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S.B. Karavashkin, O.N. Karavashkina

As we can see from the preliminary analysis, the vibration pattern essentially transforms in case of inequal stiffness coefficients. Each of three regions has its salient features that require their broad investigation. Regarding the low-frequency pattern of geophysical vibrations, in this work we will limit our investigation by the first region.

If the condition (33) was true, then in the band 0 < < _lt   the general solution for a semi-finite homogeneous elastic lumped line takes the following form:

for  i k

As depend only on the parameters of elastic line but do not depend on time and index i, basing on (34)-(35), we can state that with the inequal longitudinal and transverse stiffness coefficients in the before-bend region, the superposition of standing and progressive waves forms, depending not only on the line parameters but on the vibration frequency. With it, the longitudinal vibrations can produce in a line also under the transverse external force, and those transverse – also under the longitudinal external force, which is basically impossible in case of equal stiffness coefficients.

In the after-bend region the progressive wave forms; its amplitude depends not only on the line parameters and the bend angle, but on vibration frequency, too. As we said above, with it the phase delay for longitudinal and transverse components differ, and this complicates the resulting pattern of the vibration process. Particularly, in the region of in-phase total phase delays we see the positive inclination of a progressive wave (i.e., the wave propagates with the angle ahead). With the antiphase total phase delay we see the negative inclination of a wave (i.e., the wave propagates with the angle back). These regions take turns.