A comprehensive investigation of dual-damped Euler-Bernoulli beam under moving mass on Pasternak foundation via spectral and central difference methods

Abstract

This study investigates the dynamic behavior of a dual-damped Euler-Bernoulli beam carrying a moving mass and supported on a Pasternak foundation, with the aim of improving prediction and control of vibration in structural systems. The beam model incorporates both internal (material) and external (viscous) damping and is discretized spatially using the Chebyshev collocation method (high-order spectral accuracy). Time integration is performed with an explicit central-difference scheme. Convergence and stability of the high-order spatial discretization with explicit time stepping are assessed, and extensive parametric studies are carried out over inertia, foundation shear stiffness, and damping coefficients. Numerical results validated across simulation cases show clear repeatable trends: increases in mass per unit length, foundation shear stiffness, and viscoelastic (internal and external) damping all substantially reduce peak deflection amplitudes and mid-span displacement. The moving-mass model predicts lower critical speeds and larger dynamic amplification better than equivalent moving-force approximations. The combined dual-damped, high-order numerical scheme provides an accurate efficient tool for analyzing beam dynamics under moving loads. Results highlight practical design levers (inertia, shear stiffness, damping) that engineers can tune to mitigate vibration in civil, structural, and biomechanical applications, and identify parameter ranges most susceptible to resonance.