Peculiarities of inclined force action upon one-dimensional homogeneous elastic lumped line

TL;DR

This paper derives exact analytic solutions for one-dimensional elastic lines under inclined external forces, revealing implicit wave propagation and extending findings to unforced and distributed vibrations, generalizing the wave equation.

Contribution

It introduces a general implicit function solution for inclined force effects on elastic lines, expanding understanding of wave propagation in such systems.

Findings

Implicit wave solutions describe inclined force effects

Extended analysis to unforced and distributed vibrations

Generalized wave equation solutions for elastic lines

Abstract

Exact analytic solutions for one-dimensional elastic lumped line under affection of external force inclined to the axe of line is analyzed. It is shown that in this case an inclined wave being described by implicit function propagates along the line. The conclusions were extended both to unforced vibrations in the line and to distributed-parameters line vibrations. Solution in the form of implicit function is proved as a generalizing one for the wave equation