摘要:

The equations of linear elasticity for rotationally symmetric deformations are expanded using a small parameter related to the thickness to radius of curvature ratio of the shell to obtain the classical thin shell equations of conical shells as a first approximation. These classical equations with variable coefficients permit further asymptotic expansions in the cases of steep as well as shallow cones, yielding systems of equations with constant coefficients. Solutions of these equations are used to compute the influence coefficients relating edge loads and edge displacements.

ISSN:0022-2526    

DOI:10.1002/sapm198878291

年代:1988

数据来源: WILEY

摘要:

The first part of this paper summarizes the mathematical modeling of free‐electron lasers (FEL), and the remainder concerns general perturbation methods for solving FEL and other strictly nonlinear oscillatory problems with slowly varying parameters and small perturbations. We review and compare the Kuzmak‐Luke method and that of near‐identity averaging transformations. In order to implement the calculation of explicit solutions we develop two approximation schemes. The first involves use of finite Fourier series to represent either the leading approximation of the solution or the transformation of the governing equations to a standard form appropriate for the method of averaging. In the second scheme we fit a cubic polynomial to the potential such that the leading approximation is expressible in terms of elliptic functions. The ideas are illustrated with a number of examples, which are also solved numerically to assess the accuracy of the various approxima

ISSN:0022-2526    

DOI:10.1002/sapm1988782111

年代:1988

数据来源: WILEY