Analysis and computation of the vibration spectrum of the shallow circular cylindrical shell with rectangular domain

An asymptotic method of Bolotin, for the computation of eigenvalues of self-adjoint problems on rectangular domains, is extended to the shallow shell equations for the vibrating circular cylindrical shell. These same eigenfrequencies are then computed using the Legendre-tau spectral method. The asymptotic and numerical results are seen to be in good agreement and, as expected, approach those of the flat plate as the curvature tends to zero.     

FREE VIBRATION ANALYSIS OF CANTILEVER PLATES WITH STEP DISCONTINUITIES IN PROPERTIES BY THE METHOD OF SUPERPOSITION

Utilizing the superposition method, an analytical type solution is obtained for the free vibration eigenvalues and mode shapes of a cantilever plate with step discontinuities in plate properties. Property discontinuity lines run parallel to the clamped edge of the plate. Verification tests are performed for limiting cases by comparing computed eigenvalues with known eigenvalues for plates with uniform properties. Very good agreement is also obtained when computed results are compared with those obtained experimentally utilizing a test plate with discontinuities in thickness. Computed eigenvalues and mode shapes are presented for the benefit of other researchers. Besides the general interest, the problem has an application in the modelling of certain multi-story buildings during seismic studies.     

Effect of different heating methods on deformation of metal plate under upsetting mechanism in laser forming

In a laser forming process, different forming mechanisms have different deformation behaviors. The aim of laser forming is to acquire plane strain under an upsetting mechanism, while a plate undergoes a small bending deformation. In some industrial applications, the bending strain should not occur. To achieve high-precision forming, the deformation behaviors of a metal plate when an upsetting mechanism plays a dominant role are studied in the paper. Several heating methods are proposed to reduce the plane strain difference along the thickness direction and little bending deformation resulting from a small temperature difference between the top and bottom surfaces of the plate. The results show that negligible bending deformation and a uniform plastic plane strain field can be obtained by simultaneously heating the top and bottom surfaces with the same process parameters. A conventional scanning method needs a larger spot diameter and slower scanning speed under the upsetting mechanism, but a smaller spot diameter and quicker scanning speed may be selected using the simultaneous heating method, which can greatly widen the potential scope of process parameters.     

Variation of discrete spectra

A formula [see (1) below] estimating collectively the variation of eigenvalues of a symmetric matrix under a perturbation is extended to the case of discrete eigenvalues of a selfadjoint operator in Hilbert space, under the assumption that the perturbation is compact. For this purpose, the notion of an extended enumeration of discrete eigenvalues is introduced.     

Unified Krylov-Bogoliubov-Mitropolskii method for solving nth order non-linear systems with slowly varying coefficients

The unified Krylov-Bogoliubov-Mitropolskii (KBM) method is extended for obtaining the transient response of an n-th order (n?2) non-linear system with slowly varying coefficients. The method is a generalization of KBM method and covers all the three cases when the eigenvalues of the unperturbed equation are real, complex conjugate, or purely imaginary. It is shown that by suitable substitution for the eigenvalues in the general result that the solution corresponding to each of the three cases can be obtained. The method is illustrated by examples.     

Free vibration analysis of corner-supported rectangular plates with symmetrically distributed edge beams

Analytical type solutions are obtained for the free vibration frequencies and mode shapes of thin corner-supported rectangular plates with symmetrically distributed reinforcing beams, or strips, attached to the plate edges. The method of superposition is employed. Equations governing reactions at plate-beam interfaces are developed in dimensionless form. The approach is comprehensive in that both lateral and rotational stiffness, and inertia, of the beam are incorporated into the analysis. For illustrative purposes computed eigenvalues and mode shapes are presented for two plate-beam systems of realistic geometries. It is shown that the method is easily extended to cover the case where the edge beams do not have a symmetrical distribution. This appears to be the first comprehensive analytical study of this problem of industrial interest.     

Solutions of the Lévy type for the free vibration analysis of diagonally supported rectangular plates

A Lévy type solution is developed for the vibratory response of a simply supported rectangular plate subjected to a harmonic force distributed along the diagonal. The solution is then extended to determine the free vibration response of the same rectangular plate with inelastic lateral support on the diagonal. It is found that there is an excellent agreement between computed eigenvalues obtained here and those obtained by the author in an earlier paper in which a Navier type solution was utilized. The significant advantages inherent in the present Lévy type solution are discussed.     

Analytical method for determining eigenvalues in the problem of vibrations of a plate moving in gas

An analytical method for determining eigenvalues for differential equations using special functions is presented. As an example, vibrations of an infinite-width cantilever plate moving with the supersonic velocity in a gas are described. For a two-dimensional problem, the analytical dependence between the plate eigenvibration characteristics and velocity was obtained, which allows us to make conclusions about motion stability. The developed technique can be applied to study many problems whose solution is associated with finding of eigenvalues. In contrast to similar techniques, the described method yields sufficiently accurate analytical expressions for eigenvalues, which allows one to use them in specific calculations.     

中厚板弯曲问题的Kriging插值无网格法

基于Reissner-Mindlin板弯曲理论,将Kriging插值无网格法应用于中厚板弯曲问题,推导相应的离散方程.该方法可以只依赖于一组离散的节点建立试函数,有效地避免了复杂的网格划分和网格畸变的影响.相对于无网格法中常用的移动最小二乘近似而言,滑动Kriging插值法的形函数满足Kronecker delta函数性质,可以直接施加本质边界条件.算例分析表明,用Kriging插值无网格法分析中厚板弯曲问题,具有效率高,精度高和易于实现等优点.     

一种分析周期加筋板声辐射的高效方法

为了研究周期加筋板的声辐射特性,建立了一种计算水中周期加筋板在简谐点力作用下的远场辐射声压的高效方法。该方法借助于傅里叶变换法只要先将耦合系统的声振方程,加强筋的弯曲和扭转运动方程,声学波动方程和耦合边界条件转换到波数域中,联合求解得到一组关于平板横向位移的无限大耦合代数方程组,再将该方程组截断成有限大小由数值方法求出波数域中的位移响应,便可结合稳相法得到远场辐射声压。与现有方法给出的结果对比发现二者完全吻合,验证了本文方法的有效性;通过数值方法研究了激励力位置、板厚,加强筋间距和宽度对周期加筋板声辐射特性的影响,得到了具有实际意义的结论。      

薄板弯曲大变形高阶非线性偏微分方程推导与优化算法研究

针对薄板弯曲大变形问题, 运用变分原理, 建立了薄板弯曲大变形问题的高阶非线性偏微分方程. 运用有限差分法和动态设计变量优化算法原理, 以离散坐标点的上未知挠度为设计变量, 以离散坐标点的差分方程组构建目标函数, 提出了薄板弯曲大变形挠度求解的动态设计变量优化算法, 编制了相应的优化求解程序. 分析了具有固定边界、均布载荷下的矩形薄板挠度的典型算例. 通过与有限元的结果对比, 表明了本文求解算法的有效性和精确性, 提供了直接求解实际工程问题的基础.     

Field deformation and loss by curvature in gain guided and index anti-guided fibers

Gain guided and index anti-guided fiber, being a new kind of fiber with a great potential application on large mode area lasing devices, has the inevitable geometric curvature, which induces field deformation and bending losses. In this paper, the method of complex-value extended Fourier-Bessel series is introduced on optical field deformation and bending losses by geometric curvature in the case of this new fiber. Comparing with conventional fibers, gain guided and index anti-guided fiber has better performance on anti-curvature; the quantity of optical intensity centre being shifted from fiber geometric center is less than the case of conventional index guided fibers; and the bending losses decrease dramatically with the increase of curvature radius.     

边界元法分析二维线弹性裂纹扩展

用边界元法研究裂纹扩展过程.首先将尖端区域Williams渐近展开的特征分析法与边界积分方程结合,解出切口尖端附近应力奇异性区域的各应力场渐近展开项系数,获得平面切口/裂纹结构完整的位移和应力场.再基于考虑非奇异应力项贡献的最大周向应力脆性断裂准则,运用边界元法分析边缘含裂纹半圆形弯曲试样在荷载作用下的启裂方向,对裂纹扩展过程给出自动跟踪方法,通过算例证明边界元法模拟裂纹扩展过程的正确性和有效性.     

Use of lagrange multipliers with polynomial series for dynamic analysis of constrained plates part I: Polynomial series

A theory for prediction of the dynamic response of a constrained plate is presented here. The boundaries of the plate may be partially fixed, its dynamic loading is due to elastically mounted vibrating machines and its constraints include beam-like stiffeners. The theory yields the eigenvalues and modal shapes of the plate and stiffeners which comprise the system. The solution, given in Part I, is based on Galerkin's method combined with use of special polynomial series presented by Kantorovich and Krylov. These eigenvalues are used in Part II [1] for response analysis of the complete system and the eigenvalues of the complete system will be obtained by the application of Lagrange equations and multipliers. The various coefficients used in the process are presented in the Appendices to the work. Comparisons with published results show good agreement.     

费密共振和甲烷的振动能谱

用局域模模型来解释甲烷的伸展和弯曲振动能谱，其中伸展振动和弯曲振动间的相互作用用费密共振项来描写，它由一个伸展振子的玻色产生（或湮没）算子和两个弯曲振子的玻色湮没（或产生）算子乘积的T_d不变组合构成．这模型包含10个参数，与已发表的甲烷振动能谱的实验数据比较，得到能量的方均根偏差为12.38cm^－1． 关键词：     

Stress and mixed boundary conditions for two-dimensional dodecagonal quasi-crystal plates

For plate bending and stretching problems in two-dimensional (2D) dodecagonal quasi-crystal (QC) media, the reciprocal theorem and the general solution for QCs are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all order. The method developed by Gregory and Wan is used to generate necessary conditions which the prescribed data on the edge of the plate must satisfy in order that it should generate a decaying state within the plate; these decaying state conditions are obtained explicitly for axisymmetric bending and stretching of a circular plate when stress or mixed conditions are imposed on the plate edge. They are then used for the correct formulation of boundary conditions for the interior solution. For the stress data, our boundary conditions coincide with those obtained in conventional forms of plate theories. More importantly, appropriate boundary conditions with a set of mixed edge-data are obtained for the first time. Furthermore, the corresponding necessary conditions for transversely isotropic elastic plate are obtained directly, and their isotropic elastic counterparts are also obtained.      

Pauli Equation for Non-Abelian Dyons in Moduli Space

Undertaking the study of behaviour of an extended dyon moving in the generalized electromagnetic field of another non-Abelian dyon in moduli space, Dirac's equation has been solved for energy eigenvalues and it has been shown that spin momentum of an interacting non-Abelian dyon behaves as extra energy source. Introducing suitable spinors, the Pauli equation for a spin-1/2 non-Abelian dyon moving in the field of another non-Abelian dyon has been solved in moduli space and it has been shown that ad hoc introduction of spin in the system of two non-Abelian dyons perceptibly modifies the energy eigenvalues and eigenfunctions of bound states of the system.     

Absorption of bending waves in a plate driven by a normal force source encircled with monopole-dipole resonators

The field produced by a harmonic point source of normal force in a plate with resonators is studied. The origin of the force is encircled with a ring of closely spaced identical monopole-dipole resonators responsive to both the displacement and tilt of the plate. For these resonators, parameters are determined that ensure the complete absorption of the divergent cylindrical bending wave generated in the plate by the point source of normal force.     

用超对称幺正变换解扩展的J—C模型

研究发现对于描述强度有关的辐射场与二能级原子的相互作用的J－C哈密吨量存在超对称结构,用超对称幺正变换将哈密顿量对角化,得到了它的本征方程和本征值。     

Harmonic Inversion of Recurrence Spectra of Nonhydrogen Atom in an Electric Field

An extended harmonic inversion method is analytically continued to approach bifurcation region of the dosed orbits thus to obtain highly resolved spectra of lithium atom in external field. The suitable band-limited signal is generated by a semielassieal uniform approximation. By decimating the selected signal window and solving the algebraic set of nonlinear equations the quantum eigenvalues are properly fitted, which reveal the fine resonance structure hidden in low resolution spectrum. The study is made at the sealed energy ε= -2.7, relevant bifurcation effects and corescattered impacts have to be taken into account. It is demonstrated that the present method is a useful technique for the semiclassieal quantization of system with mixed regular-chaotic classical dynamics.