scholarly journals Publisher's Note: “Using approximate inertial manifold approach to model turbulent non-premixed combustion” [Phys. Fluids 33, 035125 (2021)]

2021 ◽  
Vol 33 (5) ◽  
pp. 059902
Author(s):  
Maryam Akram ◽  
Venkat Raman
Keyword(s):  
Premixed Combustion ◽  
Inertial Manifold ◽  
Approximate Inertial Manifold

scholarly journals Using approximate inertial manifold approach to model turbulent non-premixed combustion

2021 ◽  
Vol 33 (3) ◽  
pp. 035125
Author(s):  
Maryam Akram ◽  
Venkat Raman
Keyword(s):  
Premixed Combustion ◽  
Inertial Manifold ◽  
Approximate Inertial Manifold

scholarly journals Reduction of dimension of approximate intertial manifolds by symmetry

1999 ◽  
Vol 60 (2) ◽  
pp. 319-330
Author(s):  
Anibal Rodriguez-Bernal ◽  
Bixiang Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Inertial Manifolds ◽  
Inertial Manifold ◽  
Partial Differential ◽  
Approximate Inertial Manifold ◽  
Approximate Inertial Manifolds ◽  
The Relationship

In this paper, we study approximate inertial manifolds for nonlinear evolution partial differential equations which possess symmetry. The relationship between symmetry and dimensions of approximate inertial manifolds is established. We demonstrate that symmetry can reduce the dimensions of an approximate inertial manifold. Applications for concrete evolution equations are given.

Wavelet approximate inertial manifold in nonlinear solitary wave equation

2000 ◽  
Vol 41 (8) ◽  
pp. 5773-5792 ◽  
Author(s):  
Lixin Tian
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Inertial Manifold ◽  
Approximate Inertial Manifold

scholarly journals Approximate Inertial Manifold-Based Model Reduction and Vibration Suppression for Rigid-Flexible Mechanical Arms

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Lisha Xu ◽  
Hua Deng ◽  
Chong Lin ◽  
Yi Zhang
Keyword(s):  
Model Reduction ◽  
Dynamic Model ◽  
Input Signal ◽  
Angular Displacement ◽  
Target Position ◽  
Response Analysis ◽  
Inertial Manifold ◽  
Residual Vibration ◽  
Approximate Inertial Manifold ◽  
Simulation Results

The dynamic characteristics of the mechanical arm with a rigid-flexible structure are very complex. The reason is that it is a complex DPS (distributed parameter system) with infinite dimension and nonlinearity in essence due to the rigid-flexible coupling. So, accurately positioning and controlling the rigid-flexible mechanical arms could be difficult. Therefore, a model reduction method of rigid-flexible mechanical arms based on the approximate inertial manifold is put forward. To repress the residual vibration of the end of the mechanical arm, a feedforward control strategy is designed. The high-dimensional solution of the vibration equation of the rigid-flexible mechanical arms is projected into the complete space composed of orthogonal decomposition modes. By using Galerkin’s method, the system is simplified and the approximate solution is obtained through the interaction between high-order and low-order modes. The truncated finite mode is also used to construct a lowest-order dynamic model on the basis of approximate inertia manifold. Given the reduced-order rigid-flexible mechanical arms dynamic model, dynamic response analysis is conducted to optimize the target position error and end residual vibration. A limited number of sinusoidal signals approximately combine the input signal, by using the particle swarm optimization algorithm to optimize the input signal, and the amplitude of the sinusoidal signal is corrected. The simulation results depict the superiority of the proposed method, which greatly suppresses the end residual vibration of the mechanical arm and realizes the accurate positioning of the end of the mechanical arm. In addition, the hardware experimental device of the rigid-flexible mechanical arms is constructed, and the experimental verification of the above method is put into effect. The simulation results of angular displacement and end vibration of the reduced model are accordant which is shown by the experimental results of the hardware platform.

scholarly journals Approximate inertial manifold-based order reduction of rigid-flexible coupling manipulator

2021 ◽  
Vol 260 ◽  
pp. 03014
Author(s):  
Lisha Xu ◽  
Xiaoshan Qian ◽  
Chong Lin
Keyword(s):  
Controller Design ◽  
Order Reduction ◽  
Order System ◽  
Response Analysis ◽  
Inertial Manifold ◽  
Approximate Inertial Manifold ◽  
Deformation Response ◽  
Flexible Deformation ◽  
Order Reduction Method ◽  
Manifold Theory

An order reduction method for the flexible deformation response analysis of rigid flexible manipulators is proposed based on the approximate inertial manifold theory. This method allows a lower dimensional simplified model to be constructed from a subspace smaller than the entire state space. In this paper, truncated three-order modes are used to construct a first-order system of AIM. Compared with the traditional Galerkin method, the results show that the proposed method can reduce the degree of freedom of the system and improve the computational efficiency without obviously losing the precision of the solution, which is convenient for the subsequent vibration analysis and controller design of the system.

An approximate inertial manifold for computing Burgers' equation

1992 ◽  
Vol 60 (1-4) ◽  
pp. 175-184 ◽  
Author(s):  
L.G. Margolin ◽  
D.A. Jones
Keyword(s):  
Burgers Equation ◽  
Inertial Manifold ◽  
Approximate Inertial Manifold

A NEW APPROXIMATE INERTIAL MANIFOLD AND ASSOCIATED ALGORITHM

2006 ◽  
Vol 26 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Kaitai Li ◽  
Zhongfeng Xu ◽  
Xiaozhong Yang
Keyword(s):  
Inertial Manifold ◽  
Approximate Inertial Manifold

Wavelet approximate inertial manifold and numerical solution of Burgers' equation

2002 ◽  
Vol 23 (10) ◽  
pp. 1140-1152 ◽  
Author(s):  
Tian Li-xin ◽  
Xu Bo-qiang ◽  
Liu Zeng-rong
Keyword(s):  
Numerical Solution ◽  
Burgers Equation ◽  
Inertial Manifold ◽  
Approximate Inertial Manifold
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