scholarly journals 2022) A Method of Vibration Analysis of Stack by Partial Differential Equation

1966 ◽  
Vol 41 (0) ◽  
pp. 140
Author(s):  
Kazuyoshi Uchida
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Vibration Analysis ◽  
Partial Differential

Analysis for transverse shake vibration of high-rise buildings based on partial differential equation

2021 ◽  
Vol 64 (1) ◽  
pp. 103-111
Author(s):  
Li Li ◽  
◽  
Raquel Martínez ◽  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Energy Consumption ◽  
Vibration Analysis ◽  
High Energy ◽  
Lateral Vibration ◽  
Partial Differential ◽  
High Rise ◽  
The Galerkin Method ◽  
High Energy Consumption

In order to overcome the problems of long analysis time, low accuracy and high energy consumption in traditional lateral vibration analysis methods of high-rise buildings, a new method of lateral vibration analysis of high-rise buildings based on partial differential equation is proposed. Based on Hamilton's principle, the partial differential equation of lateral vibration of high-rise buildings is established, and the Galerkin method is used to solve the partial differential equation until the discrete solution is obtained, and then the displacement response of high-rise buildings under different excitation frequencies is obtained. The experimental results show that compared with the traditional method, the proposed method has the advantages of short calculation time, high accuracy and low energy consumption.

Qxygen transfer in gravity flow sewers

2000 ◽  
Vol 42 (3-4) ◽  
pp. 417-422 ◽  
Author(s):  
T.Y. Pai ◽  
C.F. Ouyang ◽  
Y.C. Liao ◽  
H.G. Leu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dissolved Oxygen ◽  
Flow Velocity ◽  
Molecular Diffusion ◽  
Eddy Diffusion ◽  
Partial Differential ◽  
Diffusion Term ◽  
Sewer Pipes ◽  
Gravity Sewer

Oxygen diffused to water in gravity sewer pipes was studied in a 21 m long, 0.15 m diameter model sewer. At first, the sodium sulfide was added into the clean water to deoxygenate, then the pump was started to recirculate the water and the deoxygenated water was reaerated. The dissolved oxygen microelectrode was installed to measure the dissolved oxygen concentrations varied with flow velocity, time and depth. The dissolved oxygen concentration profiles were constructed and observed. The partial differential equation diffusion model that considered Fick's law including the molecular diffusion term and eddy diffusion term were derived. The analytic solution of the partial differential equation was used to determine the diffusivities by the method of nonlinear regression. The diffusivity values for the oxygen transfer was found to be a function of molecular diffusion, eddy diffusion and flow velocity.

scholarly journals The Boundary Proportion Differential Control Method of Micro-Deformable Manipulator with Compensator Based on Partial Differential Equation Dynamic Model

Micromachines ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 799
Author(s):  
Xiangli Pei ◽  
Ying Tian ◽  
Minglu Zhang ◽  
Ruizhuo Shi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dynamic Model ◽  
Control Method ◽  
System Modeling ◽  
Working Environment ◽  
Partial Differential ◽  
External Interference ◽  
Differential Control ◽  
Differential Control Method

It is challenging to accurately judge the actual end position of the manipulator—regarded as a rigid body—due to the influence of micro-deformation. Its precise and efficient control is a crucial problem. To solve the problem, the Hamilton principle was used to establish the partial differential equation (PDE) dynamic model of the manipulator system based on the infinite dimension of the working environment interference and the manipulator space. Hence, it resolves the common overflow instability problem in the micro-deformable manipulator system modeling. Furthermore, an infinite-dimensional radial basis function neural network compensator suitable for the dynamic model was proposed to compensate for boundary and uncertain external interference. Based on this compensation method, a distributed boundary proportional differential control method was designed to improve control accuracy and speed. The effectiveness of the proposed model and method was verified by theoretical analysis, numerical simulation, and experimental verification. The results show that the proposed method can effectively improve the response speed while ensuring accuracy.

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