Parametric Dynamic Instability of a Nonlocal Axially Moving Nano-Beam with Harmonic Length Under Thermo-Mechanical Forces

Abstract

This paper investigates the dynamic instability behavior of an axially moving nano-beam with time-varying length, placed in a thermal environment and resting on a viscoelastic Pasternak-type foundation while subjected to axial loading. The governing equations of motion are formulated using the Euler–Bernoulli beam theory, incorporating nonlocal elasticity effects, and derived via Hamilton's principle. Floquet theory is employed to identify regions of parametric instability in the amplitude–frequency domain of the beam's longitudinal oscillations. A comprehensive parametric study is conducted to evaluate the influence of various physical factors, including geometric dimensions, axial velocity, nonlocal effects, thermal variations, axial forces, and viscoelastic foundation properties. The results demonstrate that the dynamic stability of the nano-beam is highly sensitive to these parameters. Notably, increasing the length of the nano-beam and the amplitude of longitudinal oscillations makes the system more prone to instability, whereas greater beam thickness and foundation stiffness enhance system stability. Thermal loads and compressive axial forces tend to destabilize the structure, while tensile loading and viscoelastic damping promote stability. The findings provide fundamental insights into the design of nano-scale moving beam systems under coupled thermal and mechanical fields and offer design guidelines for achieving dynamic robustness in advanced nanoelectromechanical systems (NEMS). © 2025 Elsevier B.V., All rights reserved.