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101.
The method of multiple scales and the related method of averaging are commonly used tostudy slowly modulated oscillations. If the system of interest is a slightlyperturbed harmonic oscillator, then these techniques can be applied easily. If the unperturbed system is strongly nonlinear (though possiblyconservative), then these methods can run into difficulties due to the impossibilityof carrying out required analytical operations in closed form.In this paper, we abandon the requirement of closed form analyticaltreatment at all stages. Instead, Galerkin projections are used toobtain approximate realizations of the method of multiple scales. Thispaper adapts recent work using similar ideas for approximaterealizations of the method of averaging. A key contribution of thepresent work is in the systematic identification and removal of secularterms in the general nonlinear case, a procedure that is more difficultthan for the perturbed harmonic oscillator case, and that is unnecessaryfor averaging.A strength of the present work is that the heuristics (Galerkin)and asymptotics (multiple scales) are kept distinct,leaving room for systematic refinement of the formerwithout compromising the asymptotic features of the latter. 相似文献
102.
Assuming that the disc material can be modeled either as Mooney–Rivlin or as Hookean and the steel ring enclosing the disc as Hookean, the energy release rates as a function of the crack length are evaluated and compared. Two loadings are considered––one in which the surface of the star shape hole in the disc is loaded by a uniform pressure and the other in which the temperature of the composite body is uniformly raised. It is found that the linear and the nonlinear analyses give qualitatively similar results for the two loadings. For each load, the energy release rate increases with an increase in the starter crack length, reaches a maximum value and then decreases gradually. 相似文献
103.
104.
Hans Grabmüller 《Journal of Elasticity》1998,53(2):77-107
This paper investigates axisymmetric deformations of curved annular membranes subjected to a partially vanishing vertical
surface load and to radial edge loads or displacements. The frame of the membrane model we deal with is the nonlinear small-strain
theory. The determination of the principal stresses reduces to the solution of a single nonlinear second order ODE. Analysis
becomes explicit on the unloaded membrane part while the loaded part is treated by methods which have been previously developed.
In particular, the ranges of those stress and displacement boundary data are determined which admit for wrinkle-free solutions
only, i.e. for solutions governed by a nonnegative radial and circumferential stress component. For such a tensile state,
a curved membrane flattens out on the unloaded portions.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
105.
In nonlinear elasticity the exact geometry of deformation is combined with general constitutive relations. This allows a very sophisticated interaction of deformations in different material directions. Based on the Cosserat theory for planar deformations of nonlinearly elastic rods we demonstrate some paradoxical bending effects caused by a nontrivial interaction of extension, flexure, and shear. The analytical results are illustrated by numerical examples. 相似文献
106.
提出了一种三线性滞回阻尼模型。用Krylov-Bogoliubov缓变系灵敏法研究了正弦型激励下单自由度三线性滞回系统的稳态响应。当本文的三线性模型退化为双线性模型时。本文结果与Caughey的结果是一致的。研究结果还发现。这种系统的稳态解总是稳定的,没有振幅的跳跃现象发生。但在激振力力幅达到一定值时能够发生无界响应。此外还发现,稳态振动达到峰值振幅时滞回面积(即最大滞回面积)对峰值振幅的比值和激振力力幅成正比。这个结论与双非线性滞回系统的相应结论是一致的。 相似文献
107.
IntroductionThe dynamic behavior of the nonlinear structure under wind excitation has beenobserved very complicated.Taking guyed masts as an example,only a few collapsingaccidents occurred under extreme atmospheric conditions[1],many took place under mild… 相似文献
108.
APPLICATION OF WAVELET TRANSFORM TO BIFURCATION AND CHAOS STUDY 总被引:2,自引:0,他引:2
I.IntroductionThetypesofmotionforanonlinearvibrationsystemmaybeperiodic,quasiperiodicorchaotic.Foragivensetofparametersofthesystem,Poincarkmap,powerspectral,waveformandLyapunovexponentareusuallyutilizedtoseewhethertheresponseofthesystemischaoticornot,butitisdiftlculttodeterminepreciselytheexistingdomainsorattractingbasinsofdifferenttypesofmotionsinparametricspaceorinitialvaluespaceonlyfromgraphicsstudy,andcomputingLyapunovexponentistimeconsuming.Aswavelettransformcanreveallocalpropertyinboth… 相似文献
109.
采用样条函数构造的位移模式,出了非理想压杆稳定极限承载力及稳定平衡全过程的样条函数分析法。本方法可以考虑任意实际初始缺陷和材料弹塑性加卸载效应的影响。计算表明,本方法精度高,速度快。 相似文献
110.
In this Note we present an approach to determine the local minima of a specific class of minimization problems. Attention is focused on the inextensibility condition of flexible rods expressed as a nonconvex constraint. Two algorithms are derived from a special splitting of the Lagrangian into the difference of two convex functions (DC). They are compared to the augmented Lagrangian methods used in this context. These DC formulations are easily extended to contact problems and applied to the determination of confined buckling shapes. To cite this article: P. Alart, S. Pagano, C. R. Mecanique 330 (2002) 819–824. 相似文献