SOLUTION OF DYNAMIC RESPONSE OF FRAMED STRUCTURE USING PIECEWISE BIRKHOFF POLYNOMIAL

In this paper, the piecewise Birkhoff interpolation polynomials and the modal superposition method were employed for the solution of dynamic response of m.d.o.f. system. The related formulae are derived. Because an exact result can be obtained when each loading can be represented by a piecewise polynomial, the proposed method not only can considerably reduce computational effort compared to the traditional step-by-step integration solution technique, but also can thoroughly avoid the problems of accuracy, convergence and stability encountered in many other numerical procedures.     

A high-order multi-dimensional HLL-Riemann solver for non-linear Euler equations

This article presents a numerical model that enables to solve on unstructured triangular meshes and with a high-order of accuracy, a multi-dimensional Riemann problem that appears when solving hyperbolic problems.For this purpose, we use a MUSCL-like procedure in a “cell-vertex” finite-volume framework. In the first part of this procedure, we devise a four-state bi-dimensional HLL solver (HLL-2D). This solver is based upon the Riemann problem generated at the centre of gravity of a triangular cell, from surrounding cell-averages. A new three-wave model makes it possible to solve this problem, approximately. A first-order version of the bi-dimensional Riemann solver is then generated for discretizing the full compressible Euler equations.In the second part of the MUSCL procedure, we develop a polynomial reconstruction that uses all the surrounding numerical data of a given point, to give at best third-order accuracy. The resulting over determined system is solved by using a least-square methodology. To enforce monotonicity conditions into the polynomial interpolation, we develop a simplified central WENO (CWENO) procedure.Numerical tests and comparisons with competing numerical methods enable to identify the salient features of the whole model.     

The mass normalization of the displacement and strain mode shapes in a strain experimental modal analysis using the mass-change strategy

The classic experimental modal analysis (EMA) is a well-known procedure for determining the modal parameters. The less frequently used strain EMA is based on a response measurement using strain sensors. The results of a strain EMA are the modal parameters, where in addition to the displacement mode shapes the strain mode shapes are also identified. The strain EMA can be used for an experimental investigation of a stress–strain distribution without the need to build a dynamical model. It can also be used to determine the modal parameters when, during modal testing, a motion sensor cannot be used and so a strain sensor is used instead. The displacement and strain mode shapes that are determined with the strain EMA are not mass normalized (scaled with respect to the orthogonality properties of the mass-normalized modal matrix), and therefore some dynamical properties of the system cannot be obtained. The mass normalization can be made with the classic EMA, which requires the use of a motion sensor. In this research a new approach to the mass normalization in the strain EMA, without using a motion sensor, is presented. It is based on the recently introduced mass-change structural modification method, which is used for the mass normalization in an operational modal analysis. This method was modified in such a way that it can be used for the mass normalization in the strain EMA. The mass-normalized displacement and strain mode shapes were obtained using a combination of the proposed approach and the strain EMA. The proposed approach was validated on real structures (beam and plate).     

地脉动作用下主机装置靶室结构稳定性分析与评估

在大型固体激光器结构稳定性设计中,数值模拟结果是结构稳定性设计的主要依据,故数值模拟的可信度至关重要。为了评估装置稳定性计算结果的可信度,基于现代模型验证与确认技术中关于不确定性源的量化及传播分析方法、模型形式误差与预测推断的叠加方法研究,对靶球结构的最大位移响应进行了预测推断。稳定性分析中为了快速进行不确定性参数的传播和灵敏度分析,使用二次响应面模型作为代理模型,灵敏度分析结果表明模态阻尼比对靶球结构的稳定性影响更大。对关心量的稳定性预测结果表明,靶球结构最大位移响应的上界与稳定性设计指标相比,安全裕度仍大于7,说明主机装置的稳定性设计具有足够的可信度。     

Numerical simulation of propagation of a femtosecond optical soliton in a single-mode fiber with allowance for the imaginary part of Raman response

We consider the effect of Raman inertial response of a medium on the stability of a first-order femtosecond soliton. Numerical solution to the high-order nonlinear Schrödinger equation, with the complex Raman term, describing propagation of a femtosecond optical soliton in a single-mode fiber, is obtained. It is shown that a soliton solution of the high-order nonlinear Schrödinger equation exists under certain conditions imposed on the equation coefficients. These conditions lead to limitations on the wavelength, fiber type, and the highest energy. Results of numerical solutions are in agreement with available experimental data.     

Direct Numerical Simulation of the Rayleigh-Taylor Instability with the Spectral Element Method

A novel method is proposed to simulate Rayleigh-Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier-Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh-Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh-Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh-Taylor instabilities of turbulent flows.     

High-order non-uniform grid schemes for numerical simulation of hypersonic boundary-layer stability and transition

The direct numerical simulation of receptivity, instability and transition of hypersonic boundary layers requires high-order accurate schemes because lower-order schemes do not have an adequate accuracy level to compute the large range of time and length scales in such flow fields. The main limiting factor in the application of high-order schemes to practical boundary-layer flow problems is the numerical instability of high-order boundary closure schemes on the wall. This paper presents a family of high-order non-uniform grid finite difference schemes with stable boundary closures for the direct numerical simulation of hypersonic boundary-layer transition. By using an appropriate grid stretching, and clustering grid points near the boundary, high-order schemes with stable boundary closures can be obtained. The order of the schemes ranges from first-order at the lowest, to the global spectral collocation method at the highest. The accuracy and stability of the new high-order numerical schemes is tested by numerical simulations of the linear wave equation and two-dimensional incompressible flat plate boundary layer flows. The high-order non-uniform-grid schemes (up to the 11th-order) are subsequently applied for the simulation of the receptivity of a hypersonic boundary layer to free stream disturbances over a blunt leading edge. The steady and unsteady results show that the new high-order schemes are stable and are able to produce high accuracy for computations of the nonlinear two-dimensional Navier–Stokes equations for the wall bounded supersonic flow.     

Improved damage detection method based on Element Modal Strain Damage Index using sparse measurement

An improved damage detection method based on the concept of Element Modal Strain Damage Index is introduced. The proposed methods attempts to address some of the weaknesses of the damage detection method based on modal curvatures. The use of numerical differentiation procedures is identified as the main cause for the poor performance of the modal curvature method under sparse and noisy measurement. An improved damage index that does not rely on numerical differentiation is then formulated. The proposed damage index can be calculated using only modal displacement and modal rotation. A penalty-based minimization approach is then used to find the unknown modal rotation using sparse and noisy modal displacement measurement. Numerical simulation and experiment validation confirm the relative advantage of the proposed method compared with modal curvature-based approaches.     

Energy stable numerical methods for hyperbolic partial differential equations using overlapping domain decomposition

Overlapping domain decomposition methods, otherwise known as overset grid or chimera methods, are useful for simplifying the discretization of partial differential equations in or around complex geometries. Though in wide use, such methods are prone to numerical instability unless numerical diffusion or some other form of regularization is used, especially for higher-order methods. To address this shortcoming, high-order, provably energy stable, overlapping domain decomposition methods are derived for hyperbolic initial boundary value problems. The overlap is treated by splitting the domain into pieces and using generalized summation-by-parts derivative operators and polynomial interpolation. New implicit and explicit operators are derived that do not require regularization for stability in the linear limit. Applications to linear and nonlinear problems in one and two dimensions are presented, where it is found the explicit operators are preferred to the implicit ones.     

Modal analysis by free vibration response only for discrete and continuous systems

This work aims to develop the algorithm for modal analysis by free vibration response only (MAFVRO), in particular for the general or non-proportional viscous damping system model. If the structural displacement or acceleration response due to free vibration can be measured, the system response matrices, including the displacement, velocity and acceleration, can be obtained through numerical differential or integration methods. These response matrices can then be applied to the developed MAFVRO method to determine the structural modal parameters. The numerical differential and integration methods are introduced and adopted to establish the modal parameter prediction program for the non-proportional damping model of MAFVRO. This work also shows the applications of MAFVRO to the multiple degree-of-freedom (mdof) systems and the cantilever beam, respectively. Both the discrete and continuous systems are demonstrated for the feasibility of the MAFVRO algorithm. The developed method uses the free vibration output response only and can obtain the structural modal parameters successfully.     

房间脉冲响应模拟法及混响时间盲估计应用

在构建混响语声数据集时,由于缺乏真实长混响房间脉冲响应且模拟的房间脉冲响应与真实不符,因而导致数据驱动的混响时间盲估计模型性能下降。提出了一种基于条件生成对抗网络的房间脉冲响应模拟法,该方法利用真实的房间脉冲响应训练条件生成对抗网络,可以根据指定的混响时间模拟更加真实的房间脉冲响应。使用不同方法模拟的房间脉冲响应构建训练集用于训练盲估计模型,通过声学实验评估模型性能。实验结果表明,由该方法模拟的房间脉冲响应训练的估计模型在不同信噪比下均具有最小的均方根误差且在长混响情况下显著优于其他模型。     

An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces

This paper is devoted to developing a multi-material numerical scheme for non-linear elastic solids, with emphasis on the inclusion of interfacial boundary conditions. In particular for colliding solid objects it is desirable to allow large deformations and relative slide, whilst employing fixed grids and maintaining sharp interfaces. Existing schemes utilising interface tracking methods such as volume-of-fluid typically introduce erroneous transport of tangential momentum across material boundaries. Aside from combatting these difficulties one can also make improvements in a numerical scheme for multiple compressible solids by utilising governing models that facilitate application of high-order shock capturing methods developed for hydrodynamics. A numerical scheme that simultaneously allows for sliding boundaries and utilises such high-order shock capturing methods has not yet been demonstrated. A scheme is proposed here that directly addresses these challenges by extending a ghost cell method for gas-dynamics to solid mechanics, by using a first-order model for elastic materials in conservative form. Interface interactions are captured using the solution of a multi-material Riemann problem which is derived in detail. Several different boundary conditions are considered including solid/solid and solid/vacuum contact problems. Interfaces are tracked using level-set functions. The underlying single material numerical method includes a characteristic based Riemann solver and high-order WENO reconstruction. Numerical solutions of example multi-material problems are provided in comparison to exact solutions for the one-dimensional augmented system, and for a two-dimensional friction experiment.     

Estimation of interfacial forces in time domain for linear systems

A structural path rank ordering process under transient excitations requires a good knowledge of the interfacial path forces, which are difficult to directly measure. Four time domain methods to estimate the interfacial forces are proposed and comparatively evaluated with application to linear time-invariant, proportionally damped discrete systems. First, the transient response is derived by modal analysis and a direct time domain technique to calculate the interfacial forces is outlined. Next, the frequency domain estimation methods, based on the sub-system concept are reviewed, and an inverse Fourier transform scheme is introduced. An indirect method of estimating interfacial force in transient state is then developed through an inverse procedure of modal analysis. The sub-system approach is employed to obtain the interfacial forces based on the forced vibration response of the original system and modal data of the sub-system. Finally, an approximate time domain scheme is suggested that could be used only if the system properties are known or precisely estimated. Although the proposed indirect methods are designed for eventual experimental applications, this article provides numerical feasibility studies via a simple source-path-receiver system (with parallel vibration paths) that has five translational degrees of freedom. The proposed methods are compared under ideal impulse force excitation input and a periodic sawtooth load (without and with Gaussian noise) to observe the starting transients as well as subsequent motions and interfacial forces. Preliminary comparisons with a laboratory experiment are very promising.     

Rows of optical vortices from elliptically perturbing a high-order beam

An optical vortex (phase singularity) with a high topological strength resides on the axis of a high-order light beam. The breakup of this vortex under elliptic perturbation into a straight row of unit-strength vortices is described. This behavior is studied in helical Ince-Gauss beams and astigmatic, generalized Hermite-Laguerre-Gauss beams, which are perturbations of Laguerre-Gauss beams. Approximations of these beams are derived for small perturbations, in which a neighborhood of the axis can be approximated by a polynomial in the complex plane: a Chebyshev polynomial for Ince-Gauss beams, and a Hermite polynomial for astigmatic beams.     

Damped Mathieu Equation with a Modulation Property of the Homotopy Perturbation Method

In this article, the main objective is to employ the homotopy perturbation method (HPM) as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients. As a simple example, the nonlinear damping Mathieu equation has been investigated. In this investigation, two nonlinear solvability conditions are imposed. One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases. The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the first-order solvability condition. The approach assumed here is so significant for solving many parametric nonlinear equations that arise within the engineering and nonlinear science.     

基于静动态重构的高阶DG/FV混合格式在二维非结构网格中的推广

通过比较间断Galerkin有限元方法(DGM)和有限体积方法(FVM),提出"静态重构"和"动态重构"的概念,进一步建立基于静动态"混合重构"算法的三阶DG/FV混合格式.在DG/FV混合格式中,单元平均值和一阶导数由DGM方法"动态重构",二阶导数利用FVM方法"静态重构";在此基础上,构造高阶多项式插值函数,得到...     

Perturbation analysis of clad parabolic-index waveguides

A first-order perturbation technique is used to obtain the eigenfunction correction due to the cladding in a square-law dielectric waveguide. Regions both near to and far from cut-off are considered separately. It is shown that far from cut-off the fractional power carried by the guide core increases over that in the homogeneous case but that near cut-off the power in the core is less than in a homogeneous guide. Thus the stability of the modal power with variation of wavelength is increased over that in a homogeneous guide.     

Maximum likelihood estimator of operational modal analysis for linear time-varying structures in time–frequency domain

This paper investigates the problem of modal parameter estimation of time-varying structures under unknown excitation. A time–frequency-domain maximum likelihood estimator of modal parameters for linear time-varying structures is presented by adapting the frequency-domain maximum likelihood estimator to the time–frequency domain. The proposed estimator is parametric, that is, the linear time-varying structures are represented by a time-dependent common-denominator model. To adapt the existing frequency-domain estimator for time-invariant structures to the time–frequency methods for time-varying cases, an orthogonal polynomial and z-domain mapping hybrid basis function is presented, which has the advantageous numerical condition and with which it is convenient to calculate the modal parameters. A series of numerical examples have evaluated and illustrated the performance of the proposed maximum likelihood estimator, and a group of laboratory experiments has further validated the proposed estimator.     

Molecular g-tensors from analytical response theory and quasi-degenerate perturbation theory in the framework of complete active space self-consistent field method

The molecular g-tensor is an important spectroscopic parameter provided by electron para magnetic resonance (EPR) measurement and often needs to be interpreted using computational methods. Here, we present two new implementations based on the first-order and second-order perturbation theories to calculate the g-tensors within the complete-active space self-consistent field (CASSCF) wave function model. In the first-order method, the quasi-degenerate perturbation theory (QDPT) is employed for constructing relativistic CASSCF states perturbed with the spin–orbit coupling operator, which is described effectively in one-electron form with the flexible nuclear screening spin–orbit approximation introduced recently by us. The second-order method is a newly reported approach built upon the linear response theory which accounts for the perturbation with respect to external magnetic field. It is implemented with the coupled–perturbed CASSCF (CP-CASSCF) approach, which provides an equivalent of untruncated sum-over-states expansion. The comparison of the performances between the first-order and second-order methods is shown for various molecules containing light to heavy elements, highlighting their relative strength and weakness. The formulations of QDPT and CP-CASSCF approaches as well as the derivation of the second-order Douglas–Kroll–Hess picture change of Zeeman operators are given in detail.     

Implicit preconditioned WENO scheme for steady viscous flow computation

A class of lower–upper symmetric Gauss–Seidel implicit weighted essentially nonoscillatory (WENO) schemes is developed for solving the preconditioned Navier–Stokes equations of primitive variables with Spalart–Allmaras one-equation turbulence model. The numerical flux of the present preconditioned WENO schemes consists of a first-order part and high-order part. For first-order part, we adopt the preconditioned Roe scheme and for the high-order part, we employ preconditioned WENO methods. For comparison purpose, a preconditioned TVD scheme is also given and tested. A time-derivative preconditioning algorithm is devised and a discriminant is devised for adjusting the preconditioning parameters at low Mach numbers and turning off the preconditioning at intermediate or high Mach numbers. The computations are performed for the two-dimensional lid driven cavity flow, low subsonic viscous flow over S809 airfoil, three-dimensional low speed viscous flow over 6:1 prolate spheroid, transonic flow over ONERA-M6 wing and hypersonic flow over HB-2 model. The solutions of the present algorithms are in good agreement with the experimental data. The application of the preconditioned WENO schemes to viscous flows at all speeds not only enhances the accuracy and robustness of resolving shock and discontinuities for supersonic flows, but also improves the accuracy of low Mach number flow with complicated smooth solution structures.