)
where , . The solutions for critical regime ( = ₀ ) depend on the number n evenness. With the even n the values _xi and _yi are infinite, and with the odd n the solutions take the following form: for the x-component
	(25)
and for the y-component
	(26)
It means, they practically coincide with the solutions (14)-(15).

In Figures 7 and 8, the typical diagrams are presented dependently on the external force frequency and its inclination angle to the axis x relatively. They were constructed on the basis of above solutions for the closed-loop elastic line.