Stability and modal interactions of an axially translating beam contact-coupled to a stationary in-span axial rod with a tip mass

This paper develops and validates a distributed-parameter model for an axially translating simply supported Bernoulli–Euler beam in continuous contact with a stationary in-span axial rod carrying an optional tip mass. Unlike lumped in-span oscillator idealizations, the contacting subsystem is modeled as a finite-length axial member, so its longitudinal stiffness and inertia together with the concentrated tip inertia enter the coupled dynamics explicitly via the normal-contact compatibility condition. A nondimensional formulation is derived and discretized using two approaches: an assumed-modes Galerkin expansion and a finite-element model. The resulting complex-eigenvalue problem is solved via continuation in dimensionless transport speed with modal correspondence using MAC-based mode tracking and special handling of divergence–restabilization transitions. Close agreement between the Galerkin and FEM spectra over the transport-speed range cross-validates the formulation and implementation. The results demonstrate that a stationary distributed axial subsystem can substantially modify the dynamics of the translating beam, producing divergence-type instability, flutter-type modal interaction, and transport-induced redistribution of modal participation between the beam and the rod–tip-mass subsystem. The proposed framework therefore extends conventional lumped-oscillator descriptions and provides a basis for assessing the stability and modal characteristics of translating beams interacting with stationary compliant in-span subsystems. Computational codes are released to enable the reproduction of the reported results and exploration of alternative parameter combinations.