Volume 38, Number 4, August 2020
|Page(s)||774 - 783|
|Published online||06 October 2020|
Generalized Multi-Symplectic Numerical Implementation of Dynamic Responses for Saturated Poroelastic Timoshenko Beam
School of Mechanics and Civil Engineering, Northwestern Polytechnical University, Xi'an 710072, China
2 School of Sciences Mechanics, Chang'an University, Xi'an 710064, China
Based on the porous media theory and Timoshenko beam theory, properties of dynamic responses in fluid-solid coupled incompressible saturated poroelastic Timoshenko beam are investigated by generalized multi-symplectic method. Dynamic response equation set of incompressible saturated poroelastic Timoshenko beam is presented at first. Then a first order generalized multi-symplectic form of this dynamic response equation set is constructed, and errors of generalized multi-symplectic conservation law, generalized multi-symplectic local momentum and generalized multi-symplectic local energy are also derived. A Preissmann Box generalized multi-symplectic scheme of the dynamic response equation set is presented, the discrete errors of generalized multi-symplectic conservation law, generalized multi-symplectic local momentum conservation law and generalized multi-symplectic local energy conservation law are also obtained. In view of the dynamic responses of incompressible saturated poroelastic Timoshenko cantilever beam with two ends permeable and free end subjected to the step load, the transverse dynamic response process of the solid skeleton is simulated numerically, the evolution processes of solid effective stress and the equivalent moment of the pore fluid pressure over time are also presented numerically. The effects of fluid-solid coupled interaction parameter and slenderness ratio of the beam on the solid dynamic response process are revealed, as well as the effects on all generalized multi-symplectic numerical errors are checked simultaneously. From results obtained, the processes for solid deflection, solid effective stress and the equivalent moment of the pore fluid pressure approaching to their steady response values are all shortened with increasing of fluid-solid coupled interaction parameter, while the response process of solid deflection and the pore fluid equivalent moment are lengthened with increasing of slenderness ratio of the beam. Moreover, the steady value of solid deflection is much closer to the static deflection value of classic single phase elastic Euler-Bernoulli beam with increasing of the slenderness ratio. As time goes on, the solid skeleton of the beam will support all outside load, so equivalent moment of the pore fluid pressure becomes zero at last. In addition, it is presented all generalized multi-symplectic numerical errors decrease with the decreasing of parameters representing the dissipation effect for the dynamic system.
Key words: saturated porous media / saturated poroelastic Timoshenko beam / cantilever beam / solid skeleton / dynamic response / effective stress / porosity / darcy permeability coefficient / attenuation vibration / dissipation / multi-symplectic method / generalized multi-symplectic method / numerical implementation / local conserved structure
关键字 : 饱和多孔介质 / Timoshenko梁 / 悬臂梁 / 固相骨架 / 动力响应 / 有效应力 / 孔隙度 / Darcy渗流系数 / 衰减振动 / 耗散 / 多辛算法 / 广义多辛 / 数值实现 / 局部保结构
© 2020 Journal of Northwestern Polytechnical University. All rights reserved.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.