应用数学和力学

2023 Vol. 44, No. 5

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Dynamics and Control
Fluid Mechanics
Applied Mathematics

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Dynamics and Control

A Fundamental Surface Theory for Kinetic Analogy of Thin Elastic Shells

XUE Yun, CHEN Liqun

2023, 44(5): 489-498. doi: 10.21656/1000-0887.430222

Abstract(727) HTML (226) PDF(129)

Abstract:
The generalization of the Kirchhoff kinetic analogy from thin elastic rods to thin elastic shells, namely the generalized Kirchhoff kinetic analogy, needs a corresponding novel expression of the classical surface theory with its fundamental properties described by means of the concept and method of ...

Hamiltonian Structures and Stability Analysis for Rigid-Liquid Coupled Spacecraft Systems

YI Zhonggui, YUE Baozeng, LIU Feng, LU Tao, DENG Mingle

2023, 44(5): 499-512. doi: 10.21656/1000-0887.430379

Abstract(657) HTML (251) PDF(69) [Cited by] (2)

Abstract:
For the dynamics problems of rigid-liquid coupling spacecraft systems with liquid propellant, a 3D rigid pendulum model was used to simulate the nonlinear sloshing behavior of the propellant. On this basis, the Hamiltonian structure of the rigid-liquid coupling spacecraft system was studied, the $ \...

Research on Constraint Following Control of Flexible Joint Manipulators Based on Singular Perturbation

OU Jingsong, LI Rong, YIN Hui, WANG Huajian

2023, 44(5): 513-524. doi: 10.21656/1000-0887.430024

Abstract(747) HTML (260) PDF(74) [Cited by] (19)

Abstract:
For the control of 2-link flexible joint manipulators, a control method based on the singular perturbation theory and the Udwadia-Kalaba (U-K) method was proposed. The control design was implemented by 2 steps. First, the system order was reduced based on the singular perturbation method and the sys...

Study on Natural Vibration Characteristics of L-Shaped Cantilever Beams With the Differential Quadrature Method

LI Zhichao, HAO Yuxin

2023, 44(5): 525-534. doi: 10.21656/1000-0887.430382

Abstract(764) HTML (248) PDF(98) [Cited by] (2)

Abstract:
The L-shaped cantilever beam structure has many unique advantages such as large flexibility, strong designability, full utilization of space and various deformation modes during vibration, and is widely regarded and studied. A differential quadrature method was proposed to solve the natural frequenc...

Fluid Mechanics

Simulation and Prediction of the Evaporation Process of Ethanol Droplets Impacting High Temperature Wall

MA Xiaojing, ZHOU Xin, TUSONGJIANG Kari, XU Hanwen

2023, 44(5): 535-542. doi: 10.21656/1000-0887.430139

Abstract(605) HTML (327) PDF(66) [Cited by] (3)

Abstract:
The coupled level set and volume of fluid (CLSVOF) method was used to establish a numerical model for ethanol droplets impacting high temperature wall through introduction of the dynamic contact angle to describe the wetting characteristics of the wall surface. The boiling and evaporation process of...

Study on Collision Characteristics of Rotating Rod Strings in Annulus Fluid With Wellbores Based on Nested Grids

YUE Qianbei, WANG Xiaoxiao, CAO Wen, LIU Yueqiu, LI Hui, XU Yanlu

2023, 44(5): 543-559. doi: 10.21656/1000-0887.430183

Abstract(662) HTML (264) PDF(49) [Cited by] (1)

Abstract:
To solve the contact problem between the rod string immersed in annulus fluid and the wellbore, a numerical solution method for the collision was established based on the nested grid technology. The annulus fluid domain was divided into 2 sub-domains: the background grid and the component grid. Then...

Dynamic Mechanism and Energy Evolution of the Waterwheel Chaotic Rotation

WANG Heyuan, XIAO Shengzhong, MEI Pengfei, ZHANG Xi

2023, 44(5): 560-572. doi: 10.21656/1000-0887.420336

Abstract(656) HTML (288) PDF(58) [Cited by] (2)

Abstract:
To reveal the mechanism of the waterwheel chaotic rotation, the dynamic mechanism and the energy conversion of the waterwheel chaotic rotation were studied with the method of moment analysis. The mathematical model for the Malkus waterwheel rotation was transformed into the Kolmogorov system. Based ...

Applied Mathematics

The SAV Scheme Based on the Barycentric Interpolation Collocation Method for the Allen-Cahn Equation

HUANG Rong, DENG Yangfang, WENG Zhifeng

2023, 44(5): 573-582. doi: 10.21656/1000-0887.430149

Abstract(827) HTML (219) PDF(105) [Cited by] (3)

Abstract:
The scalar auxiliary variable (SAV) approach combined with the barycentric interpolation collocation method was proposed to solve the 2D Allen-Cahn equation. Two unconditional energy-stable SAV schemes were constructed based on the Crank-Nicolson scheme and the 2nd-order backward difference scheme f...

New Class of Difference Schemes With Intrinsic Parallelism for the KdV-Burgers Equation

PAN Yueyue, YANG Xiaozhong

2023, 44(5): 583-594. doi: 10.21656/1000-0887.430128

Abstract(631) HTML (208) PDF(75) [Cited by] (1)

Abstract:
The KdV-Burgers equation as a standard equation for turbulent, has a profound physical background and its fast numerical methods are of great practical application value. A new class of parallel difference schemes were proposed for the KdV-Burgers equation. Based on the alternating segment technolog...

An Alternating Direction Multiplier Method for 4th-Order Variational Inequalities With Curvature Obstacle

ZHANG Linsen, CHENG Lan, ZHANG Shougui

2023, 44(5): 595-604. doi: 10.21656/1000-0887.430243

Abstract(581) HTML (194) PDF(47) [Cited by] (4)

Abstract:
A self-adaptive alternating direction method of multipliers was proposed for the approximation solution of variational inequalities with biharmonic operators and curvature obstacle. An augmented Lagrange functional was introduced with an auxiliary variable to express the curvature function, and a co...

Preset-Time Consensus of Heterogeneous Fractional-Order Nonlinear Multi-Agent Systems

GONG Ping

2023, 44(5): 605-618. doi: 10.21656/1000-0887.430223

Abstract(704) HTML (299) PDF(66)

Abstract:
The preset-time consensus problem of a class of heterogeneous fractional-order nonlinear multi-agent systems was studied. A type of time-varying function-based preset-time fractional integral controllers were designed, to convert the fractional-order nonlinear multi-agent system into a 1st-order non...