Initial-condition consideration by transferring and loading reconstruction for the dynamic analysis of linear structures in the frequency domain
Initial-condition consideration by transferring and loading reconstruction for the dynamic analysis of linear structures in the frequency domain
复制标题
频域线性结构动态分析中传递和加载重构的初始条件考虑
DOI：
10.1016/j.jsv.2014.09.043
复制
发表时间：
2015
影响因子：
4.7
通讯作者：
Bingchen Liang
中科院分区：
文献类型：
--
作者：
Fushun Liu;Huajun Li;Weiying Wang;Bingchen Liang
传统的频域动力分析方法只能计算系统的稳态响应，通常采用快速傅立叶变换（FFT）。本文提出了一种新的考虑初始条件的频域方法。将外载荷分解为Prony级数，并将系统的初始条件转化为重构载荷，重构载荷是初始载荷与相应的初始条件在拉普拉斯域内的组合。与传统的频域方法类似，在时域中使用逆傅立叶变换（IFT）来计算系统的响应。一个理论发展是初始条件可以组合成相应的重构载荷，这避免了FFT所需的周期性假设。另一个改进是，初始外载荷的分解只需要很短的测量时间，这表明了一个良好的计算效率的复杂系统的潜在能力。单自由度的数值计算结果表明，由于引入了IFT，只要初始条件为零，该方法就能达到与频域法相似的效果。当考虑非零初始条件时，所提出的方法具有与时域方法相似的精度，但应该注意的是，所提出的方法在零时刻的响应上存在误差。从四自由度系统的数值结果中可以得出相同的结论，这表明了解决多自由度系统的能力。第三个例子是一个三维（3D）框架结构，通过随机生成不同的组件，受到更一般的外部载荷;初始条件使用两个系列的随机数模拟：一个是初始位移，另一个是初始速度。结果表明，该方法获得了与时域方法一致的响应，但由于运动方程在频域求解，计算量较小。此外，还对早期出现的大部分相对误差给出了原因和相应的解决措施。
Traditional frequency-domain dynamic analysis methods can only compute the steady-state responses of the system, typically by employing the fast Fourier transform (FFT). In this paper, a new frequency-domain method that can consider the initial conditions is proposed. External loadings are decomposed into Prony series, and the initial conditions are transferred from the system into the reconstructed loadings, which are combinations of the initial loadings and the corresponding initial conditions in the Laplace domain. Similar to the traditional frequency-domain method, the inverse Fourier transform (IFT) is used to compute the responses of the system in the time domain. One theoretical development is that the initial conditions can be combined into the corresponding reconstructed loadings, which avoids the required periodic assumption for the FFT. The other improvement is that the decomposition of the initial external loadings requires only a short duration of measurements, which indicates a good potential capability of the computing efficiency for complex systems. The numerical results from a single degree-of-freedom (DOF) indicate that the proposed method can perform similar to the frequency-domain method if only the initial conditions are set to zero values because the IFT is used. When non-zero initial conditions are considered, the proposed method has a similar accuracy to the time-domain method, but one should note that the proposed method has an error on the response at time zero. One can draw identical conclusions from the numerical results of a four-DOF system, which demonstrates the ability to address multiple-DOF systems. The third example is a three-dimensional (3D) frame structure subjected to more general external loadings by randomly generating different components; the initial conditions are simulated using two series of random numbers: one is for the initial displacements and the other is for the initial velocities. The results show that the proposed method obtains consistent responses with the time-domain method, but it has better computation cost because the equations of motion are solved in the frequency domain. In addition, the reason and corresponding measurement on most relative errors at the early time are also provided.