考虑初始条件的结构振动方程的频域算法  

Frequency-domain Algorithm for Structural Vibration Equations Considering Initial Conditions

作　　者：郑向远 李冬安 邹荔兵 王中权 ZHENG Xiangyuan;LI Dong’an;ZOU Libing;WANG Zhongquan(Shenzhen International Graduate School,Tsinghua University,Shenzhen 518055,China;Institute of Ocean Engineering,Tsinghua University,Beijing 100084,China;Mingyang Smart Energy Group Limited,Zhongshan 528436,China;Southern Offshore Wind Power Joint Development Co,LTD,Zhuhai 519006,China)

机构地区：[1]清华大学深圳国际研究生院,广东深圳518055 [2]清华大学海洋工程研究院,北京100084 [3]明阳智慧能源集团股份公司,广东中山528436 [4]南方海上风电联合开发有限公司,广东珠海519006

出　　处：《湖南大学学报（自然科学版）》2023年第3期32-40,共9页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(52071186);广东省海洋经济高质量发展重点推进计划项目(GDNRC[2020]048);深圳市高等学校稳定资助重大专项项目(WDZC20200819174646001)。

摘　　要：为了在离散频域内求出由非零初始条件与外加荷载共同作用引起的结构的动力响应,基于傅里叶变换(FT)和有限差分公式,推导出了狄拉克δ函数及其一阶导数的离散傅里叶变换(DFT),构建了一类新频域算法.利用这一算法,有效克服了传统的频域算法中由非零初始位移导致的动力响应数值发散.用三个数值算例来研究算法性能,分别是单自由度(SDOF)线性系统、4000个自由度的桁架结构、顶端具有集中质量的悬臂梁;它们均具有非零初始位移和初始速度.计算结果表明:改进后的频域算法与传统的数值算法算得的结果一致,且精度与效率更高,适用于求解各种类型的线性结构振动的动力响应.In order to solve the structural dynamic response caused by nonzero initial condition and external load in the discrete frequency domain,a new frequency domain algorithm is constructed.The discrete Fourier transform(DFT)of Diarcδfunction and its first derivative is derived based on the Fourier transform(FT)and finite difference formula.With this new algorithm,the numerical divergence of dynamic response caused by nonzero initial displacement in the traditional frequency domain algorithm is effectively overcome.Three numerical examples are used to further study the performance of this algorithm.They are a linear system of single degree of freedom(SDOF),a 4000-DOF truss structure,and a cantilever beam with concentrated mass at the top,respectively.These structures all have nonzero initial displacement and initial velocity.The numerical results show that the improved frequency domain algorithm provides consistent results with the traditional numerical method,and has higher accuracy and efficiency,which is suitable for solving the dynamic response of various linear vibration problems.

关 键 词：结构动力学 频域分析 初值问题 Δ函数 有限差分法 

分 类 号：O241.81[理学—计算数学]