Effect of approximation fidelity on vibration-based elastic constants identification

Some applications such as identification or Monte Carlo based uncertainty quantification often require simple analytical formulas that are fast to evaluate. Approximate closed-form solutions for the natural frequencies of free orthotropic plates have been developed and have a wide range of applicability, but, as we show in this article, they lack accuracy for vibration based material properties identification. This article first demonstrates that a very accurate response surface approximation can be constructed by using dimensional analysis. Second, the article investigates how the accuracy of the approximation used propagates to the accuracy of the elastic constants identified from vibration experiments. For a least squares identification approach, the approximate analytical solution led to physically implausible properties, while the high-fidelity response surface approximation obtained reasonable estimates. With a Bayesian identification approach, the lower-fidelity analytical approximation led to reasonable results, but with much lower accuracy than the higher-fidelity approximation. The results also indicate that standard least squares approaches for identifying elastic constants from vibration tests may be ill-conditioned, because they are highly sensitive to the accuracy of the vibration frequencies calculation.     

Non‐Covalent Immobilization of Rare Earth Heterobimetallic Frameworks and their Reactivity in an Asymmetric Michael Addition

Heterobimetallic Lewis acid catalysts are broadly useful and methods to recycle them have immediate applications. However, their immobilization through covalent binding can be challenging. Non‐covalent immobilization of supported asymmetric catalysts is attractive due to ease of preparation and potential for reversible binding. We report a novel non‐covalent binding strategy for Shibasaki’s REMB framework {RE=rare earth metal; M=Li, Na, K; B=BINOL; RE:M:B=1:3:3, [M₃(sol)_n][(BINOLate)₃RE] } and explore the reactivity of the supported catalyst.