The incremental harmonic balance method was extended to analyze the flutter of systems with multiple structural strong nonlinearities. The strongly nonlinear cubic plunging and pitching stiffness terms were considered in the flutter equations of two-dimensional airfoil. First, the equations were transferred into matrix form, then the vibration process was divided into the persistent incremental processes of vibration moments. And the expression of their solutions could be obtained by using a certain amplitude as control parameter in the harmonic balance process, and then the bifurcation, limit cycle flutter phenomena and the number of harmonic terms were analyzed. Finally, numerical results calculated by the Runge-Kutta method were given to verify the results obtained by the proposed procedure. It has been shown that the incremental harmonic method is effective and precise in the analysis of strongly nonlinear flutter with multiple structural nonlinearities.
Reaktion am Tröpfchen: Die enantioselektive Kaskadenreaktion von α‐Ketosäuren mit Aldehyden gelingt mit dem Titelkatalysator in Wasser als Lösungsmittel. Fluoreszenzbilder zeigen, dass sich der Katalysator hauptsächlich auf der Oberfläche von Emulsionströpfchen befindet. Optisch aktive Isotetronsäuren können mit dieser Methode erhalten werden, und die Emulsionströpfchen sind für die hohe Reaktivität und Enantioselektivität verantwortlich.
In recent years, there are many reports about the synthesis of 2,3-disubstituted indole by cyclization. Most of these approaches are catalyzed by different transition metals and metal-free catalysis conditions using phenylnydrazines, anilines and nitrobenzenes as main substrates. These methods have been a powerful strategy to obtain 2,3-disubstituted indoles. The recent progress of the synthesis of 2,3-disubstituted indoles by cyclization with the different substrates systems is summarized.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.