基于辛数学方法的一维声子晶体禁带计算

将一维声子晶体的原胞简化为有限多个自由度的弹簧振子结构,在辛对偶变量体系下探讨晶格振动,引入辛数学方法确定波矢与本证值的色散关系。通过本证值计数法计算特征频率,从而得到禁带区间。与传统集中质量法相比,该算法的计算结果与之吻合很好,且提高了计算精度和计算效率,更重要的是在低频处收敛性更好。     

基于模态综合和移频方法的中频段模态计算

采用基于特征约束模态降阶的模态综合方法计算结构中频段振动特性时,针对低阶特征约束模态不能截断的问题,引入了移频方法对子结构动力学方程进行变换,并推导了移频后低阶特征约束模态与系统中频段模态的关系,结果表明：采用移频方法后,低阶特征约束模态可以截断。采用该方法计算了某白车身有限元模型160~190Hz频段内的振动特性,结果表明：采用移频方法后,保留的特征约束模态阶数较少,系统振动特性的计算时间较短,说明该方法有助于提高复杂结构中频段振动特性的计算效率。     

波纹芯体夹层板分频段隔声性能的多参数优化

应用遗传算法与梯度算法相结合的混合优化算法,在结构质量及整体刚度约束下,分两个频段对波纹芯体夹层板在中置点声源激励下平均透射声功率进行单参数和多参数优化分析,其中优化目标函数,即夹层板透射声功率用谱元法和Rayleigh积分进行建模计算。优化结果表明,单参数和多参数优化都能明显改善波纹芯体夹层板在高频段（701 Hz～1 500 Hz）的隔声性能,但两种方法在低频段（1 Hz～700 Hz）效果均不显著,证明单纯针对结构参数优化能够有效地抑制由局部模态引起的透射声峰值,但是对结构整体模态引起的透射声峰值影响有限。进一步对比表明,对具有多个结构参数的波纹芯体夹层板,其隔声性能多参数联合优化结果明显优于单参数优化结果。     

An improved series expansion method of frequency response function under medium and high frequency excitations

In view of the computational divergence in the series expansion method of frequency response function under medium and high frequency excitations, a new improved algorithm for dynamics system response is proposed. Structural modes are divided into available low order modes and truncated high order modes. The frequency response function of truncated high order modes is expanded by the application of Taylor series on the basis of power series expansion and modal superposition method. According to the coupling characteristics between low order and high order modes to mass and stiffness matrices, the contribution of truncated high order modes to the frequency response function is expressed as the low order mode matrix and system matrix. The present method considers the relation between structure frequency and excitation frequency. The results show that the improved algorithm expands the series expansion method to the range of medium and high frequency excitations, and the calculation accuracy of the frequency response function is improved under the incomplete modal conditions. Numerical results validate that this method is feasible and has good convergence.     

少量测点条件下提高结构法向振速重建精度和分辨率的方法

为了解决少量测点条件下利用近场声全息技术重建结构表面法向振速精度和分辨率不高甚至失效的问题,提出了一种基于声压声辐射模态的全息面插值算法,可有效提高结构法向振速重建精度和分辨率。计算全息面声压声辐射模态向量;根据声压声辐射模态收敛性,求取截断声压声辐射模态展开系数的最小二乘解或Tikhonov正则化解,由此计算出插值点处的声压值;利用插值后的全息面数据重建结构表面法向振速。简支平板激励仿真和音箱实验均表明,少量测点条件下利用该方法能够有效提高结构法向振速重建精度和分辨率,验证了方法的有效性。同时音箱实验验证了方法的可行性。     

改进的降阶牛顿迭代数值子结构方法

充分利用结构在地震作用下的局部非线性特征,数值子结构方法将原本复杂的结构非线性分析转化为以初始弹性刚度迭代的主结构等效线弹性分析和屈服构件隔离子结构非线性分析。由于主结构采用常刚度迭代分析收敛速度较慢,尚有一定局限性,于是该文提出一种改进的降阶牛顿迭代数值子结构方法。在主结构系统中,将塑性自由度位移场作为基本未知量,设计牛顿算法进行非线性迭代分析,并由隔离子结构跨平台非线性分析计算得到屈服单元的内力和切线刚度。对一平面15层3跨钢结构进行地震弹塑性时程分析,模拟结果表明:该文提出的方法是准确、可靠的,接近传统牛顿算法的二次收敛,且对于局部非线性结构系统,需要集成和分解的矩阵规模远小于传统方法。     

Subspace iteration accelrated by using Chebyshev polynomials for eigenvalue problems with symmetric matrices

Bathe's algorithm of subspace iteration for the solution of the eigenvalue problem with symmetric matrices is improved by incorporating an acceleration technique using Chebyshev polynomials. This method of acceleration is particularly effective for this kind of iteration. The rate of convergence of the iteration scheme presented is considerably improved when compared with the original one, and satisfactory rates of convergence can be obtained for a wider range of eigenvalues.     

C+L波段掺铒光纤光源模拟算法

提出了利用打靶法模拟双级双程泵浦结构掺铒光纤宽带光源的算法,该算法通过对打靶法的初值校正部分进行改进,加入了阻尼因子与下降因子,并把这两个因子同时应用到初值校正中,从而克服了传统打靶法在铒纤长度较长时校正矩阵奇异造成的算法不收敛的缺点.结合宽带光源的理论模型,给出了算法的实际过程,模拟得到了在光纤最佳长度处的C L波段输出谱型,并通过实验证实了模拟与实验结果相符合.最后讨论了导致宽带光源输出谱型不是最佳的因素,随着光纤长度增加导致的损耗,以及两端泵浦功率的比值,并给出了在泵浦功率比是最佳和不是最佳两种情况下的实验谱型.     

一维嵌套结构声子晶体透射特性

设计新型周期嵌套结构一维声子晶体,由采用传递矩阵法所得纵波与横波透射率谱图获得较传统一维晶格结构宽数倍的巨带隙与局域模。通过研究结构参数与带隙关系,获得有利于宽带隙产生条件及对局域模影响最大因素。通过控制掺杂材料厚度及位置,能较好实现局域模的精确调控,可显著增强声子晶体低频滤波效应。通过详述研究结果的物理机理,提出准缺陷耦合及缺陷共振等概念。     

求多项式全部零点的快速Halley算法

在Halley圆盘迭代法的基础上,用圆盘算术构造了一种求多项式全部零点的快速Halley算法,并在与Halley迭代法相同的条件下建立了它的收敛性定理,该算法取得了七阶收敛速度。数值结果表明该算法是十分有效的。     

腐蚀方式对Q345等边角钢疲劳性能的影响

塔体构件的疲劳性能随服役期内降雨分布等环境腐蚀因素的改变而发生变化。为此,该文首先基于单点-成组法结合相关系数优化法推导了不同腐蚀方式作用下S-N曲线方程的参数表达式及其回归方法,并建议了相应的实现算法。基于此,建立了不同腐蚀方式的P-S-N曲线方程。同时,对相同腐蚀时间内3种腐蚀方式作用下的39根足尺Q345等边角钢构件进行了腐蚀疲劳试验,观察了试件在#x0201c;浸泡-晾置#x0201d;腐蚀方式中的腐蚀状态,研究了不同腐蚀方式中试件的疲劳破坏模式。然后,由试验结果分析了各腐蚀方式中疲劳寿命的变化规律,建立了相应的S-N曲线模型,给出了各腐蚀方式中反映S-N曲线参数随可靠度变化规律的表达式,并结合理论推导及参数分析建立了各腐蚀方式作用下Q345等边角钢构件的P-S-N曲面模型。最后,采用该模型探讨了不同腐蚀方式中Q345等边角钢构件疲劳寿命的变化规律,结果表明:1)相同腐蚀时间内疲劳荷载越小腐蚀方式对构件疲劳寿命的影响越明显;2)腐蚀越严重疲劳寿命随可靠度增加减小的幅度越大。     

Assessment of the co-elution problem in gas chromatography-mass spectrometry using non-linear optimization techniques

Multivariate curve resolution based on the minimization of an objective function (MCR-FMIN) defined directly from the non-fulfillment of constraints was applied for the first time as a deconvolution method to separate co-eluted gas chromatographic-mass spectrometric (GC-MS) signals. Simulated and real (standard real mixture and limon oil) GC-MS data were used to evaluate the feasibility of this method. The MCR-FMIN solutions have been obtained based on the rotation of principal component analysis (PCA) solutions using the non-linear optimization algorithms. Calculation of the initial values of R rotation matrix using model free analysis methods such as fixed-size moving window-evolving factor analysis (FSMW-EFA), evolving latent projective graphs (ELPGs), and heuristic evolving latent projection (HELP) was proposed for faster convergence and avoiding to be stuck in local minima in MCR-FMIN algorithm. The band boundaries of feasible solutions (MCR-BANDS) obtained using MCR-FMIN were calculated for simulated data to assess the reliability of the method. In addition, the results of this method were compared with those of two most common self-modeling curve resolution (SMCR) methods of multivariate curve resolution-alternating least square (MCR-ALS) and HELP. A reasonable result can be obtained by selecting proper constraints, such as non-negativity, unimodality, normalization, and selectivity. However, when the number of components or the level of noise in each peak cluster increase, the convergence of algorithm becomes difficult and the results are not reliable. For quick and accurate analysis of co-eluted multi-component problematic GC-MS data MCR-FMIN can be considered as an alternative method to the MCR-ALS and HELP methods.     

Coupled Dielectric Nanoparticles Manipulating Metamaterials Optical Characteristics

In this paper, we investigate the concept and theory of all-dielectric metapatterned structures that manipulate electric and magnetic optical characteristics. A 3-D array of dielectric particles is designed, where the spheres operate in their magnetic modes and their couplings offer electric modes. An analytical solution for the problem of plane wave scattering by 3-D array of dielectric nanospheres is presented. FW multipole expansion method is applied to express the optical fields in terms of the electric and magnetic dipole modes and the higher order moments. By enforcing the boundary conditions at the surface of each sphere, with the use of the translational addition theorem for vector spherical wave functions, required equations to determine the scattering coefficients are obtained. Novel materials features in optics are demonstrated. Electric and magnetic scattering coefficient resonances around the same frequency band are obtained. It is highlighted how a metapatterned structure constructed from dielectric nanosphere unit cells can provide electric and magnetic modes resulting in backward wave phenomenon. A comprehensive circuit model based on the RLC (resistor, inductor, and capacitor) realization is presented to successfully analyze the scattering performance of a dielectric nanosphere. To better understand the physics of an array of spheres, circuit models for the interactions, and couplings between spheres are also accomplished. The engineered dispersion diagram for a 3-D array of identical highly coupled nanospheres is scrutinized, verifying that the high couplings between spheres can offer the backward wave characteristics.     

Genetic algorithm for ellipsometric data inversion of absorbing layers

A new data reduction method is presented for single-wavelength ellipsometry. A genetic algorithm is applied to ellipsometric data to find the best fit. The sample consists of a single absorbing layer on a semi-infinite substrate. The genetic algorithm has good convergence and is applicable to many different problems, including those with different independent measurements and situations with more than two angles of incidence. Results are similar to those obtained by other inversion techniques.     

A method for solving high-order real symmetric eigenvalue problems

A new method for solving structural dynamics problems has been proposed by the author in a separate paper.¹ This method of solution produces a high order real symmetric eigenvalue problem of the form ( A ? λ B ? λ² C ? λ³ D …) U = 0. An algorithm for solving such an eigenvalue problem using simultaneous iteration is presented in this paper. Methods of accelerating the convergence and reducing the amount of computation are also described. A numerical example is given in which the algorithm is used to calculate the eigenvalues and eigenvectors of a framed structure.     

正弦声信号在钻柱中传播的有限差分法模拟

将钻柱简化为理想周期性管结构,利用有限差分方法,对不同频率的正弦声信号在周期性管结构中传输过程中,存在透射系数及衰减系数差异较大的现象进行数值模拟与分析,得到不同频率的正弦声信号穿过周期性管结构后信号的时域及频域分布。分别对400 Hz和500 Hz的正弦声信号在周期性管结构中传输进行了模拟。模拟结果表明：处于带通频率的正弦声信号在周期性管结构中传播波形失真小,频谱变化小,传播性能良好;带阻频率的正弦声信号在周期性管结构中传播波形失真严重,频谱变化很大,几乎不能通过。模拟结果与同类研究成果有较好的一致性。验证该模型和所采用的数值方法的有效性,为钻柱中声信号传输的数值模拟及与其类似的实际问题的数值模拟提供参考。     

An Efficient SQUID NDE Defect Detection Approach by?Using?an?Adaptive?Finite-Element?Modeling

Incorporating the finite-element method for the modeling of the SQUID NDE response to a predefined defect pattern, an adaptive algorithm has been developed for the reconstruction of unknown defects using an optimization algorithm for updating of the forward problem. The defect reconstruction algorithm starts with an initial estimation for the defect pattern. Then the forward problem is solved and the obtained field pattern is compared with the measured signal from the SQUID NDE system. The result is used by an optimization algorithm to update the defect structure to be incorporated in the FEM forward problem for the next iteration. Since the mentioned model based inverse algorithm normally consumes a lot of computational resources, the number of iterations plays an important role in the determination of the total response convergence time. Consequently, different optimization algorithms have been applied and their performances are compared. In this work by incorporating an efficient forward model and using the stochastic and deterministic optimization algorithms for defect updating we have investigated their performance on the inversion of the SQUID NDE signal and also their ability to defect reconstruction in the noisy environment.     

An assumed covariant strain based 9-node shell element

A new shell element, which is free from serious locking problems and which does not possess hourglass modes, is proposed. Solutions obtained with this element exhibit good convergence and are satisfactorily insensitive to mesh distortion. The element also exhibits good convergence for plates with variable thickness. This element is based on the use of assumed covariant strains which are obtained from the covariant strain field defined with respect to the element natural co-ordinate system. Only the linear version for thin shell cases is considered. The element performance is tested by application to several standard plate and shell problems. A problem involving variable thickness is also presented.     

The accelerated power method

An algorithm is presented to accelerate the convergence of the inverse iteration method for the solution of algebraic symmetric eigensystems. The algorithm is based on the use of the Ritz analysis during inverse iteration to generate improved trial vectors at virtually no extra cost. Examples are shown to illustrate the computational advantages of the method. The results are compared with those obtained using the subspace iteration method, the determinant search method and the accelerated subspace iteration method.     

信号去噪阈值参数选择的自适应退火遗传算法

提出了一个用于小波阈值去噪中最优阈值参数选取的自适应退火遗传算法,提出一种新的自适应退火策略用于选择概率的计算以增强算法的收敛性,在交叉和变异概率的选取上也进行了自适应处理,以进一步改善算法的稳定性和收敛性.计算机仿真结果表明,该算法可稳定有效地选取最优的去噪阈值参数.