基于势能判据的约束模态综合法截断准则  

Mode cut-off criterion of constrained mode synthesis method based on a potential energy criterion

作　　者：姜忻良[1] 王菲[1] 

机构地区：[1]天津大学建工学院,天津300072

出　　处：《振动与冲击》2011年第2期32-38,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金重大研究计划资助项目(90815025);国家自然科学基金资助项目((50878143);天津市应用基础及前沿技术研究计划资助项目(09JCZDJC25300)

摘　　要：为提高大型复杂结构体系的计算效率,在深入分析约束模态综合法原理的基础上,定义了由不同主模态截断阶数产生的位移向量组成的线性空间,建立该空间上的一个函数,通过数学定理详细证明了该函数是线性空间上的范数,并以该范数的最大值定义势能判据,推导出势能判据与子结构主模态截断数量之间的关系,据此提出了一种基于势能判据的子结构主模态截断准则。此外对于约束模态综合法,还推导了以机械能为判据的情况,证明了约束模态法中子结构的机械能随截断主模态数量的变化曲线并不是单调的,故不适用于约束模态法。最后将势能判据截断准则应用到地基土-高层建筑相互作用体系的地震响应分析问题中,进一步对所提出的模态截断准则的计算精度进行对比研究。研究结果表明,所提出的势能判据截断准则是十分有效的,而应用于振型叠加法的机械能判据不宜应用于约束模态综合法中。To improve computational efficiency,the constrained mode synthesis method was discussed and a linear space consisting of displacement vectors calculated with different mode cut-off numbers was defined.A function was also defined and verified to be a norm of this linear space mathematically.Then,adopting the maximum value of this norm to define a potential energy criterion.The relationship between the potential energy criterion and the mode cut-off number was derived.Consequently,a mode cut-off criterion based on the potential energy criterion was proposed.In addition,the criterion adopting the mechanical energy for the constrained mode synthesis method was considered.It was proved that the mechanical energy is not a monotonic function versus the mode cut-off number,so it is not suitable for the constrained mode synthesis method.Finally,the proposed potential energy criterion was applied to seismic analysis of a soil and multi-story building interaction system,the results were compared with those not using the mode synthesis method.It was shown that the proposed mode cut-off criterion based on the potential energy criterion is effective while based on the mechanical energy criterion generally used in the mode superposition method is not suitable for the constrained mode synthesis method.

关 键 词：地震响应分析 约束模态综合法 势能判据 模态截断准则 子结构 范数 

分 类 号：TU311.3[建筑科学—结构工程]