培养拓展性思维的教学探索——以阻尼比对单自由度体系动力响应影响为例

Teaching practice for extended thoughts training:a case study on the influence of damping in the dynamic response of SDOF system

土木工程属于相对比较传统的专业,主干课程以数学、力学和结构类课程为主,在课程教学中开展培养拓展性思维的教学探索,强调所学知识的综合应用。文章以工程结构中常见的单自由度体系动力响应为例进行探讨,该内容是结构动力学、建筑结构抗震等课程的基础内容。单自由度体系动力方程可简化为二阶微分方程,常见情况下阻尼比小于0.2,增大阻尼可以减小结构动力响应,课程教学中针对这个一般意义上的普通命题开展拓展性思维训练,由助教牵头学生提出问题、查阅资料并解决问题,讨论了一般小阻尼情况下的结构响应变化情况,分析了临界阻尼和过阻尼情况下阻尼与结构响应的关系,从而帮助学生正确认识阻尼在结构动力响应分析中的影响。

Civil engineering is a relatively traditional discipline which mainly contains mathematical,mechanical and structural courses. Teaching practice for extended thoughts training was carried out during courses to achieve comprehensive application of learned knowledge. The paper takes dynamic response of single degree of freedom（SDOF） system, which is common in structures, as an example. This section is the basic content in structural dynamics and seismic design courses. Dynamic equation of SDOF system can be simplified into a second order differential equation. In general case the damping ratio is less than 0. 2 and dynamic response of structures can be usually decreased by increasing damping ratio. Extended thoughts training was carried out during teaching process based on this general assumption. During courses, teaching assistant guided students to raise questions,refer to literature and solve problems. The paper discusses the change of structural responses in small damping ratio cases and analyses the relationship between damping ratios and structural responses in critical damping and over damping cases to assist students establish correct understandings of the influence of damping in the dynamic responses of structures.