动力系数反应谱教学中极值法的应用及案例分析  

Application and Case Study of Extremum Method for Teaching Dynamic Coefficient Response Spectrum

作　　者：张士科[1] 肖建清[1] 于锦彩 ZHANG Shike;XIAO Jianqing;YU Jincai(School of Civil Engineering and Architecture, Anyang Normal University, Anyang 455000, China)

机构地区：[1]安阳师范学院建筑工程学院,河南安阳455000

出　　处：《安阳师范学院学报》2021年第2期133-137,共5页Journal of Anyang Normal University

基　　金：安阳师范学院2019年校级教育教学改革重点项目“基于工程教育认证的土木工程专业课程体系与教学内容研究与实践”(项目编号ASJY-2019-BZD-009);河南省高等学校青年骨干教师培养计划(项目编号2018GGJS122);河南省新工科研究与实践项目(项目编号2020JGLX065)。

摘　　要：基于高等数学中极值法求最值的原理,结合力学的实践特点,提出了用极值法分析任意动力荷载作用下动力系数反应谱的思想。以线性渐增荷载为例,介绍了极值法求解动力反应的过程,推导了在动力荷载作用下的动力系数与动荷载时间比值之间的函数关系式。结果表明该方法能有效地进行结构动力学强迫振动部分的动力反应分析,同时也方便了教师的教学和学生的自学,对提高该课程的教学质量,帮助学生提高自主学习能力都有重要的意义。According to the principle of extremum method to find the most value in higher mathematics, the extreme approach is presented to analyze the dynamic coefficient response spectrum under the random dynamic loading by combining with the practice characteristics of mechanics. Taking the linear progressive loading as an example, the process of solving dynamic response spectrum via extremum method is introduced, meanwhile, the functional function between dynamic coefficient and time ratio under dynamic loading is derived. Results illustrate that the extremum method can effectively perform the analysis of dynamic reaction for the forced vibration of structure. This is convenient and helpful for teacher teaching and student self-study, and can improve the teaching effect and quality of structural mechanics.

关 键 词：结构动力学 极值法 动力系数 反应谱 强迫振动 

分 类 号：O342[理学—固体力学] TU311.4[理学—力学]