Dynamic analysis of cracks using the SGBEM for elastodynamics in the Laplace-space frequency domain

Dynamic analysis of a system can be carried out either in the time or frequency domains. Time responses/histories of this system may be directly obtained using time-domain formulations. In the frequency domain, analysis can be performed in either the Fourier or Laplace spaces. The symmetric-Galerkin boundary element method (SGBEM) for 2-D elastodynamics in the Fourier-space frequency domain has been previously reported in the literature. In this paper, the SGBEM for elastodynamics in the Laplace-space frequency domain using the standard continuous quadratic element and its application to dynamic analysis of cracks is presented for the first time. The technique developed is employed together with the fast Laplace inverse transform by Durbin to obtain time-dependent results for several typical examples including both crack and non-crack problems. These results are highly accurate when compared to those obtained from other numerical techniques. It is shown in this work that the very same boundary element code can be utilized to perform frequency domain analysis in either the Fourier or Laplace spaces. However, if time responses are required, the accuracy and computational effectiveness of the analysis may depend on the type of space selected as it determines the type of transforms (inverse Fourier/Laplace transforms) needed for converting frequency solutions to the desired time responses.     

Combination of Newmark method and natural element method for elastodynamics

The natural element method (NEM) is a meshless method. The trial and test functions of the NEM are constructed using natural neighbor interpolations which are based on the Voronoi tessellation of a set of nodes. The NEM interpolation is linear between adjacent nodes on the boundary of the convex hull, which makes imposition of essential boundary conditions easy to implement. We investigate the performance of the NEM combined with the Newmark method for problems of elastodynamics in this article. Applications are considered for a cantilever beam with different initial load conditions. The NEM numerical results are compared with the finite element method. NEM shows promise for these applications.     

Frequency domain analysis for fluorescence recovery after photobleaching

Fourier transformation is evaluated as a means of improving precision in the analysis of fluorescence-recovery-after-photobleaching (FRAP) data. Simulations of FRAP data of 2m points, where m is an integer, are Fourier transformed to obtain the frequency domain data. Analogous to frequency domain techniques in nanosecond spectroscopy, frequency domain analysis of FRAP data is shown to provide more precise results. For a single exponential decay acquired over a time window of five decay constants, frequency domain analysis increases the precision by six fold without requiring that any more data be acquired. For a double exponential decay with decay constants that differ by a factor of two and noise of 5% relative standard deviation, time domain analysis is unable to distinguish this from a single exponential decay (chi2=1.1), whereas frequency domain analysis reveals that it does not fit to a single exponential decay (chi2=2.5). For a double exponential decay with five-fold differing decay constants, improved precision is obtained in the frequency domain for both of the decay constants, as well as the fractional amount of each. In contrast to nanosecond spectroscopy, the FRAP analysis described here combines the higher precision of the frequency domain with the direct observation in the time domain to facilitate the assessment of artifacts.     

基于变窗函数方法的频率检测技术研究

针对常用的频谱校正技术检测短记录信号时受负频谱的泄露干涉影响而难以应用这一技术瓶颈,提出了基于变窗函数方法的-套显式全新测频方法,并采用仿真手段对提出的方法进行研究、考核.结果表明,采用Rectangular窗、Hanning窗、Blanckman窗进行组合得出的3个频率计算公式测频绝对误差均在10r4倍频率分辨率数量级.并且运用该方法不用考虑被测信号中直流分量的影响,虽然当CiR小于0.5时误差随频率下降而增加,但这足以满足工程实践的需要.确认频率计算公式涉及到的奇点效应是引起误差变大的主要原因,只要适时调整分析样本数这一效应就能够得到很好地避免.     

Frequency domain analysis of elastic bounded domains using a new semi-analytical method

In this paper, a new semi-analytical method is developed for solving two-dimensional elastodynamic problems in the frequency domain, employing Fast Fourier Transform. Using specific non-isoparametric elements, the boundary of the problem’s domain is discretized. By employing higher-order Chebyshev mapping functions, special shape functions, Clenshaw–Curtis quadrature, and implementing a weak form of weighted residual method, coefficient matrices of equation system become diagonal. This fact results in a set of decoupled Bessel differential equations to be used for solving the whole system. This means that the governing Bessel differential equation for each degree of freedom (DOF) becomes independent from other DOFs of the domain. For each DOF, the Bessel differential equation is solved for a specific frequency. Finally, the time history of responses may be obtained by using Inverse Fast Fourier Transform. Three numerical examples are presented to demonstrate the accuracy of the present new method.     

数字前馈跟踪控制器的频域迭代设计方法

 数字前馈控制器用于提高伺服系统跟踪性能,在工程应用中通常包含如下设计环节：闭环对象参数辨识、闭环离散化和设计前馈控制器,上述各环节都会引入设计误差,最终导致所设计的前馈控制器跟踪性能变差.针对上述问题,利用闭环对象的实测频率特性数据,提出一种新型的频域迭代设计方法,能有效消除各环节误差.通过对设计过程的频率特性差值的变化分析,给出了迭代算法的步骤.该方法将反馈控制思想引入前馈控制器设计过程,根据频率特性差值,不断修正对象频率特性数据,通过设计过程的迭代,使跟踪误差显著减小.以某飞行转台伺服系统为例,进行数值仿真和应用研究,结果表明了该方法的有效性,能显著拓宽伺服系统的跟踪频带,减小对低频信号的跟踪误差．     

Time domain analysis by the point-matched finite element method

The solution of Maxwell's equations using the point-matched finite-element time-domain approach is presented. The solution scheme is explicit and does not require the solution of any matrix equations. The solution is carried out over a finite domain terminated using appropriate absorbing boundary conditions. Far-field quantities are obtained from the near-field solution by first computing the frequency-domain solutions from the time-domain solution using the fast Fourier transform and then using a near-field to far-field transformation algorithm.<>     

Frequency domain analysis of nonlinear systems driven by multiharmonic signals

This paper examines the output properties of static power-series nonlinearities driven by periodic multiharmonic signals with emphasis given to their effect on linear frequency response function (FRF) measurements. The analysis is based on the classification of nonlinear distortions into harmonic and interharmonic contributions. The properties of harmonic contributions are examined in detail and explicit formulae are derived, by which the number of harmonic contributions generated at the test frequencies can be calculated for odd-order nonlinearities up to, and including, the ninth order. Although an analytic solution for any odd-order nonlinearity is still under investigation, a heuristic methodology is developed that solves this problem. It is shown that the derived formulae provide a useful tool in the examination of the behavior of FRF measurements in the presence of nonlinear distortions. Based on these formulae, different approaches in classifying nonlinear distortions are then compared with respect to their suitability in assessing the influence of system nonlinearities on linear FRF measurements.     

Frequency domain analysis of microstrip filters and antennae using an adaptive frequency sampling moment method

In this paper, an adaptive frequency sampling technique is applied to the moment method for the analysis of microstrip filters and patch antennae. The analysis of microstrip low-pass filter and patch antenna in the frequency domain has been usually done with uniform frequency step. An adaptive frequency sampling technique can significantly reduce the time taken for the analysis through the frequency range without reducing the accuracy of the results.     

Completeness of corrective smoothed particle method for linear elastodynamics

 Two different solution algorithms of the corrective smoothed particle method (CSPM) are developed and examined with linear elastodynamic problems. One is to use the corrective first derivative approximations to solve the stress-based momentum equations, with stresses evaluated from the strains. This is an approach that has widely been adopted in smoothed particle hydrodynamics (SPH) methods. The other is new, in which the corrective second derivative approximations are used to directly solve the displacement-based Navier equations. The former satisfies the nodal completeness condition but lacks integrability; on the contrary, the latter is truly complete. Numerical tests show that the latter outperforms the former as well as other existing SPH methods, as expected. Received 1 April 1999     

Frequency domain analysis for stability robustness of multivariable feedback systems

Abstract

This paper presents techniques for analyzing stability robustness of multivariable control systems. The upper bounds for each element of the allowable perturbation matrices can be obtained whether highly structural information is available or not. Approaching from testing the nonsingularity of a matrix by its eigenvalues instead of using matrix norms, the main algorithm involved is the computation of the spectral radii of certain nonnegative matrices. Due to the fact that any matrix norm is never less than the spectral radius of the same matrix, less conservative results are obtained using our criteria as compared with those obtained by utilizing matrix norms.     

The improved element-free Galerkin method for two-dimensional elastodynamics problems

In this paper, we derive an improved element-free Galerkin (IEFG) method for two-dimensional linear elastodynamics by employing the improved moving least-squares (IMLS) approximation. In comparison with the conventional moving least-squares (MLS) approximation function, the algebraic equation system in IMLS approximation is well-conditioned. It can be solved without having to derive the inverse matrix. Thus the IEFG method may result in a higher computing speed. In the IEFG method for two-dimensional linear elastodynamics, we employed the Galerkin weak form to derive the discretized system equations, and the Newmark time integration method for the time history analyses. In the modeling process, the penalty method is used to impose the essential boundary conditions to obtain the corresponding formulae of the IEFG method for two-dimensional elastodynamics. The numerical studies illustrated that the IEFG method is efficient by comparing it with the analytical method and the finite element method.     

Mixed variational principles in space and time for elastodynamics analysis

Summary Nonlinear elastodynamics problems are approached from the point of view of a mixed variational principle. It is shown that four different functionals lead to different formulations of the problem with different independent fields. One of the functionals is specialized to the case of spatial beams undergoing large deformations, and small strains. The extension of these functionals to the case in which kinematic constraints are presented leads to the useful concept of dual constraints, which can be advantageously employed in treating problems involving contact, impact, and changing topology.     

导管架式海上升压站初始条件下瞬态响应频域计算方法研究EI北大核心CSCD

导管架式海上升压站的瞬态响应分析依赖时域积分法,初始条件引起的瞬态响应中阶次较高的振动成分,必须取足够小的计算时间步长才能得到较准确的结果。针对海上升压站的瞬态响应分析,提出一种基于Laplace变换的频域计算方法。该方法通过振动系统的特征值分析得到传递函数的极点和零点,进而计算传递函数的极值和留数,同时将初始条件考虑到瞬态响应的极值和留数中,经Laplace逆变换得到时域瞬态响应。分别采用四自由度系统和导管架式海上升压站数值模型对此方法进行验证,并与Newmark⁃β法进行对比,结果表明该方法计算的瞬态响应与Newmark⁃β法计算结果吻合较好,并能够避免Newmark⁃β法由于时间步长较大引起的误差,说明了该方法的正确性。     

舰用柴油机抗冲击性能频域分析

舰用设备抗冲击性能的频域分析是一种常用的工程评估方法。建立了某型柴油机的有限元模型,通过主要部件的模态试验进行了修正。根据国军标GJB1060.1-91的规定,基于DDAM方法确定了计算模型的冲击输入,并对柴油机模型在三向冲击输入下的冲击响应进行了分析。结果表明,柴油机抗冲击性能的频域分析是一种有效的评估方法,通过评估,本文的柴油机模型符合国军标的要求。