Optimal design of beams under flexural vibration

The minimum weight design of a cantilever beam in flexural vibration is considered. The aim is the maximization of a given natural bending frequency (usually the first) for a given beam weight or equivalently the minimization of beam weight for a specified value of a natural frequency. The beams considered are of rectangular section and are subject, in a range of cases presented, to a variety of constraints on lower and upper bounds on the cross-section dimensions or to the specification of a point mass at the end of the beam. Simple bending theory is regarded as applicable to the problem. A variational statement of the problem is made and the necessary conditions for a minimum are obtained as a system of non-linear equations which are solved numerically. Results are given in the form of tables and of figures showing computed optimum profiles. Some experiments on a sample set of beams of equal mass are described briefly. The optimum profile beam was found to have the greatest fundamental frequency, in support of the theoretical predictions.     

Nondiffracting beams in periodic media

We identify nondiffracting beams in two-dimensional periodic systems, exhibiting symmetry properties and phase structure characteristic of the band(s) they are associated with.     

Dynamic stability of parametrically-excited linear resonant beams under periodic axial force

The parametric dynamic stability of resonant beams with various parameters under periodic axial force is studied.It is assumed that the theoretical formulations are based on Euler-Bernoulli beam theory.The governing equations of motion are derived by using the Rayleigh-Ritz method and transformed into Mathieu equations,which are formed to determine the stability criterion and stability regions for parametricallyexcited linear resonant beams.An improved stability criterion is obtained using periodic Lyapunov functions.The boundary points on the stable regions are determined by using a small parameter perturbation method.Numerical results and discussion are presented to highlight the effects of beam length,axial force and damped coefficient on the stability criterion and stability regions.While some stability rules are easy to anticipate,we draw some conclusions:with the increase of damped coefficient,stable regions arise;with the decrease of beam length,the conditions of the damped coefficient arise instead.These conclusions can provide a reference for the robust design of parametricallyexcited linear resonant sensors.     

Laser beams with periodic polarization properties

The possibility of generating beams with longitudinally periodic polarization properties is considered.     

四注行波管周期永磁聚焦系统的优化设计

根据电子注参数、布里渊磁场公式及周期聚焦系统轴向磁通密度峰值经验公式,计算出永磁聚焦系统轴向峰值磁通密度,利用Ansoft Maxwell 3D软件建立了四注行波管周期永磁聚焦系统仿真模型,对模型结构尺寸进行了参数化分析,研究了周期永磁聚焦系统结构尺寸对聚焦系统通道内磁通密度的影响,确定了磁聚焦系统结构最佳尺寸配合,优化设计出了四注行波管周期永磁聚焦系统。其电子注通道中心轴线上轴向磁通密度峰值B_z=309 mT,横向磁通密度B_t=2.86 mT,B_t/B_z=0.92%。     

Optimal design of thin walled I beams for extreme natural frequency of torsional vibrations

The optimal design of thin-walled I beams so as to extremize the natural frequency of torsional vibration is considered. It is assumed that only one dimension of the cross-section, except for the web height, may be variable in given limits, along the axis of the beam. The optimality condition for the variable dimension is settled by means of Pontryagin's maximum principle. The effect of the constant, axial loads is also included. the solution of the problem formulated is generally found in an iterative way. Some numerical examples of optimization of the I beam with variable widt of flanges are given.     

Optimal design of thin-walled I beams for a given natural frequency of torsional vibrations

A method of extremum weight design of thin-walled I beams for a given natural frequency of torsional vibrations is presented. The effects of warping stresses and constant axial loads are taken into account. The optimality condition for only one (except for the web height) dimension of the cross-section, variable along the axis of the beam, is derived by using Pontryagin's maximum principle. The solution of the problem formulated, with account also taken of the additional geometrical conditions, is obtained in an iterative way. Some numerical examples of optimal design of an I beam with variable flange width, for a specified fundamental frequency, are given.     

Caustic design in periodic lattices

We study curved trajectory dynamics and design in discrete array settings. We find that beams with power law phases produce curved caustics associated with the fold and cusp type catastrophes. A parabolic phase produces a focus that suffers from spherical aberrations. More important, we find that by designing the initial phase or wavefront of the beam we can construct trajectories with pure power law caustics as well as aberration-free focusing of discrete waves.     

Propagation of light laser beams in one- and two-dimensional periodic structures

Diffraction spreading and narrowing of a laser beam within a holographic periodic structure were studied numerically and experimentally. We compared two different approaches to solving the diffraction problem for periodic structures. The developed optimized calculation algorithm is useful for numerical simulation of the diffracted field and allows conclusions on spatial behavior properties. Possible applications of light beam propagation control are considered.     

Photofabrication of periodic microstructures in azodye-doped polymers by interference of laser beams

Volume holographic gratings and two-dimensional periodic microstructures in azodye-doped polymethylmethacrylate were fabricated, respectively, by interference of two coherent beams of a femtosecond laser and by interference of three coherent beams of a nanosecond laser. The dependence of the first-order Bragg diffraction efficiency and the photoinduced refractive-index modulation of the gratings on the intensity of the writing light was investigated. The measurements of the absorption spectra before and after irradiation with the writing light suggest that the photoinduced gratings were refractive-index-modulated gratings, which arose from a photoinduced decomposition reaction of the azodye molecules through multiphoton absorption. In the experiments involving the interference of three beams, the period of the two-dimensional periodic microstructures was changed by adjusting the angle between the three writing beams. Received: 10 July 2002 / Revised version: 5 September 2002 / Published online: 20 December 2002 RID="*" ID="*"Corresponding author. Fax: +81-774/955206, E-mail: jhsi@photon.jst.go.jp     

Probing molecular free energy landscapes by periodic loading

Single molecule pulling experiments provide information about interactions in biomolecules that cannot be obtained by any other method. However, the reconstruction of the molecule's free energy profile from the experimental data is still a challenge, in particular, for the unstable barrier regions. We propose a new method for obtaining the full profile by introducing a periodic ramp and using Jarzynski's relation for obtaining equilibrium quantities from nonequilibrium data. Our simulated experiments show that this method delivers significant more accurate data than previous methods, under the constraint of equal experimental effort.     

Optimal beams for propagation through random media

The problem of maximizing the intensity that is transferred from a transmitter aperture to a receiver aperture is considered in which the propagation medium is random. Two optimization criteria are considered: maximal expected intensity transfer and minimal scintillation index. The beam that maximizes the expected intensity is shown to be fully coherent. Its coherent mode is determined as the principal eigenfunction for a kernel that is determined through the second-order moments of the propagation Green's function. The beam that minimizes the scintillation index is shown to be partially coherent in general, with its coherent modes determined by minimizing a quadratic form that has nonlinear dependence on the coherent-mode fields, and on the second- and fourth-order moments of the propagation Green's function.     

周期薄壁开口梁中的双耦合振动带隙

本文研究了由两种材料组合构成的周期性薄壁开口梁的弯曲和扭转双耦合振动。基于双耦合振动方程，给出了平面波展开法。当填充比不变时，晶格常数是影响带隙相对宽带的一个因素；当晶格常数和填充比不变时，杨氏模量是影响带隙宽带的主要因素，而不是密度。利用有限元法计算了有限周期结构的振动频率响应，在带隙频率范围内，振动衰减40dB左右。这些发现对于声子晶体的应用具有重要意义。     

Stochastic extraction of periodic attosecond bunches from relativistic electron beams

Intense laser waves can form a time-dependent gate, which transmits or reflects particles depending on their initial phases. When faced by a relativistic electron beam, such a barrier slices it by randomly scattering all but some particles, which nearly conserve their velocity. Subfemtosecond or attosecond periodic electron bunches are then formed downstream and can be used, for example, to generate coherent x rays via Thomson backscattering of the laser light.     

Machine-learning-driven on-demand design of phononic beams

The development of phononic crystals, especially their interaction with topological insulators, allows exploration of the anomalous properties of acoustic/elastic waves for various applications. However, rapidly and inversely exploring the geometry of specific targets remains a major challenge. In this work, we show how machine learning can address this challenge by studying phononic crystal beams using two different inverse design schemes. We first develop the theory of phononic beams using the transfer matrix method. Then, we use the reinforcement learning algorithm to effectively and inversely design the structural parameters to maximize the bandgap width. Furthermore, we employ the tandem-architecture neural network to solve the training-difficulty problem caused by inconsistent data and complete the task of inverse structure design with the targeted topological properties. The two inverse-design schemes have different adaptabilities, and both are characterized by high efficiency and stability. This work provides deep insights into the combination of machine learning, topological property,and phononic crystals and offers a reliable platform for rapidly and inversely designing complex material and structure properties.