Linear and nonlinear 2D finite element analysis of sloshing modes and pressures in rectangular tanks subject to horizontal harmonic motions

The influence of nonlinear wave theory on the sloshing natural periods and their modal pressure distributions are investigated for rectangular tanks under the assumption of two-dimensional behavior. Natural periods and mode shapes are computed and compared for both linear wave theory (LWT) and nonlinear wave theory (NLWT) models, using the finite element package ABAQUS. Linear wave theory is implemented in an acoustic model, whereas a plane strain problem with large displacements is used in NLWT. Pressure distributions acting on the tank walls are obtained for the first three sloshing modes using both linear and nonlinear wave theory. It is found that the nonlinearity does not have significant effects on the natural sloshing periods. For the sloshing pressures on the tank walls, different distributions were found using linear and nonlinear wave theory models. However, in all cases studied, the linear wave theory conservatively estimated the magnitude of the pressure distribution, whereas larger pressures resultant heights were obtained when using the nonlinear theory. It is concluded that the nonlinearity of the surface wave does not have major effects in the pressure distribution on the walls for rectangular tanks.     

On the general linear (Bogoliubov-) transformation for bosons

Using a Baker-Campbell-Hausdorff formula for the disentangling of exponential operators, a simple straight-forward derivation of Bogoliubov-transformation matrix elements could be given by elementary algebra. Recent much more complicated derivations by means of hypergeometric functions are simplified considerably. Matrix elements and their generating functions are new for the general linear transformation for bosons. The surprising result of Aronsonet al., that the linear transformation matrix element is equivalent to the rotation matrix element is discussed in the framework of the coupled boson theory of angular momentum. Possible applications of the formalism for quantum optics and for nuclear models are sketched briefly.     

高功率隔离器单模与多模工作退偏特性

以传统结构隔离器为模型,应用琼斯理论,比较分析了单模与多模激光入射时高功率隔离器热致退偏特性。研究结果表明:高功率隔离器热致退偏可分为线性双折射致退偏与圆双折射致退偏;两种退偏均与入射激光功率的平方成正比;在光功率一定的条件下,线性双折射致退偏不随光斑半径的变化而变化,圆双折射致退偏随光斑半径的增大而减小;在其它条件相同的条件下,多模光场能够有效地降低隔离器热致退偏,多模时线性双折射致退偏仅为单模时退偏的60%,圆双折射致退偏也比单模时要小,减小幅度随光斑半径的增加而增加。     

高功率隔离器单模与多模工作退偏特性

以传统结构隔离器为模型,应用琼斯理论,比较分析了单模与多模激光入射时高功率隔离器热致退偏特性。研究结果表明：高功率隔离器热致退偏可分为线性双折射致退偏与圆双折射致退偏;两种退偏均与入射激光功率的平方成正比;在光功率一定的条件下,线性双折射致退偏不随光斑半径的变化而变化,圆双折射致退偏随光斑半径的增大而减小;在其它条件相同的条件下,多模光场能够有效地降低隔离器热致退偏,多模时线性双折射致退偏仅为单模时退偏的60%,圆双折射致退偏也比单模时要小,减小幅度随光斑半径的增加而增加。     

Galloping of iced quad-conductors bundles based on curved beam theory

Galloping refers to wind-induced, low-frequency, large-amplitude oscillations that have been more frequently observed for a bundle conductor than for a single conductor. In the present work two different models are built to investigate the galloping of a bundle conductor: (1) a finite curved beam element method and (2) a hybrid model based on curved beam element theory. The finite curved beam element model is effective in dealing with the spacers between the bundled conductors and the joint between the conductors and spacers that can be simulated as a rigid joint or a hinge. Furthermore, the finite curved beam element model can be used to deal with large deformation. The hybrid model invokes the small deformation hypothesis and has a high computational efficiency. A hybrid model based on conventional cable element theory is also programmed to be compared with the aforementioned models based on curved beam element theory. Numerical examples are presented to assess the accuracy of the different models in predicting the equilibrium conductor position, natural frequencies and galloping amplitude. The results show that the curved beam element models, involving more degrees of freedom and coupling of translational and torsional motion, are more accurate at simulating the static and dynamic characters of an iced quad-conductor bundle. The use of hinges, rather than rigid connections, reduces the structural response amplitudes of a galloping conductor bundle.     

Design of a 50 kW, wideband Ka-band slow wave cyclotron amplifier

A two-stage slow wave cyclotron amplifier is investigated to demonstrate a high power, stable, and broad Ka-band radiation source, operating at a low beam power (~60 kV, ~5 amps) and a low magnetic field (~7 kG). A linear theory predicts that the second harmonic gyro-BWO is competing in the amplifier and can be stabilized by inserting a sever in the interaction circuit. A slow-time-scale non-linear code, with a sever included, predicts a saturated gain of 24-28 dB, an efficiency of 15-17%, and an instantaneous bandwidth of 15-20% at a beam axial velocity spread of 2%. A broadband RF coupler, a mode converter, and a RF vacuum window are designed by the use of a 3D electromagnetic, finite element code. Measured RF characteristics are in good agreement with predictions     

电流变技术中的控制理论及参数优化

针对ER型动力元件,阐述了含ER技术的机械系统控制方程的建立方法,运用控制理论建立了其状态方程。同时,对其进行了一般性分析及参数优化设计。发现电流变动力元件可以很简单地依靠调整工作位置来改善元件的动态性能。ER型流体控制元件属典型阻尼元件。     

The basic principles of intracavity photothermal spectroscopy

The basic theory of intracavity photothermal deflection is analysed. Its main applications to linear spectroscopy and high power laser beam modulation are briefly discussed.     

超声波检测计算机模拟和仿真的研究及应用现状

随着高性能计算机的广泛应用，超声检测模拟和仿真的研究方兴未艾。本文对这些研究所选择的数学模型和方法进行了综合评述，探讨了Gaussiam模型、声线模型、衍射理论、有限积分技术等的应用，涉及的方法包括各种解析方法及有限差分、有限元、边界元等数值方法。     

Theory of noise in a kilo-Hz cascaded high-energy Yb-doped nanosecond pulsed fiber amplifier

A theoretical analysis of noise in a high-power cascaded fiber amplifier is presented. Unlike the noise theory in low power communication, the noise of a high power system is redefined as the leaked output energy between pulses with coherent beat noise uncounted. This definition is more appropriate for high power usage in which the pulse energy receives more attention than the pulse shape integrity. Then the low power pre-amplifying stages are considered as linear amplification and analyzed by linear theory. In the high-power amplification stages, the inversion is assumed to recover linearly in the time interval between pulses. The time shape of the output pulse is different from that of the input signal because of different gains at the front and back ends of the pulse. Then, a criterion is provided to distinguish the nonlinear and linear amplifications based on the signal-to-noise ratio （SNR） analysis. Then, an experiment that shows that the output SNR actually drops off in nonlinear amplification is performed. The change in the noise factor can be well evaluated by pulse shape distortion.     

Free vibration of antisymmetric,angle-ply laminated plates including transverse shear deformation by the finite element method

A finite element formulation of the equations governing the laminated anisotropic plate theory of Yang, Norris and Stavsky, is presented. The theory is a generalization of Mindlin's theory for isotropic plates to laminated anisotropic plates and includes shear deformation and rotary inertia effects. Finite element solutions are presented for rectangular plates of antisymmetric angle-ply laminates whose material properties are typical of a highly anisotropic composite material. Two sets of material properties that are typical of high modulus fiber-reinforced composites are used to show the parametric effects of plate aspect ratio, length-to-thickness ratio, number of layers and lamination angle. The numerical results are compared with the closed form results of Bert and Chen. As a special case, numerical results are presented for thick isotropic plates, and are compared with those for 3-D linear elasticity theory and Mindlin's thick plate theory.     

Spectral description of fluctuating electromagnetic fields of solids using a self-consistent approach

A new way to evaluate the spectral-correlation properties of thermal fields of solids is suggested. The principal element here is the surface linear response function of an inhomogeneous electron subsystem of solids. Along with straightforward calculations using the known response functions, the suggested method allows calculating the response functions self-consistently based on the time dependent density functional theory. The self-consistent calculation of the linear response function followed by an application of the fluctuation–dissipation theorem yields spectral power densities of the fluctuating electromagnetic fields.     

毫米波段高功率绕射辐射振荡器的研究

 提出采用大口径、浅褶皱和短周期分段式慢波结构作为高功率毫米波绕射辐射振荡器的高频系统。采用通用理论对器件的色散特性进行了分析,用PIC方法对整体器件进行了模拟。在此基础上,开展了实验研究工作,测试了器件输出微波功率和频率。初步实验结果与理论分析和PIC模拟结果的趋势基本吻合。     

Dynamic analysis of linear viscoelastic cylindrical and conical helicoidal rods using the mixed FEM

The objective of this study is to investigate the influence of the rotary inertia on dynamic behavior of linear viscoelastic cylindrical and conical helixes by means of the Laplace transform-mixed finite element formulation and solution. The element matrix is based on the Timoshenko beam theory. The influence of rotary inertias is considered in the dynamic analysis, which is original in the literature. Rectangular, sine and step type of impulsive loads are applied on helices having rectangular cross-sections with various aspect ratios. The Kelvin and standard models are used for defining the linear viscoelastic material behavior; and by means of the correspondence principle (the elastic-viscoelastic analogy), the material parameters are replaced with their complex counterparts in the Laplace domain. The analysis is carried out in the Laplace domain and the results are transformed back to time space numerically by modified Durbin?s algorithm. First, the solution algorithm is verified using the existing open sources in the literature and afterwards some benchmark examples such as conical viscoelastic rods are handled.     

高功率毫米波绕射辐射振荡器高频特性研究

讨论了高功率毫米波绕射辐射振荡器的高频特性。利用线性理论和PIC模拟相结合的方法对器件的高频特性进行了比较仔细的分析。分析结果表明,合理地选择电子注的参量（电流、电压）及高频结构的尺寸（波纹深度、半径、周期等）可以获得较高的输出功率并且具有较好的频谱纯度。     

Aperture averaging of optical scintillations: power fluctuations and the temporal spectrum

Using a recently developed theory of scintillation that is valid under all fluctuation conditions, including the focussing and saturation regimes, we develop general models for predicting power fluctuations (or aperture averaging) over finite-size collecting apertures. Inner-scale effects are introduced using a modified atmospheric spectrum for refractive-index fluctuations that includes a high-wavenumber bump. Where comparisons can be made, these models of aperture averaging are in good agreement with previous asymptotic models and experimental data. In addition to the aperture-averaging factor, we calculate the temporal spectrum associated with power fluctuations over various aperture sizes and conditions of turbulence. These later results clearly show the transfer of power distribution from high to low frequencies as the size of the collecting aperture is increased. The transfer of power is more pronounced in the saturation regime where high frequencies (fastest fluctuations) can be averaged out even for relatively small apertures.     

高功率激光装置的线性传输特性

在菲涅耳数的基础上重新定义了衍射特征量,并将其定义扩展至聚焦或发散光路,定义了一个光学系统中各光学元件衍射特征量的符号。通过全新的定义和扩展,研究了波前畸变对近场调制度的影响以及正弦调频光谱色散平滑光束衍射传输引入的幅频调制的大小。以神光-Ⅲ主机主放大级为例,研究了元件波前畸变对近场调制度的影响以及正弦调频光谱色散平滑光束衍射传输引入的幅频调制的大小。衍射特征量与能流分布F相结合,可以作为评价高功率激光装置线性传输效应的一项受限指标,指导高功率激光装置的设计。     

高功率激光装置的线性传输特性

在菲涅耳数的基础上重新定义了衍射特征量,并将其定义扩展至聚焦或发散光路,定义了一个光学系统中各光学元件衍射特征量的符号。通过全新的定义和扩展,研究了波前畸变对近场调制度的影响以及正弦调频光谱色散平滑光束衍射传输引入的幅频调制的大小。以神光-Ⅲ主机主放大级为例,研究了元件波前畸变对近场调制度的影响以及正弦调频光谱色散平滑光束衍射传输引入的幅频调制的大小。衍射特征量与能流分布F相结合,可以作为评价高功率激光装置线性传输效应的一项受限指标,指导高功率激光装置的设计。     

The effect of modified gravity on weak lensing

We study the effect of modified gravity on weak lensing in a class of scalar-tensor theory that includes f(R) gravity as a special case. These models are designed to satisfy local gravity constraints by having a large scalar-field mass in a region of high curvature. Matter density perturbations in these models are enhanced at small redshifts because of the presence of a coupling Q that characterizes the strength between dark energy and non-relativistic matter. We compute a convergence power spectrum of weak lensing numerically and show that the spectral index and the amplitude of the spectrum in the linear regime can be significantly modified compared to the ΛCDM model for large values of |Q| of the order of unity. Thus weak lensing provides a powerful tool to constrain such large coupling scalar-tensor models including f(R) gravity.     

Numerical simulation of a piano soundboard under downbearing

A finite element model of a piano soundboard is used to study the effect of the strings tension (downbearing) on its vibration, considering the ribs, the bridges and the crown. The downbearing is modeled with the prestress theory. Prestress calculation with linear and nonlinear models including geometric rigidity are compared in terms of the modal frequencies. The effects of the downbearing in modal frequencies and mobility are investigated and the importance of the crown on these results is evaluated. A simple phenomenological law is exhibited, which characterizes the evolution of eigenfrequencies with downbearing, including the initial crown.