集中载荷作用下具有光滑中心波纹膜片的非线性分析

波纹膜片是一种薄壳弹性体，由于它的参数很多，又相互制约，所以使得它的设计很复杂。在大多数位移式仪器仪表中，要求波纹膜片产生至少和膜片厚度是同样数量级的弹性位移。这就要求使用薄壳的几何非线性理论进行分析。大多数学者研究波纹膜片的弯曲问题，是采用扁壳理论讨论具有浅波纹的膜片。而工程实际中，经常遇到深波纹膜片，这就要求从一般壳体大挠度方程进行求解。本文采用轴对称旋转壳体的简化Re-issner方程。研究了在中心集中载荷作用下具有光滑中心波纹膜片的非线性弯曲问题。应用积分方程方法，可以获得膜片的特征关系（载荷-中心挠度关系）和应力分布。文末给出实例计算的数值结果。     

波纹壳的光弹性贴片法应力测定

1. 前言波纹壳是工程上广泛应用的一种弹性元件。研究波纹壳的应力应变分布状况,对于确定波纹壳的强度和弹性具有重要的工程应用价值和理论意义。图1所示为U形波纹壳及其受力情况示意图。波纹壳是由半圆弧的圆环壳和环板联结组成的,受轴向力作用。本文通过光弹性贴片法测定了该壳体A-B段上的应力应     

复合载荷作用下具有光滑中心波纹膜片的非线性分析

采用轴对称旋转壳体的简化Reissner方程，研究了在复合载荷作用下具有光滑中心波纹膜片的非线性弯曲问题。应用积分方程方法，可以获得膜片的特征关系（载荷－中心挠度关系）。文末给出了实例计算的数值结果。     

正弦波纹扁球壳的非线性强迫振动

波纹壳是传感器弹性元件的一类重要形式,也是精密仪器仪表弹性元件中的一类重要形式。由于波纹壳形状复杂、参数众多、厚度薄,对其进行非线性分析非常重要同时也是十分困难的。本文考虑一种在传感器弹性元件中有重要应用价值的正弦波纹浅球壳体,将这种壳体视为结构上的圆柱正交异性扁球壳,根据Andryewa的思想,分别得到了正弦波纹壳径向、环向在拉伸、弯曲下的等价的四个各向异性参数;建立了正弦波纹扁球壳的非线性强迫振动微分方程;得到了正弦波纹扁球壳非线性强迫振动的共振周期解及幅频特性曲线。     

均布载荷作用下具有光滑中心波纹膜片的非线性分析

采用轴对称旋转壳体的简化Reissner方程，研究了在均布载荷作用下具有光滑中心波纹膜片的非线性弯曲问题。应用格林函数方法，波纹膜片的非线性边值问题化为了非线性积分方程的求解。为了求解积分方程并防止发散，一个插值参数被引入到迭代格式中。计算表明，当载荷很小时，任何插值参数值均能保证迭代的收敛性，取插值参数值接近或等于1获得较快的收敛速度，而当载荷较大时，插值参数值不能取得过大。绘出了波纹膜片的特征曲线，得到的特征曲线可供设计参考。可以断言，当载荷不大时，特征曲线是近似线性的，随着载荷的增大，特征曲线开始向上弯曲，明显偏离线性。本文中提出的解决方法适应于任意轴向截面的波纹壳体。     

浅正弦波纹圆薄板在静载荷下的非线性振动

根据最小作用量原理,由本问题的泛函通过变分推导出浅正弦波纹圆薄板在静载荷下的动力变分方程,选取波纹圆薄板中心最大振幅为摄动参数,用摄动变分法进行求解,得到了精确度较高的最低非线性回有频率。     

波纹环形板在轴对称任意载荷作用下的非线性弯曲

本文以正交异性板理论为基础,提出了一种波纹环形板非线性弯曲的Cheby-shev级数解法,推导出具有硬中心的波纹环形板在任意轴对称载荷作用下的弹性特征方程.文中计算了几个典型的算例,数值结果表明本文的方法对目前文献中常见的方法有一定的改进和推广.     

均布载荷作用下带边缘大波纹膜片的非线性弯曲

采用轴对称旋转壳体的简化Reissner方程，研究了在均布载荷作用下具有硬中心的带边缘大波纹膜片的非线性弯曲问题．应用积分方程方法，获得了具有夹紧固定和滑动固定两种外边界的膜片的特征关系，即荷载-中心挠度曲线．作为算例，给出了夹紧固定膜片中的应力分布．     

集中载荷作用下变厚度开顶扁球壳的非线性稳定问题

首先应用逐步加载法将具有硬中心的开顶扁球壳在集中载荷作用下的非线性微分方程组线性化，然后利用样条配点法解线性微分方程组，得到了临界载荷的大小。     

板壳式换热器波纹倾角对换热和阻力性能影响

研究了波纹倾角（α=45°，60°，75°）对板壳式换热器单流道内单相流动与换热过程的影响，分析了波纹流道内的速度分布、湍动能分布、压力分布和温度分布；基于范宁摩擦阻力因子f和Nu与Re的关系，提出了板壳式换热器不同波纹倾角下换热特性和流动阻力特性的预测关联式；通过计算不同波纹倾角下的综合性能评价指标（performance evaluation criteria,PEC）和面积质量因子（j/f）综合评价了流动与换热性能。结果表明：波纹倾角是影响圆形板间流体流动形态的因素之一，随着波纹倾角增大，会出现“十字交叉流”向“曲折流”转变；所提出的关联式能够很好地预测板壳式换热器内阻力与换热性能，阻力特性偏差在±14%范围内，换热特性偏差在±7%范围内；α为45°时，j/f较大，流道内阻力相对小；α为60°时，PEC较大，流道内换热性能相对强。     

On Design Models in Stability Problems for Corrugated Cylindrical Shells

Three design techniques for stability analysis of longitudinally corrugated cylindrical shells are examined. The first two account for the true geometry of the shell and the third one replaces the corrugated shell with an equivalent orthotropic shell using reduction formulas. The exact formulations employ classical and Timoshenko-type theories. The techniques are analyzed by an example of sinusoidally corrugated shells. It is shown that the exact formulation permits finding practically important relations for corrugation parameters, which raises considerably the specific critical loads.     

Timoshenko-Type Theory in the Stability Analysis of Corrugated Cylindrical Shells

A technique is proposed for stability analysis of longitudinally corrugated shells under axial compression. The technique employs the equations of the Timoshenko-type nonlinear theory of shells. The geometrical parameters of shells are specified on discrete set of points and are approximated by segments of Fourier series. Infinite systems of homogeneous algebraic equations are derived from a variational equation written in displacements to determine the critical loads and buckling modes. Specific types of corrugated isotropic metal and fiberglass shells are considered. The calculated results are compared with those obtained within the framework of the classical theory of shells. It is shown that the Timoshenko-type theory extends significantly the possibility of exact allowance for the geometrical parameters and material properties of corrugated shells compared with Kirchhoff–Love theory.     

METHOD OF GREEN＇S FUNCTION OF CORRUGATED SHELLS

By using the fundamental equations of axisymmetric shallow shells of revolution, the nonlinear bending of a shallow corrugated shell with taper under arbitrary load has been investigated. The nonlinear boundary value problem of the corrugated shell was reduced to the nonlinear integral equations by using the method of Green＇s function. To solve the integral equations, expansion method was used to obtain Green＇s function. Then the integral equations were reduced to the form with degenerate core by expanding Green＇s function as series of characteristic function. Therefore, the integral equations become nonlinear algebraic equations. Newton＇ s iterative method was utilized to solve the nonlinear algebraic equations. To guarantee the convergence of the iterative method, deflection at center was taken as control parameter. Corresponding loads were obtained by increasing deflection one by one. As a numerical example,elastic characteristic of shallow corrugated shells with spherical taper was studied.Calculation results show that characteristic of corrugated shells changes remarkably. The snapping instability which is analogous to shallow spherical shells occurs with increasing load if the taper is relatively large. The solution is close to the experimental results.     

Nonlinear bending of corrugated diaphragm with large boundary corrugation under compound load

IntroductionCorrugateddiaphragmisatypeofelasticthinshells .Itsdesignisverycomplicatedbecauseoftoomanyparametersthatinfluenceeachother.Inanumberofinstrumentsmeasuringdisplacements,corrugateddiaphragmissubjectedtoelasticdisplacementthatisatleastthesameorderasitsthickness,sothatitisnecessarytousegeometricalnonlineartheoryofthinshellstoanalyze.Sofarasweknow ,inmostcases,investigatorsdiscussedonlytheproblemofcorrugateddiaphragmwithuniformanddensecorrugationsundertheactionofaunique(uniformlyorconcen…     

Nonlinear vibration of corrugated shallow shells under uniform load

Based on the large deflection dynamic equations of axisymmetric shallow shells of revolution, the nonlinear forced vibration of a corrugated shallow shell under uniform load is investigated. The nonlinear partial differential equations of shallow shell are reduced to the nonlinear integral-differential equations by the method of Green's function. To solve the integral-differential equations, expansion method is used to obtain Green's function. Then the integral-differential equations are reduced to the form with degenerate core by expanding Green's function as series of characteristic function. Therefore, the integral-differential equations become nonlinear ordinary differential equations with regard to time. The amplitude-frequency response under harmonic force is obtained by considering single mode vibration. As a numerical example, forced vibration phenomena of shallow spherical shells with sinusoidal corrugation are studied. The obtained solutions are available for reference to design of corrugated shells     

Stability of circumferentially corrugated cylindrical shells under external pressure

Corrugated shells of revolution that may be considered cylindrical when the corrugation amplitude is small are analyzed for stability. The corrugations are transverse to the axis of revolution. Isotropic and orthotropic shells with sine-shaped meridian under uniform external compression are analyzed for stability. It is shown that the stability of corrugated shells can be significantly improved, compared with cylindrical shells, by selecting appropriate number and amplitude of half-waves. A relationship between the buckling modes and the change in the critical loads is established     

HIGH-FREQUENCY VIBRATIONS OF CORRUGATED CYLINDRICAL PIEZOELECTRIC SHELLS

Coupled extensional and flexural cylindrical vibrations of a corrugated cylindrical piezoelectric shell consisting of multiple pieces of circular cylindrical surfaces smoothly connected along their generatrix are studied. To validate the results for the case of relatively thick shells or equivalently high-frequency modes with short wavelengths, existing analysis is extended by considering shear deformation and rotatory inertia. An analytical solution is obtained. Based on the solution, resonant frequencies and mode shapes are calculated.