Variable separation method for solving boundary value problems of isotropic linearly viscoelastic bodies

2020 ◽  
Vol 231 (9) ◽  
pp. 3583-3606
Author(s):  
A. A. Svetashkov ◽  
N. A. Kupriyanov ◽  
M. S. Pavlov ◽  
A. A. Vakurov
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Separation Method ◽  
Variable Separation ◽  
Variable Separation Method ◽  
Viscoelastic Bodies

scholarly journals Load Localization and Reconstruction Using a Variable Separation Method

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Jing Zhang ◽  
Fang Zhang ◽  
Jinhui Jiang
Keyword(s):  
Impulse Response ◽  
Time History ◽  
Separation Method ◽  
Location Information ◽  
Engineering Practice ◽  
Variable Separation ◽  
Response Matrix ◽  
Optimization Function ◽  
Load Location ◽  
Variable Separation Method

Load identification is very important in engineering practice. In this paper, a novel method for load reconstruction and localization is proposed. In the traditional load localization method, location information is coupled to the impulse response matrix. The inversion of the impulse response matrix leads the process of load localization to be time-consuming. So we propose a variable separation method to separate the load location information from the impulse response matrix. An error optimization function of load histories in different modes is employed to determine the true load location. After locating the external load, the load time history can be easily reconstructed by the measurement responses and determinate impulse response matrix. This method is verified by simulations of a simply supported beam acted by a sine load and an impact separately. An experiment is also carried out to validate the feasibility and accuracy of the proposed method.

Painlevé Integrability and Abundant Localized Structures of (2+1)-dimensional Higher Order Broer-Kaup System

2002 ◽  
Vol 57 (12) ◽  
pp. 929-936 ◽  
Author(s):  
Ji Lin ◽  
Hua-mei Li
Keyword(s):  
Phase Shift ◽  
Coherent Structures ◽  
Higher Order ◽  
Separation Method ◽  
Variable Separation ◽  
Localized Structures ◽  
Painlevé Property ◽  
Variable Separation Method ◽  
Truncated Painlevé Expansion

It is proven that the (2+1) dimensional higher-order Broer-Kaup system the possesses the Painlevé property, using the Weiss-Tabor-Carnevale method and Kruskal’s simplification. Abundant localized coherent structures are obtained by using the standard truncated Painlevé expansion and the variable separation method. Fractal dromion solutions and multi-peakon structures are discussed. The interactions of three peakons are investigated. The interactions among the peakons are not elastic; they interchange their shapes but there is no phase shift

Study of the Variable Separation Solutions and Chaotic Behaviors for the Extended (2+1)-Dimensional Shallow Water Wave System

2013 ◽  
Vol 329 ◽  
pp. 144-147
Author(s):  
Xiao Xin Zhu ◽  
Song Hua Ma ◽  
Qing Bao Ren
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Water Wave ◽  
Mapping Method ◽  
Separation Method ◽  
Wave System ◽  
Variable Separation ◽  
Wave Excitation ◽  
Shallow Water Wave ◽  
Variable Separation Method

With the mapping method and a variable separation method, a series of variable separation solutions to the extended (2+1)-dimensional shallow water wave (ESWW) system is derived. Based on the derived solitary wave excitation, some chaotic behaviors are investigated.

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