考虑以下奇异摄动椭圆问题ε2Δu+(u-a(y))(1-u2)=0 inΩ,(u)/(n)=0 on Ω,其中Ω是R2中一个光滑区域,-1<a(y)<1,ε是一个小参数,n是Ω的外法向,假设Γ={y∈Ω:a(y)=0}是Ω中一条简单光滑的闭曲线使得Γ把Ω分成Ω+与Ω-...考虑以下奇异摄动椭圆问题ε2Δu+(u-a(y))(1-u2)=0 inΩ,(u)/(n)=0 on Ω,其中Ω是R2中一个光滑区域,-1<a(y)<1,ε是一个小参数,n是Ω的外法向,假设Γ={y∈Ω:a(y)=0}是Ω中一条简单光滑的闭曲线使得Γ把Ω分成Ω+与Ω-2个分支.在Γ上(a)/(ν>0,其中ν是Ω+的外法向量.在[5]中,M.del Pino,M.Kowalczyk和J.Wei构造一族具有如下形状的解uε当uε→0 uε→1inΩ-且uε→-1inΩ+.证明了在uε处的线性化问题的最小特征值具有渐近形式:-μ0ε+o(ε),其中μ0>0.展开更多
By taking a rolling-spring isolation system as the study object, the effects of the non-uniform distribution of rolling friction coefficient on its isolation performance were analyzed by a compiled computer program. T...By taking a rolling-spring isolation system as the study object, the effects of the non-uniform distribution of rolling friction coefficient on its isolation performance were analyzed by a compiled computer program. The results show that the errors associated with the structural maximum relative displacement, acceleration and residual displacement due to ignoring the friction variability sequentially grow. This rule is weakened by the spring action, however, the unreasonable spring constant will cause sympathetic vibration. Under the condition of large friction variability, in the calculation of the structural maximum relative displacement and acceleration, the friction variability should be considered. When the structural residual displacement is concerned, the variability of rolling friction coefficient should be fully considered regardless of the friction variability.展开更多
基金Projects(51308549,51378504,51478475) supported by the National Natural Science Foundation of ChinaProject(2015JJ3159) supported by the Natural Science Foundation of Hunan Province,ChinaProject(2015CX006) supported by the Innovation-driven Plan in Central South University,China
文摘By taking a rolling-spring isolation system as the study object, the effects of the non-uniform distribution of rolling friction coefficient on its isolation performance were analyzed by a compiled computer program. The results show that the errors associated with the structural maximum relative displacement, acceleration and residual displacement due to ignoring the friction variability sequentially grow. This rule is weakened by the spring action, however, the unreasonable spring constant will cause sympathetic vibration. Under the condition of large friction variability, in the calculation of the structural maximum relative displacement and acceleration, the friction variability should be considered. When the structural residual displacement is concerned, the variability of rolling friction coefficient should be fully considered regardless of the friction variability.
