Stochastic modeling of periodic beams under uncertain boundary conditions and environmental fluctuations

Periodic structures have been attracting a great deal of academic and industrial interest lately, due to their distinctive vibration and wave propagation behavior, which can be explored for the development of innovative solutions to structural dynamics and vibroacoustic problems. Although such a potential has been demonstrated in a large number of studies, the investigation of detrimental effects, which can be present in practical applications, is still necessary. This paper reports investigations on the combined influence of uncertainties affecting ambient temperature — which alters material properties and induces stress-stiffening due to constrained thermal dilatation — and boundary conditions (BCs) on the bandgap characteristics of periodic beams. The space-dependent temperature fluctuations are represented as a one-dimensional stationary Gaussian random field, discretized using the Karhunen-Loève expansion, while non-ideal BCs, represented as springs, are modeled as discrete random variables. Sampling-based stochastic analyses of the central frequency and bandwidth of the beam’s attenuation bands are performed using Monte Carlo simulations. The results demonstrate that the variability in the attenuation band features is influenced not only by the coefficients of variation (CVs) of the input random quantities, but also by the correlation length of the random temperature fluctuations. Numerical simulations reveal that the bandgap central frequency is primarily affected by the temperature random field, while the BCs govern the bandwidth. Although low CV and standard deviation values are obtained for the dispersion of the bandgap features, reliability analyses indicate that some designs exhibit low reliability. Increased variability in both the bandgap central frequency and bandwidth is observed for greater temperature correlation lengths and CVs. The contributions of the study include the proposal of a comprehensive stochastic modeling procedure duly accounting for relevant random influences, and evidencing that those influences can be significant, requiring consideration in the design of robust periodic structures.