Riemann-Liouville Fractional Cosine Functions

In this paper, a new notion, named Riemann-Liouville fractional cosine function is presented. It is proved that a Riemann-Liouville $\alpha$-order fractional cosine function is equivalent to Riemann-Liouville $\alpha$-order fractional resolvents introduced in [Z.D. Mei, J.G. Peng, Y. Zhang, Math. Nachr. 288, No. 7, 784-797 (2015)]

Advances and trends in plastic forming technologies for welded tubes

AbstractWith the implementation of environmental protection, sustainable development and conservation-oriented policies, components and parts of thin-walled welded tubes have gained increasing application in the aircraft and automotive industries because of their advantages: easily achieving forming and manufacturing process at low cost and in a short time. The current research on welded tube plastic forming is mainly concentrated on tube internal high-pressure forming, tube bending forming, and tube spinning forming. The focuses are on the material properties and characterization of welded tubes, finite element modeling for welded tube forming, and inhomogeneous deformation behavior and the mechanism and rules of deformation coordination in welded tube plastic forming. This paper summarizes the research progress in welded tube plastic forming from these aspects. Finally, with a focus on the urgent demand of the aviation, aerospace and automotive industries for high-strength and light-weight tubes, this paper discusses the development trends and challenges in the theory and technology of welded tube plastic forming in the future. Among them, laser tailor-welded technology will find application in the manufacture of high-strength steel tubes. Tube-end forming technology, such as tube flaring and flanging technology, will expand its application in welded tubes. Therefore, future studies will focus on the FE modeling regarding how to consider effects of welding on residual stresses, welding distortions and microstructure, the inhomogeneous deformation and coordination mechanism of the plastic forming process of tailor-welded tubes, and some end-forming processes of welded tubes, and more comprehensive research on the forming mechanism and limit of welded tubes