In-sample versus ensemble optimisation of tuned mass dampers for structures with uncertainties

Classical tuned mass damper (TMD) design assumes precisely known structural properties, but no systematic framework exists when the primary structure is uncertain due to material variability, construction tolerances, or environmental factors. This paper introduces a conceptual dichotomy in robust TMD design: in-sample optimization, which determines parameters conditionally for individual structural realizations, versus ensemble optimization, which seeks distributional robustness across the entire population of uncertain structures. This represents a fundamental departure from existing approaches, which treat uncertainty as a post-design consideration rather than embedding it within the optimization formulation itself. A probabilistic framework is developed in which structural natural frequency is modeled as a random variable, and dynamic responses are characterized through closed-form analytical expressions for mean and variance, validated against Monte Carlo simulation. The in-sample approach applies fixed-point theory to each realization and aggregates the resulting parameter distributions. The ensemble approach enforces equal-mean constraints on fixed-point frequencies across the uncertainty distribution and minimizes response variance. Comparative analyses in both frequency and time domains demonstrate that while conventional deterministic TMDs remain sensitive to detuning, both proposed strategies effectively suppress resonance amplification. The ensemble design achieves superior performance, reducing maximum structural displacement by 21.50% relative to conventional TMD, compared to 19.32% for in-sample design. Beyond parameter optimization, this work establishes in-sample versus ensemble as a transferable design philosophy for vibration control under uncertainty, with direct implications for adaptive versus mass-produced damper systems in engineering practice.