Beam-Rod Contact Stability Analysis

Axially Translating Beam Contact-Coupled to an Axial Rod with Tip Mass

This package contains MATLAB code for the Galerkin-based eigenvalue analysis of an axially translating Bernoulli--Euler beam in continuous contact with a stationary axial rod carrying a tip mass.

The script assembles the coupled beam--rod system matrices, solves the resulting state-space eigenvalue problem over a range of nondimensional transport speeds, and performs MAC-based tracking of the first modal branches. The code can reproduce the principal Galerkin results used in the accompanying manuscript, including divergence, re-stabilization, flutter-type modal interaction, and root-locus plots in the complex eigenvalue plane.

Main features:

- Exact Galerkin formulation using beam sine modes and axial rod modes

- Tip-mass-dependent rod modal roots

- Nondimensional eigenvalue sweep with respect to transport speed

- MAC-based tracking of selected modal branches

- Stability classification based on the real and imaginary parts of the eigenvalues

- Root-locus visualization of the tracked branches

- Optional mode-shape and participation-ratio plots

To run the main analysis, open and execute:

run_galerkin_beam_rod_contact_sweep.m

The default settings generate the tracked root-locus figure. Additional plots can be enabled using the plot/output switches near the beginning of the script.

A finite-element version of the code will be added in a later update.