Author(s): Lukas Reinhardt and Anna Vogel

Abstract: Discrete mass-spring systems are fundamental idealizations for representing vibration behavior in mechanical, civil, and structural engineering applications. In practical realizations, stiffness properties rarely remain perfectly uniform because of manufacturing tolerances, material degradation, assembly errors, or operational damage, leading to randomly distributed stiffness imperfections. This research investigates the vibration characteristics of discrete mass-spring systems incorporating stochastic variations in spring stiffness. A mathematical framework is developed in which randomness is modeled as spatially distributed perturbations superimposed on nominal stiffness values. Governing equations of motion are formulated using matrix representations, enabling modal and frequency-domain analyses. Statistical descriptors, including mean natural frequencies, variance, mode-shape localization indices, and response amplification factors, are evaluated to quantify the influence of uncertainty. Numerical simulations are conducted on multi-degree-of-freedom systems to examine sensitivity trends across different imperfection intensities and correlation lengths. Results demonstrate that even small random stiffness deviations can cause noticeable frequency shifts, mode splitting, and localization phenomena, particularly in higher modes. Increased disorder intensity is shown to enhance response variability under harmonic excitation and may significantly alter dynamic stability margins. Comparisons between deterministic and stochastic models highlight the limitations of idealized uniform-stiffness assumptions in predicting real system behavior. The findings provide insight into the probabilistic nature of vibration responses in imperfect discrete systems and emphasize the necessity of uncertainty-aware modeling in dynamic design. The proposed approach supports improved reliability assessment, damage detection interpretation, and robust design strategies for engineering systems where discrete structural models are employed. Overall, the research contributes to a deeper understanding of how randomly distributed stiffness imperfections govern vibration behavior and dynamic performance in mass-spring assemblies. Such knowledge is essential for engineers seeking safer, more resilient designs under unavoidable variability conditions encountered during fabrication, service life evolution, monitoring interpretation, and long-term operational uncertainty in practical discrete mechanical and structural engineering systems worldwide today broadly.

DOI: 10.22271/2707806X.2026.v7.i1a.57

Pages: 26-30 | Views: 22 | Downloads: 5

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