Hybrid uncertain natural frequency analysis for structures with random and interval fields

- Structural free vibration with hybrid random & interval fields is explored for the first time.
- Both 2D and 3D practically motivated engineering structures are investigated.
- The sharpness of eigenvalues obtained by FEM at each interval analysis is preserved.
- Statistical characteristics of extreme bounds of natural frequencies can be obtained.
- PDFs and CDFs can be robustly constructed by the proposed approach.

This paper presents a robust non-deterministic free vibration analysis for engineering structures involving hybrid, yet spatially dependent, uncertain system parameters. Distinguished from the conventional hybrid uncertain eigenvalue problem, the concept of interval field is enclosed with random field model such that, both the stochastic and non-stochastic representations of the spatial dependency of the uncertainties are simultaneously incorporated within a unified non-deterministic free vibration analysis. In order to determine the probabilistic characteristics (i.e., means and standard deviations) of the extremities of structural natural frequencies, an extended unified interval stochastic sampling (X-UISS) method is implemented for the purpose of effective hybrid uncertain free vibration analysis. By meticulously blending sharpness-promised interval eigenvalue analysis with stochastic sampling techniques, the stochastic profiles (i.e., probability density functions (PDFs) and the cumulative distribution functions (CDFs)) of the extreme bounds of the structural natural frequencies can be rigorously established by utilizing the adequate statistical inference methods. The applicability and effectiveness of the proposed computational framework are evidently demonstrated through the numerical investigations on various practically motivated engineering structures.