Optimal design of viscoelastic tuned mass dampers for structures exposed to coloured excitations

Dynamic interaction between primary and secondary structures can alter the response of buildings, bridges and other civil engineering structures to external stressors such as earthquakes and windstorms. TMDs (tuned mass dampers) are a well-known example of passive control devices that exploit this concept. ATMD consists of a secondary mass attached to the primary structure through a linear or nonlinear link. Various formulations exist to optimize the performance of TMDs, depending on the chosen criterion. Typically, the TMD is optimized considering the steady-state amplitude of motion of the primary structure, e.g., when subjected to monochromatic harmonic excitation (H∞ criterion) or white noise input (H2 criterion). Several closed-form analytical solutions have been formulated for linear TMDs with elastic and viscoelastic damping. However, the available expressions only cover the case of constitutive laws described by two or three parameters, e.g., the Kelvin-Voight model (an elastic spring in parallel with a viscous dashpot) and the standard linear solid (SLS) model (an elastic spring in parallel with a single Maxwell element). Furthermore, the inherent damping of the primary system is usually neglected, even though it can drastically affect the performance of the TMD. Similarly, the effects of coloured excitations, e.g., the Kanai-Tajimi model of ground shaking, are often disregarded, leading to sub-optimal designs. Aimed at overcoming these limitations, a new stochastic approach is proposed. The only assumptions are: I) the salient dynamic features of the TMD-controlled structure can be captured with a linear 2-DoF (degree of freedom) system; ii) the dynamic action can be represented as a stationary Gaussian process.