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Purpose: Large sun-facing deployable appendages are widely used in ultra-large spacecrafts. The effects of gravity gradient on the dynamic characteristics are always neglected due to the small size of traditional spacecrafts. Therefore, the dynamics of an axially deployable large flexible sun-facing spacecraft under gravity gradient are studied in this paper. Methods: Firstly, the extended Hamilton’s principle is utilized to derive the transverse vibration equations of the deployable appendages under a floating coordinate frame. Two kinds of deployment strategies including constant-speed deployment and practical deployment are considered. Then, the assumed mode method and Galerkin’s method are adopted to solve the governing equations. Finally, the numerical results of transverse vibration are obtained by using the symplectic Runge–Kutta method. Results: With the decrease of deploying time, the amplitude of flexible vibration decreases in the deploying process but increases in the long-time evolution for the two deploying strategies. Meanwhile, the higher orbital altitude leads to a lower vibration amplitude. In addition, the practical deploying strategy will lead to larger displacement than the constant deploying strategy even though it can avoid speed residual automatically. Conclusions: The results show that the gravity gradient force has a significant influence on the transverse vibration both in the deployment process and the long-time evolution. The results will provide constructive guidance for vibration control.

A novel tetraethylenepentamine (TEPA) functionalized magnetic mesoporous silica adsorbent (FNMs/TEPA) was prepared for adsorption of Cr(III)-EDTA from wastewater. Characterization of the prepared adsorbent certified that TEPA was modified onto the magnetic mesoporous silicon (FNMs), while FNMs/TEPA maintained the ordered mesoporous and pristine magnetic properties. The batch adsorption experiments demonstrated that TEPA significantly enhanced the removal capacity of the adsorbent for Cr(III)-EDTA. FNMs/TEPA exhibited an excellent adsorption property (13.84 mg∙g–1) at pH 4.0. Even in the existence of high concentrations of coexisting ions and organic acids, the adsorption performance of FNMs/TEPA was stable. Experimental characterization and density functional theory (DFT) demonstrated that the adsorption of Cr(III)-EDTA was ascribed to the electrostatic interaction, hydrogen bonding, and complexation between Cr(III)-EDTA and amino groups on the adsorbent surface. The analysis of the Independent Gradient Model (IGMH) shown that electrostatic interaction is the main mode of action in the adsorption process. Moreover, FNMs/TEPA demonstrated remarkable reusability in three regeneration cycles. These findings indicated that FNMs/TEPA possessed excellent application prospect in the disposal of wastewater containing Cr(III)-EDTA.

Polyethyleneimine (PEI) modified palygorskite (Pal) was used for the adsorption of Cr(VI) in aqueous solution. The absorbent was characterized by Fourier transform infrared spectroscopy (FT-IR) and thermogravimetric analysis (TGA). Characterized results confirmed that the Pal has been successfully modified by PEI. The modification of PEI increased the Cr(VI) adsorption performance of the Pal by the adsorption combined reduction mechanism, and amino groups of the adsorbent play the main role in the enhanced Cr(VI) adsorption. The maximum adsorption capacity was 51.10 mg·g−1at pH 4.0 and 25 °C. The adsorption kinetics of Cr(VI) on the adsorbent conforms to the Langmuirisotherm model. The maximum adsorption occurs at pH 3, and then the adsorption capacity of PEI-Pal was decreased with the increase of pH values. The adsorption kinetics of Cr(VI) on PEI-Pal was modeled with pseudo-second-order model. The addition of Cl−, SO42−and PO43−reduced the Cr(VI) adsorption by competition with Cr(VI) for the active sites of PEI-Pal. The Cr(VI) saturated PEI-Pal can be regenerated in alkaline solution, and the adsorption capacity can still be maintained at 30.44 mg·g−1after 4 cycles. The results demonstrate that PEI-Pal can be used as a potential adsorbent of Cr(VI) in aqueous solutions.

In this paper, the application of complex fractional moment(CFM) method in the stochastic dynamic systems with Caputo-type fractional derivative under the excitation of Gaussian white noise are investigated. By the approximation method, the FPK equation governing the amplitude is derived, and the semi-analytic solution of FPK equation is obtained by CFM method. The results are verified by numerical simulation. Meanwhile, the probability evolution of transient Probability Density Function(PDF) is analyzed when the stochastic bifurcation induced by fractional coefficient for the first time. In addition, the relation of equivalence between first passage time(FPT) and CFM is established by a novel method, the accuracy of this method is verified, the influences of system parameters change on reliability function and the FPT are discussed by the novel method. • The applicability and advantage of the CFM method in stochastic systems with Caputo fractional derivative are investigated. • A novel method based on CFM to obtain the probability distribution of first passage time is proposed in this paper. • The probability evolution of transient PDF is analyzed when the stochastic bifurcation occurs. [ABSTRACT FROM AUTHOR]