Tightly coupled aeroelastic model implementation dedicated to fast aeroelastic tailoring optimisation of high aspect ratio composite wing

This paper presents the development of a code, called GEBTAero, dedicated to very flexible aircraft (VFA) aeroelasticity and especially the evaluation of aeroelastic tailoring effect on critical speeds. GEBTAero is an open source code consisting in a tightly coupling between a geometrically exact beam theory -and a finite state induced flow unsteady aerodynamic model, including an homogenisation tool. This model has been implemented in Fortran using GEBT code and optimised open source libraries with particular focus on computation speed. Besides a non linear transient dynamic simulation capacity, a particular focus is put on the fast critical speed computation strategy using a non-iterative modal approach about the geometrically non linear deformed shape of the wing with the computation of only a few aeroelastic modes. Computation speed and accuracy of this implementation is assessed using widely used aeroelastic test cases and compared successfully to other aeroelastic codes. Configurations using aeroelastic tailoring, which are the core target of this solver, are then evaluated numerically on a representative high aspect ratio anisotropic composite wing and a simple 2-ply composite laminates with both variable ply orientations. It illustrates the strong correlation between the structural bending/twisting coupling of an unbalanced composite laminates and its critical aeroelastic speed. It also shows the high sensitivity of ply orientation on the aeroelastic behaviour.     

Influence of friction and asymmetric freeplay on the limit cycle oscillation in aeroelastic system: An extended Hénon’s technique to temporal integration

Nonlinear effects such as friction and freeplay on the control surfaces can affect aeroelastic dynamics during flight. In particular, these nonlinearities can induce limit cycle oscillations (LCO), changing the system stability, and because of this it is essential to employ computational methods to predict this type of motion during the aircraft development cycle. In this context, the present article presents a matrix notation for describing the Hénon’s method used to reduce errors when considering piecewise linear nonlinearities in the numerical integration process. In addition, a new coordinate system is used to write the aeroelastic system of equations. The proposal defines a displacement vector with generalized and physical variables to simplify the computational implementation of the Hénon’s technique. Additionally, the article discusses the influence of asymmetric freeplay and friction on the LCO of an airfoil with control surface. The results show that the extended Hénon’s technique provides more accurate LCO predictions, that friction can change the frequency and amplitude of these motions, and the asymmetry of freeplay is important to determine the LCO behavior.     

Fundamental solution of steady oscillations in thermoelastic medium with voids

ABSTRACT

The article deals with the study of plane wave propagation in the thermoelastic medium in the presence of voids. The problem is considered in the context of three-phase-lag model of generalized thermoelasticity. There exists three longitudinal waves, namely elastic (E-mode), thermal (T-mode) and volume fraction (V-mode) in addition to transverse waves which get decoupled from the rest of motion and not affected by thermal and volume fraction fields. The fundamental solution of the system of differential equations in case of steady oscillations in terms of the elementary functions has been constructed. The phase velocity and attenuation coefficient of these waves are computed numerically and presented graphically.     

超音速等离子体炬的磁流体动力学数值研究

针对设计的喉径2mm、工作电流为100A的拉瓦尔喷嘴,在二维轴对称模型的基础上,对超音速等离子体炬中的流动及其外部射流进行了数值模拟。通过在阳极喷嘴内部采用基于磁矢量势的磁流体动力学模型,避免了对磁感应强度的复杂积分计算,得到了喷嘴内部多场耦合的结果及外部射流的流动状态,分析了喷嘴内部电磁场对等离子体的加速作用及射流发展过程。结果显示,等离子体经历了亚音速→跨音速→超音速的发展过程,最终获得2.3 Ma的超音速射流。研究结果为超音速等离子体炬的工业应用提供了理论基础。     

Mechanism of [3+2] Cycloaddition of Alkynes to the [Mo3S4(acac)3(py)3][PF6] Cluster

A study, involving kinetic measurements on the stopped‐flow and conventional UV/Vis timescales, ESI‐MS, NMR spectroscopy and DFT calculations, has been carried out to understand the mechanism of the reaction of [Mo₃S₄(acac)₃(py)₃][PF₆] ([ 1 ]PF₆; acac=acetylacetonate, py=pyridine) with two RC?CR alkynes (R=CH₂OH (btd), COOH (adc)) in CH₃CN. Both reactions show polyphasic kinetics, but experimental and computational data indicate that alkyne activation occurs in a single kinetic step through a concerted mechanism similar to that of organic [3+2] cycloaddition reactions, in this case through the interaction with one Mo(μ‐S)₂ moiety of [ 1 ]⁺. The rate of this step is three orders of magnitude faster for adc than that for btd, and the products initially formed evolve in subsequent steps into compounds that result from substitution of py ligands or from reorganization to give species with different structures. Activation strain analysis of the [3+2] cycloaddition step reveals that the deformation of the two reactants has a small contribution to the difference in the computed activation barriers, which is mainly associated with the change in the extent of their interaction at the transition‐state structures. Subsequent frontier molecular orbital analysis shows that the carboxylic acid substituents on adc stabilize its HOMO and LUMO orbitals with respect to those on btd due to better electron‐withdrawing properties. As a result, the frontier molecular orbitals of the cluster and alkyne become closer in energy; this allows a stronger interaction.     

A modern approach to the solution and analysis of the Simha-Somcynsky model for the description of pressure-volume-temperature properties of polymer fluids

We revisit the Simha-Somcynsky model of polymer fluids with the purpose of developing novel theoretical and computational approaches to simplify and speed up its solution as well as the fitting of experimental data, and decrease its level of mathematical complexity. We report a novel method that allows us to solve one of the two equations of the model exactly, thus putting the level of mathematical difficulty on a par with the one of other models for polymer fluids. Moreover, we describe a computational algorithm capable of fitting all five parameters of the model in an unbiased way. The results obtained reproduce literature results and fit experimental pressure-volume-temperature and solubility parameter data for three polymers very accurately. Moreover, the new techniques allow for the investigation of the model at very low temperatures. Unexpectedly, the model predicts behaviors that could be interpreted as a glass transition, as routinely observed in dilatometry and differential scanning calorimetry, and a glass phase. We compared the predicted and experimental T g’s for cis poly(1,4-butadiene) and found an excellent quantitative agreement.     

Analyticity of resonances and eigenvalues and spectral properties of the massless Spin–Boson model

We extend the method of Pizzo multiscale analysis for resonances introduced in [5] in order to infer analytic properties of resonances and eigenvalues (and their eigenprojections) as well as estimates for the localization of the spectrum of dilated Hamiltonians and norm-bounds for the corresponding resolvent operators, in neighborhoods of resonances and eigenvalues. We apply our method to the massless Spin–Boson model assuming a slight infrared regularization. We prove that the resonance and the ground-state eigenvalue (and their eigenprojections) are analytic with respect to the dilation parameter and the coupling constant. Moreover, we prove that the spectrum of the dilated Spin–Boson Hamiltonian in the neighborhood of the resonance and the ground-state eigenvalue is localized in two cones in the complex plane with vertices at the location of the resonance and the ground-state eigenvalue, respectively. Additionally, we provide norm-estimates for the resolvent of the dilated Spin–Boson Hamiltonian near the resonance and the ground-state eigenvalue. The topic of analyticity of eigenvalues and resonances has let to several studies and advances in the past. However, to the best of our knowledge, this is the first time that it is addressed from the perspective of Pizzo multiscale analysis. Once the multiscale analysis is set up our method gives easy access to analyticity: Essentially, it amounts to proving it for isolated eigenvalues only and use that uniform limits of analytic functions are analytic. The type of spectral and resolvent estimates that we prove are needed to control the time evolution including the scattering regime. The latter will be demonstrated in a forthcoming publication. The introduced multiscale method to study spectral and resolvent estimates follows its own inductive scheme and is independent (and different) from the method we apply to construct resonances.     

Applicability of ~9Be global optical potential to reactions of ~(7,10,11,12)Be

Elastic scattering angular distributions and total reaction cross-sections of ~(7,10,11,12)Be projectiles are predicted by the systematic ~9 Be global phenomenological optical model potential for target mass numbers ranging from24 to 209. These predictions provide a detailed analysis by their comparison with the available experimental data.Furthermore, these elastic scattering observables are also predicted for some targets out of the mass number range.The results are in reasonable agreement with the existing experimental data, and they are presented in this study.