TITLE:
Monte Carlo Uncertainty Quantification and Numerical Verification of Linear Vibration Systems with Stochastic Parameters and Fixed Initial Conditions
AUTHORS:
Hanya Sun
KEYWORDS:
Monte Carlo Simulation, Uncertainty Quantification, Vibration Analysis, MDOF Systems, Natural Frequency, Transient Response
JOURNAL NAME:
World Journal of Mechanics,
Vol.16 No.10,
October
30,
2026
ABSTRACT: Monte Carlo sampling is used to characterize parameter uncertainty in linear single- and two-degree-of-freedom free-vibration benchmarks with fixed initial conditions. Each model uses 100,000 trials: uniform mass, stiffness, and damping inputs for SDOF and independent, unfiltered normal inputs for 2DOF. The SDOF undamped natural-frequency mean and sample standard deviation are 1.38036 and 0.02817 rad/s. An analytical audit reveals that the original forward Euler calculation gives 67.384% peak-displacement exceedance at 13.5 m, compared with 39.842% for the analytical response with identical samples. The original figure is retained as a documented numerical approximation; the analytical estimate supersedes its threshold result. The lower and upper 2DOF natural frequencies have means 1.80020 and 5.72171 rad/s and sample standard deviations 0.06309 and 0.18961 rad/s. Nominal damped eigencomponents have amplitude half-lives of 7.88 and 0.385 s. The 2DOF population retains 4,805 negative first-damper draws, and its central response bands do not describe an entirely passive population. Undamped modal illustrations are distinguished from damped transients. The study demonstrates uncertainty propagation and numerical verification, rather than validated manufacturing yield or service reliability. Differences between the two models do not isolate distribution-family effects.