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In this paper, based on distributed transfer function method (DTFM), the closed-form analytical solutions for vibrations of Euler–Bernoulli beam and frame structures with arbitrary number of cracks are studied. First, generalized DTFM is employed to characterize the dynamical model for a single cracked beam and its analytical solutions for eigenvalue problem and frequency response are obtained. Then, a new DTFM cracked element that encapsulates one crack of arbitrary location inside the beam is proposed. Using the DTFM cracked element and global dynamic stiffness matrix assembly technique, damaged frame structures of arbitrary form can be modeled for vibration analysis. Previous analytical methods only addressed low-frequency vibration of simple cracked beam structures, the proposed method can yield analytical solutions in the medium- and high-frequency regions, which is critical for the small crack detection in complex frames. Lastly, three numerical examples are given to illustrate the correctness and effectiveness of the DTFM in analyzing natural frequencies, modal shapes and frequency responses for cracked structures. By comparing with the Finite Element Method (FEM) and benchmarks from literatures, we proved that the DTFM has better performances in terms of accuracy and efficiency. [ABSTRACT FROM AUTHOR]

To satisfy the requirement of contingency rescue in the lunar orbit insertion phase for crewed lunar exploration missions, this paper designs the contingency point return trajectory. First, according to different failure situations of the main propulsion system in the lunar orbit insertion phase, different types of contingency return modes are analyzed and summarized. Second, considering the terminal constraints of point return, a calculation model of the contingency point return trajectory is established, and a serial optimization process is adopted to obtain a high-fidelity solution. Finally, a numerical simulation is used to verify the model. The simulation results indicate that this model can be applied to determine the contingency point return trajectories under different situations in the lunar orbit insertion phase and demonstrate the validity and feasibility of the trajectory calculation model proposed in this paper. The research conclusions can provide a reference for the design of contingency rescue schemes in the lunar orbit insertion phase for crewed lunar exploration missions. [ABSTRACT FROM AUTHOR]

High-Cr martensitic heat-resistant steel has been widely used in high-parameter thermal power units because of its excellent mechanical properties and oxidation resistance. Microstructure evolution and mechanical properties of G115 steel after different tempering were investigated. Meanwhile, the precipitation and strengthening behavior of M23C6 carbides is also systematically discussed. The results show that the precipitation of M23C6 carbides during tempering causes obvious precipitation strengthening, and that the contribution of M23C6 carbides to yield strength first increases and then decreases with the increase in tempering temperature, which is consistent with the variation of actual yield strength. From this point of view, M23C6 carbides are the major factor that governs the yield strength of tempered samples. The maximum precipitation of M23C6 carbides and the maximum degree of precipitation strengthening occur with tempering at 740 °C, and the corresponding size of M23C6 carbides is 0.106 μm. [ABSTRACT FROM AUTHOR]

Co‐based superalloys with the advantages of high melting point, high‐temperature mechanical properties, and large resistance under hot corrosion environment are potential candidates for turbine engine components. The isothermal oxidation behavior of Co–Ni–Al‐based superalloy with the addition of Mo and Cr in dry air at 1073 and 1173 K was investigated. The results showed that similar three‐layer oxides structures were composed of Co‐containing oxides, complex oxides rich in Co and Al, and Al2O3 layer formed on both 2Mo and 2Cr Co–Ni–Al‐based superalloys, and Mo‐containing oxides also existed in the subsurface. The oxides in the outer layer transferred from Co3O4 to denser CoO with the increase in temperature. The γ'‐free zone formed under the Al2O3 layer due to the depletion of Al. Co–Ni–Al‐based superalloys need to conquer a large energy barrier at an earlier stage of oxidation and exhibit good oxidation resistance at 1073 K. [ABSTRACT FROM AUTHOR]