Accounting for material property uncertainty in the preliminary vibration analysis of opto-mechanical systems

The dynamical behavior of opto-mechanical systems is crucial for ensuring the performance in noisy environments. In particular, vibration mitigation is one of the design drivers for pointing and wavefront error requirements. During the initial development stages, the typical design process is based on nominal material properties, geometries, and interface behaviors, resulting in a unique set of frequency response functions. However, this approach lacks robustness and often necessitates extensive redesigns following initial testing or the use of significant margin factors. Conversely, incorporating deviations from the baseline in a statistical manner is computationally heavy and often constrained by confidentiality issues. We give an overview of the most common techniques that can be used in large projects to account for the uncertainty in material properties. We also present a computationally light method aimed at deriving a robust family of system responses via a simple relationship between uncertainties in material properties and system responses. The proposed method is also applicable to models in a modal space representation. We compare a few parametric methodologies that account for material property uncertainties in a rigorous way, showcasing their use with real opto-mechanical systems for both ground and space telescopes. We show that the simplified method yields results comparable to more complex algorithms, offering a practical solution for early-stage design considerations.