应用数学和力学

2021 Vol. 42, No. 3

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Large-Eddy Simulation of Supersonic Capsule-Rigid Disk-Gap-Band Parachute Systems

GONG Sheng, WU Chuijie

2021, 42(3): 233-247. doi: 10.21656/1000-0887.410274

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Abstract:
The influences of the aerodynamic deceleration performance and the flow field structure characteristics of the capsule-rigid disk-gap-band parachute system at an initial Mach number of 2.0 and different block-structured adaptive mesh refinement were studied. In the unsteady compressible fluid, the hybrid WENO (weighted essentially non-oscillatory) and TCD (tuned center difference) schemes were used to simulate the shock wave and the smooth continuous flow field. The large-eddy simulation method with the stretched vortex subgrid model was used to deal with the turbulence. The results show that, at a low resolution of the block-structured adaptive mesh refinement, it is difficult to accurately simulate the important aerodynamic drag coefficient and capture the flow field characteristics of the parachute system. Subsequently, the convergence of the adaptive mesh refinement of the flow field was verified.

A Hybrid CFD and Semi-Analytical Approach to Predict Cross-Flow-Induced Fluidelastic Instability of Tube Arrays

ZHAO Xielin, FENG Zhipeng, CAI Fengchun, YE Xianhui, ZHOU Jinxiong

2021, 42(3): 248-255. doi: 10.21656/1000-0887.410205

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Abstract:
Conventional theoretical models for fluidelastic instability analysis of a tube bundle subjected to cross flow require more or less experimental fluid force data as input. It is highly desirable to develop models independent of experimental data. An improved hybrid strategy was proposed through combination of the CFD simulation and the semi-analytical approach to predict fluidelastic instability of tube arrays. The key phase lag function in the semi-analytical model was extracted from the CFD simulation, and expressed as simple piecewise functions according to velocities. The cross-flow-induced fluidelastic instability thresholds of both parallel and equilateral triangular tube arrays with a pitch-to-diameter ratio of 1.375 were obtained and good agreement was achieved in comparison with experimental results. The developed approach can be used for fluidelastic instability analysis of other tube configurations, making a useful prediction tool dramatically saving time and cost.

Interference Characteristics Analysis of Wind Tunnel Perforated Wall Based on the Linear Vortex Model

XIE Yi, LIU Guangyuan, SHI Xiaojun

2021, 42(3): 256-263. doi: 10.21656/1000-0887.410081

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Abstract:
An estimation and correction method of perforated wall-induced interference characteristics for 2D airfoils was proposed. Based on the Prandtl-Glauert velocity potential equation and linear vortices arranged on the surfaces of the airfoil and tunnel walls, the effects of the perforated wind tunnel wall on pressure distributions on the airfoil surface were solved iteratively to analyze influences of air permeability parameters of the perforated wall. Previous reference data and wind tunnel test results were used for comparison to validate the accuracy of the proposed calculation method. The comparison shows that, the effects of the perforated tunnel walls on the flow around the airfoil mainly act on the upper surface between the suction peak and the maximum thickness, and lead to lower pressure coefficients and decreased integrated lift coefficients. With the increase of the air permeability parameter of the perforated wall, the wall interference characteristics develop from the solid wall to the open boundary sharply. With good efficiency and reliability, the proposed method applies to quick estimation of the pressure on the airfoil surface in the subcritical range, and evaluation of the wall interference in the 2D airfoil tests.

Robust Servo Constrained Control of Parallel Robots Based on the Udwadia-Kalaba Method

HAN Jiang, WANG Peng, DONG Fangfang, XIA Lian, ZHAO Xiaomin

2021, 42(3): 264-274. doi: 10.21656/1000-0887.410197

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Abstract:
For the trajectory tracking control problems of 2-DOF redundant drive parallel robots, a robust servo control method based on the Udwadia-Kalaba equation was proposed. Under the influences of load, external interference and manufacturing errors, it is impossible to obtain the accurate and complete motion model for the robot, and the control performance of the robot is poor. To solve the impacts of this type of uncertainty, a robust control method was proposed to enable the system to accurately track the ideal trajectory, and ensure the uniform boundedness and the uniform ultimate boundedness of the overall system. In addition, the Udwadia-Kalaba equation was used to solve the constraint force required by the system to meet the ideal constraint in the control process. The Udwadia-Kalaba equation does not require auxiliary variables such as Lagrangian multipliers or pseudo-generalized velocities, and can handle both complete and incomplete constraints, with analytical solutions of constraint forces satisfying the trajectory obtained. The stability of this robust control method was proved theoretically with the Lyapunov function. Simulation experiments show that, the proposed robust control method can achieve high-precision tracking control along a given trajectory under non-ideal conditions.

The Noether Symmetry and Conserved Quantity of Galloping Iced Power Transmission Lines

ZHENG Mingliang, LIU Jie, DENG Bin

2021, 42(3): 275-281. doi: 10.21656/1000-0887.410189

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Abstract:
To overcome the non-structure-preserving drawbacks in traditional numerical simulation of transmission-line nonlinear vibration responses, the Noether symmetry and conserved quantity of transmission lines’ 2-way galloping under ice and wind excitation were studied. Firstly, in view of the nonlinearity of the aerodynamic force and the line geometry, a 2-DOF galloping model of vertical and torsional vibrations was established based on the analytical mechanics method. Secondly, the group analysis theory was introduced, and the condition and the conserved quantity of the Noether symmetry were given according to the invariance principle. Finally, a conserved quantity-preserving discrete numerical algorithm was constructed. The dynamic characteristics of the nonlinear mechanical structure were studied with the Noether symmetry theory. The results show that, the proposed novel method is structure-preserving in a wide range of application, and is reliable and accurate.

A Simple Closed Response Solution to Random Ground Motion for Exponential Non-Viscous-Damping Structures Based on the Clough-Penzien Spectrum Excitation

LI Chuangdi, CHEN Mingjie, GE Xinguang

2021, 42(3): 282-291. doi: 10.21656/1000-0887.410151

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Abstract:
Compared with the traditional viscous damping model, the non-viscous-damping model can more accurately describe the energy dissipation behavior of structural materials, and its constitutive relationship is usually expressed in the form of convolution of exponential functions. In view of the complexity of the response to random ground motion obtained with the existent methods for structures with non-viscous damping, a simple closed-solution method for the analysis of 0~2nd-order spectral moments of structural responses was proposed based on the Clough-Penzien (C-P) spectrum. With this method, the exact equivalent differential constitutive relation of non-viscous-damping structures was first proposed and the ground motion equation of the structure was reconstructed with the C-P spectrum filtering differential equation. Then, based on the random vibration theory, the concise closed solution of the 0~2nd-order spectral moments of the structural random responses was obtained. Accordingly, the dynamic reliability of the structure was analyzed under the first excursion criterion and the Markov distribution rule. Finally, an example was given to demonstrate the accuracy and efficiency of the closed solution.

Research on Damage Diagnosis Based on Flexibility Matrix Decomposition

LI Guoqing, LUO Shuai, SU Rui, WANG Zeming, WANG Cheng

2021, 42(3): 292-298. doi: 10.21656/1000-0887.410257

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Abstract:
To solve the influence of incomplete measured DOFs on structural damage detection under ambient excitation, based on model reduction a proportional flexibility matrix (PFM) decomposition method was proposed. By means of the additional mass method, the normalized factor of mode shapes under ambient excitation was solved. According to the relation between the normalized factor and the PFM factor, the new PFM was built. Then, with the QR matrix decomposition method, the new PFM was decomposed and the resulting triangular matrix (R matrix) was considered as the research object, which was processed with the corresponding mathematical algorithm to obtain the final damage position index. The results show that, the proposed damage position index has high accuracy and certain robustness for both a single damage and multiple damages under ambient excitation. The damage position index derived from the matrix decomposition method applies to structural damage diagnosis under environmental excitation, making a new research idea for damage diagnosis of incomplete-DOF structures.

Finite-Time and Fixed-Time Consensus for Multi-Agent Systems via Pinning Control

ZHAO Wei, REN Fengli

2021, 42(3): 299-307. doi: 10.21656/1000-0887.410190

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Abstract:
The finite-time and fixed-time consensus of multi-agent systems with bounded unknown acceleration was studied. Problems of double integrator dynamics under a leader with bounded unknowns were considered. Firstly, the protocol of pinning control was proposed. Then with the Lyapunov stability theory and the Filippov differential equations with discontinuous right hand sides, the sufficient conditions were provided to guarantee multi-agent consensus in finite time and fixed time. Finally, the numerical simulation of pinning consensus of multi-agent systems illustrates the effectiveness of the conditions.

Stability of Zero Solution for Volterra Systems With Variable Delays

HUANG Minghui, JIN Chuhua

2021, 42(3): 308-315. doi: 10.21656/1000-0887.410233

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Abstract:
A class of Volterra systems with variable delays were analyzed. By means of the Banach fixed point theorem and through construction of appropriate contractive mappings under certain conditions, the stability theorem for zero solution of the system was obtained. The strictly proved theorem improves related conclusions in previous literatures. Finally, the effectiveness of the work was verified with a simulation example.

Adaptive Exponential Synchronization of Non-AutonomousChaotic Systems With Uncertain Parameters

CHEN Xuefei, LIU Huizhao

2021, 42(3): 316-322. doi: 10.21656/1000-0887.410072

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Abstract:
The exponential synchronization of non-autonomous chaotic systems with uncertain parameters was studied. The adaptive controller was designed. Based on the Lyapunov stability theory, the exponential stability of the error system was proved. Furthermore, the synchronization time was controlled through adjustment of the control parameters. Numerical simulations of 2 non-autonomous chaotic systems with uncertain parameters were presented to illustrate the ability and effectiveness of the proposed method.

A Posteriori Error Estimation and Adaptive Algorithm for Singularly Perturbed Reaction-Diffusion Equations

BAO Xiaobing, LIU Libin, MAO Zhi

2021, 42(3): 323-330. doi: 10.21656/1000-0887.410103

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Abstract:
An adaptive grid method for singularly perturbed semilinear reactiondiffusion equations was studied. The equation was discretized by means of the upwind finite difference scheme on an arbitrary nonuniform mesh. A posteriori error estimation of the presented numerical scheme was built. In turn, the posteriori error bound was derived, and the adaptive grid generation algorithm was designed. Numerical experiments prove the effectiveness of the proposed adaptive grid method.