结构动力学中若干问题辨析  

Analysis of several problems in structural dynamics

作　　者：潘旦光[1,2] 鲁文艳 PAN Danguang;LU Wenyan(Department of Civil Engineering,University of Science and Technology Beijing,Beijing 100083,P.R.China;Beijing Key Laboratory of Urban Underground Space Engineering,University of Science and Technology Beijing,Beijing 100083,P.R.China)

机构地区：[1]北京科技大学土木工程系,北京100083 [2]北京科技大学城市地下空间工程北京市重点实验室,北京100083

出　　处：《高等建筑教育》2021年第2期79-89,共11页Journal of Architectural Education in Institutions of Higher Learning

基　　金：土木工程防灾国家重点实验室开放基金(SLDRCE15-01)。

摘　　要：针对结构动力学教学过程中运动方程建立、运动方程求解的若干问题进行讨论,主要包括动力学和静力学刚度系数的区别,频响函数和脉冲响应函数的Fourier变换条件及对动力反应的影响,滞后阻尼体系的频响函数等问题。仅考虑集中质量平动自由度的体系,动力学刚度系数是指平动自由度产生单位位移而转动自由度放松情况下所受的力,静力凝聚方法和单位位移法所得刚度系数是相同的;无论是无阻尼体系还是有阻尼体系,频响函数和脉冲响应函数的Fourier变化关系都精确成立;时域特解包含稳态振动和伴生自由振动,而频域特解仅为体系的稳态解,两者之间的差别主要在振动的初始阶段,自振频率越低,差别越大。对于滞后阻尼体系,负频率的频响函数应为正频率频响函数的共轭函数。To discuss several problems in the process of establishing and solving equations of motion in structural dynamics teaching.It mainly includes the difference of stiffness coefficients between dynamic and static mechanics as well as their relationship by the static condensation,the Fourier transformation condition from impulse response function to frequency response function and their effect on dynamic response,the frequency response function of the hysteretic damping system.For the lumped-mass system with only translational degree of freedom,the stiffness in dynamics is the force required along DOF due to unit displacement at translational DOF and relaxation of rotational DOFs,and the stiffness coefficients obtained by the static condensation method and the unit displacement method are identical;Whether a system with damping or not,the Fourier transformation relationship between the frequency response function and the impulse response function is accurate;the particular solution includes steady-state vibration and free adjoint vibration in the time domain,however,only the steady-state vibration in the frequency domain.Their difference is evident for the initial stage of vibration.The difference is more noticeable for small natural frequency.For a system with hysteretic damping,the frequency response function of the negative frequency should be the conjugate function of that of the corresponding positive frequency.

关 键 词：刚度系数 静力凝聚 时域方法 频域方法 滞后阻尼 

分 类 号：TU311.3[建筑科学—结构工程] G642.3[文化科学—高等教育学]