阻尼梁振动方程的混合有限体积元方法  

MIXED FINITE VOLUME ELEMENT METHOD FOR DAMPED BEAM VIBRATION EQUATIONS

作　　者：姜子文 王同昕 尹哲 Jiang Ziwen;Wang Tongxin;Yin Zhe(School of Mathematics and Statistics,Shandong Normal University,Jinan 250358)

机构地区：[1]山东师范大学数学与统计学院,济南250358

出　　处：《高等学校计算数学学报》2023年第1期38-55,共18页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(12171287,11501335);山东省自然科学基金(ZR2021MA063)。

摘　　要：1引言考虑如下阻尼梁振动方程初边值问题■其中u(x,t)表示位移,Ω=(0,L),0 <T <∞,a=■EI表示梁的抗弯刚度,ρ和A分别表示梁的密度和横截面积,对于均匀梁取为常数.μ(>0)为阻尼系数,L为梁的长度,源项f(x,t),初值函数φ(x)和Ψ(x)为充分光滑的已知函数,其中φ(x)和Ψ(x)分别表示梁在初始时刻的位移和速度.In this paper,an initial and boundary value problems of the damped beam vibration is investigated.We rewrite the fourth-order damped beam vibration equation as the systems of two second-order equations by introducing intermediate variables,and the existence,uniqueness and convergence of the solution of the mixed finite volume element scheme are analyzed.Finally,numerical examples are given to verify the accuracy and effectiveness of the scheme.

关 键 词：初边值问题 梁振动方程 有限体积元方法 横截面积 抗弯刚度 阻尼系数 已知函数 初始时刻 

分 类 号：O241.82[理学—计算数学]