非瞬间脉冲扰动的四阶线性和非线性微分方程边值问题变分法研究  

Variational method study on boundary value problems of fourth order linear and nonlinear differential equations with non-instantaneous pulse perturbation

作　　者：杨冬成 YANG Dongcheng(Yancheng Electromechanical Branch,Jiangsu United Vocational and Technical College,Yancheng Jiangsu 224001)

机构地区：[1]江苏联合职业技术学院盐城机电分院,江苏盐城224001

出　　处：《宁夏师范学院学报》2024年第7期42-50,共9页Journal of Ningxia Normal University

摘　　要：通过对非瞬间脉冲扰动的四阶微分方程解的存在性、边值问题和多解性分析.不同边界条件、刚度系数、质量系数、脉冲幅值下弹性竖直板中点位移和x/d=4时的辐射波高显示,刚度系数、脉冲幅值均会对弹性竖直板的振动响应和辐射波高产生正向影响,固定一边的衰减速率明显快于其他两种边界条件.The existence,boundary value problem and multi solution of the fourth-order differential equation with non-instantaneous impulsive perturbation are investigated by using the variational method theory.The midpoint displacement of the elastic vertical plate under different boundary conditions,stiffness coefficient,mass coefficient,and pulse amplitude,as well as the radiation wave height when x/d=4 show that the stiffness coefficient and pulse amplitude have a positive impact on the vibration response and radiation wave height of the elastic vertical plate,and the attenuation rate on the fixed side is significantly faster than the other two boundary conditions.

关 键 词：变分法 非瞬间脉冲 微分方程 边值 四阶 

分 类 号：O241.8[理学—计算数学]