Reliability-Based Vibration Design of Vehicle Systems with Tuned Mass Dampers (TMD)

Tuned Mass Dampers (TMDs) are widely used in the automotive industry to mitigate Noise, Vibration, and Harshness (NVH) issues across various vehicle systems. These passive devices are particularly effective in reducing structural and tactile vibrations in components subjected to resonant excitation. However, real-world applications often face challenges due to manufacturing variability and system-level build differences, which can cause deviations in both the TMD’s tuned frequency (up to ±15%) and the excitation characteristics of the host structure. These uncertainties—in both the TMD properties and the vehicle subsystem dynamics—can be modeled using statistical distributions. This paper presents a generalized methodology for vibration analysis and design under uncertainty, combining reliability engineering with dynamic vibration modeling. The approach formulates a unified mathematical framework that incorporates probabilistic and stochastic modeling to assess TMD performance under a range of build and environmental conditions. As a case study, the method is applied to assess steering column tactile vibrations, with a focus on quantifying the probability that system performance meets specified NVH targets. Multiple statistical distribution models are considered to predict the likelihood that vibrations exceed customer acceptance thresholds, potentially leading to unfavorable subjective and objective ratings. The results are validated using population-level vehicle data. While demonstrated on the steering system, the proposed methodology is applicable to any vehicle subsystem equipped with a TMD, provided that the relevant random variables—such as modal properties, excitation inputs, and build tolerances—are properly characterized. This enables robust TMD design across vehicle domains, ensuring performance consistency despite system variability.