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Research on data assimilation strategy of turbulent separated flow over airfoil

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Applied Mathematics and Mechanics(English Edition) 2022年第4期43卷 571-586页

作者： Ying ZHANG Lin DU Weiwei ZHANG Zichen DENG National Key Laboratory of Science and Technology on Aerodynamic Design and Research School of AeronauticsNorthwestern Polytechnical UniversityXi'an 710072China Complex System Dynamics and Control Academic Exchange Center School of Mathematics and StatisticsNorthwestern Polytechnical UniversityXi'an 710119China Rotor Aerodynamics Key Laboratory China Aerodynamics Research and Development CenterMianyang 621000Sichuan ProvinceChina

In order to increase the accuracy of turbulence field reconstruction,this paper combines experimental observation and numerical simulation to develop and establish a data assimilation framework,and apply it to the study of S809 low-speed and high-angle airfoil *** method is based on the ensemble transform Kalman filter(ETKF)algorithm,which improves the disturbance strategy of the ensemble members and enhances the richness of the initial members by screening high flow field sensitivity constants,increasing the constant disturbance dimensions and designing a fine disturbance *** results show that the pressure distribution on the airfoil surface after assimilation is closer to the experimental value than that of the standard Spalart-Allmaras(S-A)*** separated vortex estimated by filtering is fuller,and the eddy viscosity field information is more abundant,which is physically consistent with the observation ***,the data assimilation method based on the improved ensemble strategy can more accurately and effectively describe complex turbulence phenomena.

关键词： turbulence data assimilation ensemble disturbance strategy large angle of attack separation ensemble transform Kalman filter(ETKF)

Stability Analysis of an Axially Moving Viscoelastic Beam Under Transverse Magnetic Fields and Thermal Loads

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SSRN 2024年

作者： Wu, Sihan Xudong, Gu Zhao, Bingxin Deng, Zichen Department of Engineering Mechanics Northwestern Polytechnical University Xi’an China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an China

In this paper, an analytical method is proposed to study the stability of an axially moving viscoelastic beam under transverse magnetic fields and thermal loads. Firstly, the nonlinear control equation of the axially moving viscoelastic beam is derived by using Hamilton principle, in which the effects of thermal loads and magnetic field variations are considered based on the principle of magnetoelasticity and large deformation. Secondly, Galerkin’s method was applied to the derived continuous model to derive the discrete differential equations of each vibrating mode. Finally, the incremental harmonic balance (IHB) method was employed to determine the unstable regions in the parameter space. The influences of thermal load, axially moving velocity of the beam, viscosity coefficient, and magnetic field intensity on the regions of stability are investigated. It is found that the thermal loads, axially moving velocity and magnetic field intensity exert a significant influence on the unstable region. © 2024, The Authors. All rights reserved.

关键词： Viscoelasticity

Elucidating Platelet Interlocking Strengthening and Toughening Mechanism of Nacre: Coupled Effect of Platelet Size and Shape

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SSRN 2024年

作者： Ji, Hongmei Liang, S.M. Li, Y.Y. Li, K.X. Yan, Yi Li, Xiao Wu Northeastern University Shenyang110819 China Department of Engineering Mechanics MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi’an710072 China

The platelet interlocking is universally recognized as a pivotal factor contributing to the remarkable toughness and strength of nacre in mollusk shells. Apart from variations in shape, platelets in nacre often exhibit changes in size as well. The current study has elucidated the coupled effect of platelet size and shape on the mechanical properties of nacre across different shells (Cristaria plicata, Pinctada margaritifera, and Pteria penguin) by mechanical tests and finite element (FEM) analyses. The P. penguin shell featuring inverse dovetail platelets and a minimal platelet thickness presents the most optimal mechanical properties among three shells. The FEM analyses reveal that the tensile strength of nacreous structures is primarily governed by the platelet size, while the shape of the platelets can optimize the distribution of stress within the structures. Although the dovetail platelets enhance stiffness by interlocking, they are prone to fracturing when the thickness of the platelets is minimal. Conversely, the inverse dovetail platelets are capable of optimizing stress distribution. Specifically, in the case of small sized platelets, these inverse dovetail platelets can not only effectively prevent fracturing but also redirect crack propagation along the interface, ultimately enhancing the mechanical properties of the structures. © 2024, The Authors. All rights reserved.

关键词： Tensile strength

Path integral solutions for n-dimensional stochastic differential equations underα-stable Lévy excitation

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Theoretical & Applied Mechanics Letters 2023年第2期13卷 98-112页

作者： Wanrong Zan Yong Xu Jürgen Kurths School of Mathematics Northwest UniversityXi’an710127China Department of Applied Mathematics Northwestern Polytechnical UniversityXi’an710129China MIIT key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical UniversityXi’an710129China Potsdam Institute for Climate Impact Research Potsdam14412Germany Department of Physics Humboldt University of BerlinBerlin12489Germany

In this paper,the path integral solutions for a general n-dimensional stochastic differential equa-tions(SDEs)withα-stable Lévy noise are derived and ***,the governing equations for the solutions of n-dimensional SDEs under the excitation ofα-stable Lévy noise are obtained through the characteristic function of stochastic ***,the short-time transition probability density func-tion of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski(CKS)equation and the characteristic function,and its correctness is demonstrated by proving that it satis-fies the governing equation of the solution of the SDE,which is also called the Fokker-Planck-Kolmogorov ***,illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method,and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.

关键词： Path integral method α-stable Lévy noise Monte carlo method Fokker-Planck-Kolmogorov equation

Accelerated Stochastic Peaceman–Rachford Method for Empirical Risk Minimization

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Journal of the Operations Research Society of China 2023年第4期11卷 783-807页

作者： Jian-Chao Bai Feng-Miao Bian Xiao-Kai Chang Lin Du Research&Development Institute of Northwestern Polytechnical University in Shenzhen Shenzhen518057GuangdongChina School of Mathematics and Statistics Northwestern Polytechnical UniversityXi’an 710129ShaanxiChina Department of Mathematics The Hong Kong University of Science and TechnologyHong KongChina School of Science Lanzhou University of TechnologyLanzhou730050GansuChina School of Mathematics and Statistics the MIIT Key Laboratory of Dynamics and Control of Complex SystemsNorthwestern Polytechnical UniversityXi’an 710129ShaanxiChina

This work is devoted to studying an accelerated stochastic Peaceman–Rachford splitting method(AS-PRSM)for solving a family of structural empirical risk minimization *** objective function to be optimized is the sum of a possibly nonsmooth convex function and a finite sum of smooth convex component *** smooth subproblem in AS-PRSM is solved by a stochastic gradient method using variance reduction technique and accelerated techniques,while the possibly nonsmooth subproblem is solved by introducing an indefinite proximal term to transform its solution into a proximity *** a proper choice for the involved parameters,we show that AS-PRSM converges in a sublinear convergence rate measured by the function value residual and constraint violation in the sense of expectation and *** experiments on testing the popular graph-guided fused lasso problem in machine learning and the 3D CT reconstruction problem in medical image processing show that the proposed AS-PRSM is very efficient.

关键词： Empirical risk minimization Convex optimization Stochastic Peaceman-Rachford method Indefinite proximal term complexity

Sub-Preferential Rotational Wave Beaming in Structurally Rhombus Re-Entrant Honeycombs

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SSRN 2023年

作者： Zhu, Zhiwei Deng, Zichen State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures Shijiazhuang Tiedao University Shijiazhuang050043 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'An710072 China

Rotational waves frequently manifest in micro-structured materials and are often coupled with classical shear or longitudinal wave modes. In this study, a distinctive isolated optical branch, exhibiting very high polarization index related to joint rotation motion, is found in dispersion diagram of elastic wave propagation in structurally rhombus re-entrant honeycomb (SSRH). Through an analysis of group velocity, we further explore the wave beaming of the rotational wave propagation within the SRRH, and intriguingly, observe the emergence of sub-preferential wave beaming occurring along the short diagonal directions. This dynamic anisotropic phenomenon stems from the intricate interplay between wave frequency and structural topology. To elucidate the underlying dynamic anisotropy of rotational waves, we propose a simple rigid-spring model and derive an anisotropic coefficient that precisely captures the intricate frequency-structure coupling behavior. The obtained anisotropic coefficient unveils the formation of sub-preferential directions of the rotational wave within the SRRH. Our findings transcend the elucidation of dynamic anisotropy in lattice materials, extending to practical implications encompassing the manipulation of elastic wave propagation and the design of waveguides. © 2023, The Authors. All rights reserved.

关键词： Anisotropy

Vibration and Acoustic Radiation Suppression of Multi-Layer Composite Sandwich Plates with Imperfect Acoustic Black Hole

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SSRN 2024年

作者： Zhang, Sen Wu, Xinwei Ding, Liangzhu Ma, Yongbin Deng, Zichen School of Mechanics Civil Engineering and Architecture Northwestern Polytechnical University Xi'An710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'An710072 China

Acoustic black holes (ABHs) had been recently revealed as an effective vibration control technology. However, due to inherent defects such as weakened stiffness, structural discontinuity and manufacturing difficulties, the practical application of ABH had been limited. Therefore, a multi-layer composite sandwich plate with filled imperfect-ABH (F-IABH) was proposed in this study to attenuate the vibration and sound radiation of the multi-layer sandwich plate, and could also enhance the bearing capacity of the structure and maintain its topological continuity. The structural damping characteristics and vibroacoustic response of the F-IABH were conducted by a semi-analytical wave propagation model developed based on the symplectic method and acoustic radiation mode method. In numerical examples, the accuracy and effectiveness of the analytical model were validated by the finite element method. The results showed that F-IABH can achieve broadband vibration attenuation and noise reduction effects. Especially at low frequencies, its vibration and noise reduction effect were significantly better than ABH structures. Meanwhile, the wave damping characteristics of uniform plate, ABH plate, and F-IABH plate were analyzed. The results showed that the wave damping of F-IABH was much higher than those of uniform plate, and they can generate more propagative waves to dissipate energy. In addition, the wave damping characteristics of F-IABH and ABH plate had very similar trends. However, at lower frequencies, due to the large variation range of wave mode damping characteristics of F-IABH, its control effect on structural vibration and acoustic radiation was more significant than that of ABH plate. © 2024, The Authors. All rights reserved.

关键词： Acoustic wave propagation

Broadband Vibration Reduction of Cylindrical Shell Structures with Circumferential Taper Resonators

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SSRN 2024年

作者： Zhang, Sen Ding, Liangzhu Wu, Xinwei Ma, Yongbin Deng, Zichen School of Mechanics Civil Engineering and Architecture Northwestern Polytechnical University Xi'An710072 China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'An710072 China

In this study, a resonator with circumferential taper was proposed to achieve broadband vibration reduction of the circular cylindrical shell. The structural damping characteristics and vibration response of the circular cylindrical shell structure with circumferential taper resonators were conducted by an analytical wave propagation model developed based on the symplectic method. The taper resonator was segmented uniformly by using the Gaussian discretization method based on power law, which can accurately and efficiently handle the non-uniform characteristics of the taper resonator and the amplitude of each uniform segment was evaluated by using the analytical wave propagation model. In numerical examples, the accuracy and effectiveness of the homogenization approximation of the analytical model were validated by the finite element method. Meanwhile, the forced vibration response and damping properties of the circular cylindrical shell structure with uniform and taper resonators and with various boundary conditions were also investigated. The results showed that compared with uniform resonator, the taper resonator provided much larger damping, which its special damping capacity can even reach about 6 times of the uniform resonator. Therefore, even if the length of the taper resonator was relatively small, significant broadband vibration suppression in the primary circular cylindrical shell can also be achieved. In addition, under any boundary condition, the same parameters taper resonator can achieve broadband vibration reduction effects on circular cylindrical shell, and the distance between the excitation source and the position of the resonator can affect the vibration attenuation effect of the circular cylindrical shell. © 2024, The Authors. All rights reserved.

关键词： Resonators

Elastic Wave Propagation in Lattice Metamaterials with Koch Fractal

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Acta Mechanica Solida Sinica 2020年第5期33卷 600-611页

作者： Pengcheng Zhao Kai Zhang Zichen Deng School of Mechanics Civil Engineering and ArchitectureNorthwestern Polytechnical UniversityXi’an710072China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical UniversityXi’an710072China

In this study,the wave propagation properties of lattice metamaterials with Koch fractal structures are investigated in terms of band structures and directional wave *** analytical models of lattice metamaterials are established using the finite element method,and the dispersion relation is solved using the Bloch’s *** band structures of the lattice metamaterials with different numbers of iterations are studied,and the group velocities at a selected frequency are calculated to analyze the directional wave propagation ***,dynamic responses of the finite structures are calculated using commercial finite element software to verify the band gaps and directional wave propagation behaviors in the lattice *** results show that multiple and low band gaps are present in the lattice materials with various geometric parameters of the Koch fractal,and the position of the lowest band gap decreases as the number of iterations *** results indicate the potential applications of lattice metamaterials with Koch fractals for vibration isolation and multi-functional design.

关键词： Elastic wave propagation Lattice metamaterial Koch fractal Band gap Group velocity