Nonstationary Vibrations of a Perforated Cantilever Tube with a Translating Internal Cylinder Under Frictional Moving Contact

This paper develops a theory-first framework for the nonstationary transverse vibration of a slender perforated cantilever tube (fixed–free) excited by a translating internal cylindrical body under continuous frictional moving contact. In contrast to classical moving-load/moving-mass models with prescribed excitation, the proposed formulation treats the interaction as a spatially migrating and state-dependent forcing mechanism, where the contact magnitude is governed by an indentation-based normal law augmented with Coulomb friction and the excitation location follows the internal-body trajectory . Perforation effects are incorporated through effective (equivalent) stiffness and inertia operators, enabling systematic sensitivity studies while preserving analytical transparency. The coupled dynamics are derived from Hamilton’s principle (with non-conservative generalized forces for friction), yielding a non-autonomous PDE–ODE system that couples tube bending to the body’s axial motion and exit-speed prescription. A cantilever-consistent Galerkin modal reduction produces a reduced-order model in which migration enters explicitly through time-varying modal participation factors . A dimensionless formulation is presented to expose the governing control groups (mass ratio, contact stiffness ratio, friction number, and speed/traversal ratios) and to enable regime interpretation. Numerical examples and analysis outputs—including tip displacement/acceleration, fixed-end bending moment, STFT-based time–frequency signatures, Campbell-like speed maps, and contact-induced mode evolution—demonstrate that the translating cylinder acts as a broadband nonstationary source that can reorganize modal dominance, create speed-dependent amplification windows, and yield friction-mediated response growth. The resulting analytical scaffold provides a rigorous basis for prediction and design screening of cantilevered perforated tubular structures with internal translating elements.