S.B. Karavashkin and O.N. Karavashkina
Bend in elastic lumped line and its effect on vibration pattern
(287K, Postscript)
ABSTRACT. We prove that the bend in an elastic line does not effect on the solution pattern only, if the longitudinal and transversal stiffnesses of a line were equal. Basing on the proved theorem, we consider some models typical for the applications, particularly, models of a semi-finite elastic bended line, a homogeneous closed-loop elastic line and an elastic line having inequal longitudinal and transversal stiffness coefficients. We show that in the lines obeying the theorem conditions, with the remaining general solution, the vibration processes features are conditioned by the regularities of the co-ordinate system transformation. In case of inequal stiffness coefficients in the bend region, the complex dynamical thrusts and vibration break-downs take place, and the vibration amplitude grows. In the bend region the resonance peaks arise; their frequencies do not coincide for the wave process longitudinal and transversal components. This last leads to the fact that in one and the same elastic line, with an invariable angle of external force inclination, dependently on frequency, the longitudinal, transversal or inclined waves can propagate along the line. With it, the wave inclination does not coincide with the external force inclination, as it takes place in the lines having equal stiffness coefficients. As the examples we will consider some aspects of these models application to the geophysical problems.