共查询到20条相似文献,搜索用时 15 毫秒
1.
Baruch Karp 《International Journal of Solids and Structures》2009,46(16):3068-3077
The distinction between the near and far-fields for a semi-infinite, elastic strip has been exploited to derive conditions under which different dynamic excitations can be considered as equivalent. These different excitations are equivalent in the sense that they produce the same displacement field far from the excited end. It is shown that dynamically equivalent excitations degenerate to statically equivalent loads in the limit of a vanishing frequency. The no-radiation condition is derived, and its relation to self-equilibrated, dynamic and static loads is presented. Dynamically equivalent excitations are utilized to formulate a dynamic version of Saint-Venant’s principle for symmetric excitations with frequencies below the first cut-off frequency of a strip. It has been shown that the requirement of self-equilibrium of a load for the decay of end effects for static fields can be deduced from the requirement of zero average power for the dynamic fields. 相似文献
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This paper presents a formulation for the solution of the steady state rosponse of a semi-infinite strip with atress-free semi-infinite edges and a time-harmonie shear and normal stress applied to the end. If the end stresses form a self-equilibrated stress state, the presence or absence of a dynainic Saint-Venant region may be examined. The mathematical analysis is based on the linear equations for generalized plane stress and are solved by a biorthogonal eigenfunction expansion. The formulation is in terms of stresses and a displacement related auxiliary variable of the same differential order as the stress. Numerical solutions are presented as an indication of frequency and stress mode shape dependency. 相似文献
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Yu. I. Butenko 《Mechanics of Solids》2016,51(4):472-483
The paper deals with the problem of determining the stress-strain state near the boundary of a one-layer strip made of an orthotropic material subjected to a self-balanced load applied at the end of the strip (Saint-Venant effect, boundary effect, and boundary layer). A comparative analysis of two methods for determining the boundary effect is carried out. The first method, i.e., the solution in stresses (with respect to σy), was developed by L. A. Agalovyan and gives good results of one-layer strips. The second approach, i.e., the solution in displacements, was developed by the author, and its results for the one-layer strip practically coincides with the solution in stresses. The obtained results were also verified by FEM. But the solution of the problem of elasticity in displacements is much more promising when analyzing multilayer strips. 相似文献
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结构运行状态下的模态参数提取是结构健康监测系统需要解决的关键问题之一.自然激励技术的提出为大型复杂工程结构运行状态下的模态参数提取提供了一条新的途径.原始自然激励技术给出了单输入白噪声激励下利用结构位移响应的互相关函数进行模态识别的理论模型,对于多输入情况则缺乏相应的理论模型.本文在单输入理论模型的基础上进一步发展了自然激励技术:推导了多输入独立白噪声激励下多自由度系统结构位移响应的互相关函数的解析公式,并分析了它与单输入情况下互相关函数之间的关系;基于此互相关函数定义了一个新函数,证明它含有结构各阶模态信息,可以表达为一系列衰减正弦函数之和,并且各个组分正弦函数的频率等于各阶模态的有阻尼固有圆频率;提出了以新函数为核心的同时适用于单输入和多输入情况的模态识别算法,建立了自然激励技术的统一模型. 相似文献
6.
Global Bifurcations and Chaotic Dynamics in Nonlinear Nonplanar Oscillations of a Parametrically Excited Cantilever Beam 总被引:1,自引:0,他引:1
This paper presents the analysis of the global bifurcations and chaotic dynamics for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end. The governing nonlinear equations of nonplanar motion with parametric and external excitations are obtained. The Galerkin procedure is applied to the partial differential governing equation to obtain a two-degree-of-freedom nonlinear system with parametric and forcing excitations. The resonant case considered here is 2:1 internal resonance, principal parametric resonance-1/2 subharmonic resonance for the in-plane mode and fundamental parametric resonance–primary resonance for the out-of-plane mode. The parametrically and externally excited system is transformed to the averaged equations by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is applied to find the explicit formulas of normal forms associated with a double zero and a pair of pure imaginary eigenvalues. Based on the normal form obtained above, a global perturbation method is utilized to analyze the global bifurcations and chaotic dynamics in the nonlinear nonplanar oscillations of the cantilever beam. The global bifurcation analysis indicates that there exist the heteroclinic bifurcations and the Silnikov type single-pulse homoclinic orbit in the averaged equation for the nonlinear nonplanar oscillations of the cantilever beam. These results show that the chaotic motions can occur in the nonlinear nonplanar oscillations of the cantilever beam. Numerical simulations verify the analytical predictions. 相似文献
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In offshore engineering long slender risers are simultaneously subjected to both axial and transverse excitations. The axial load is the fluctuating top tension which is induced by the floater’s heave motion, while the transverse excitation comes from environmental loads such as waves. As the time-varying axial load may trigger classical parametric resonance, dynamic analysis of a deepwater riser with combined axial and transverse excitations becomes more complex. In this study, to fully capture the coupling effect between the planar axial and transverse vibrations, the nonlinear coupled equations of a riser’s dynamic motion are formulated and then solved by the central difference method in the time domain. For comparison, numerical simulations are carried out for both linear and nonlinear models. The results show that the transverse displacements predicted by both models are similar to each other when only the random transverse excitation is applied. However, when the combined axial dynamic tension and transverse wave forces are both considered, the linear model underestimates the response because it ignores the coupling effect. Thus the coupled model is more appropriate for deep water. It is also found that the axial excitation can significantly increase the riser’s transverse response and hence the bending stress, especially for cases when the time-varying tension is located at the classical parametric resonance region. Such time-varying effects should be taken into account in fatigue safety assessment. 相似文献
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Qing Yang Bailin Zheng Juan Li Kai Zhang 《Archive of Applied Mechanics (Ingenieur Archiv)》2014,84(1):81-94
The end problem referring to anti-plane shear deformation of a nonhomogeneous semi-infinite strip is investigated here, by using the analogous methodology proposed by Papkovich and Fadle in plane problem. Two types of nonhomogeneity are considered: (i) the shear modulus varies with the thickness coordinate x exponentially; (ii) it varies with the length coordinate y exponentially. The closed elastic solutions in trigonometric series form are derived by the eigenfunctions expansion, and the completeness of the solutions is also proved. Therefore, the elastic field caused by a self-equilibrating traction on the end could be solved in an arbitrary accuracy by taking a necessary number of terms in the series, approximatively, which is usually neglected by invoking Saint-Venant principle. By considering the biggest negative eigenvalue, the Saint-Venant Decay rates of the problem is also estimated in the last section. 相似文献
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斜拉桥中拉索承受着多种端部激励,可激发大幅空间振动.以斜拉索为对象,探究不同端部激励间相位差对其非线性振动的影响.首先,推导斜拉索无量纲离散控制方程,引入考虑相位的三向端部激励得到一般化模型;然后,针对拉索下端存在的纵桥向、竖向和横桥向激励的两两组合,受大幅或小幅激励,及其在主共振区或主参数共振区几组因素,共计12种工况,采用数值分析法分别研究了各工况下不同激励相位差时的斜拉索稳态响应.研究发现:激励相位差能加剧与激励频率相近的面内、外模态振动;在任意端部激励组合下,激励相位差不仅可使斜拉索非线性振动出现定量变化,还可改变内共振的表现形式.面内、外激励组合下,相位差对拉索响应幅值的影响以π为周期变化,且当相位差趋于π/2 + kπ (k = 0, 1, 2…)时影响最为突出;而面内激励组合下,以2π为变化周期,当相位差为π + 2kπ (k = 0, 1, 2, …)时其对稳态幅值的影响最显著.其原因是:面外激励关于拉索所在的竖直面对称,故其本质上以π为周期;而面内激励无此对称性,仍以2π为周期.因此,有无面外激励参与决定了激励间相位差对斜拉索响应的影响规律. 相似文献
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《International Journal of Solids and Structures》2005,42(9-10):2977-3000
The purpose of this research is to investigate the influence of material inhomogeneity on the decay of Saint-Venant end effects in anti-plane shear deformations of linear isotropic mixtures of elastic solids. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e. materials with spatially varying properties tailored to satisfy particular engineering applications. The spatial decay of solutions of a boundary value problem with variable coefficients on a semi-infinite strip is investigated. The results may be interpreted in terms of a Saint-Venant principle for anti-plane shear deformations of linear isotropic mixtures of elastic solids. 相似文献
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Qing Yang Bailin Zheng Kai Zhang Jianxin Zhu 《Acta Mechanica Solida Sinica》2014,27(6):588-596
The eigenvalue problem about a nonhomogeneous semi-infinite strip is investigated using the methodology proposed by Papkovich and Fadle for homogeneous plane problems. Two types of nonhomogeneity are considered: (i) the elastic modulus varying with the thickness coor- dinate x exponentially, (ii) it varying with the length coordinate y exponentially. The eigenvalues for the two cases are obtained numerically in plane strain and plane stress states, respectively. By considering the smallest positive eigenvalue, tile Saint-Venant Decay rates are estimated, which indicates material nonhomogeneity has a signifcant influence on the Saint-Venant end effect. 相似文献
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研究了半无限长轴对称压电-压磁夹层结构的圆柱体圣维南端部效应的衰减问题。圆柱的端部承受自平衡磁电弹载荷;圆柱的内外表面为机械自由表面,但承受不同的电磁边界条件,即电学短路或电学开路及磁学短路或磁学开路边界条件。基于横贯各向同性压电或压磁材料在轴对称圆柱坐标系下的本构方程,推导了关于衰减率的特征方程并求得问题的数值解。结果表明,边界条件、内外径之比、材料厚度比对结构的衰减率都有显著的影响。 相似文献
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The purpose of this research is to investigate the influence of material inhomogeneity and anisotropy on the decay of Saint-Venant end effects in anti-plane shear deformations of linear mixtures of elastic solids. The spatial decay of solutions of a boundary value problem with variable coefficients on a semi-infinite strip is investigated. The results may be interpreted in terms of a Saint-Venant principle for anti-plane shear deformations of linear anisotropic mixtures of elastic solids. As our first results have a very general point of view, we study some examples in detail. 相似文献
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转子系统的平稳/非平稳随机地震响应分析 总被引:3,自引:1,他引:3
应用虚拟激励法结合精细时程积分计算了转子系统受平稳/非平稳随机地震激励的动力响应。采用虚拟激励分析将平稳随机激励转化为稳态简谐激励,将非平稳随机激励转化为瞬态确定性激励,即使对于非对称的油膜刚度阵和阻尼阵,算法仍然简单高效,并得到精确的结果。 相似文献
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In this paper, we use the asymptotic perturbation method based on the Fourier expansion and the temporal rescaling to investigate
the nonlinear oscillations and chaotic dynamics of a simply supported rectangular plate made of functionally graded materials
(FGMs) subjected to a through-thickness temperature field together with parametric and external excitations. Material properties
are assumed to be temperature-dependent. Based on the Reddy’s third-order plate theory, the governing equations of motion
for the plate are derived using the Hamilton’s principle. The Galerkin procedure is employed to obtain a two-degree-of-freedom
nonlinear system including the quadratic and cubic nonlinear terms. The resonant case considered here is 1:2 internal resonance,
principal parametric resonance-1/2 subharmonic resonance. Based on the averaged equation in polar coordinate form, the stability
of steady state solutions is analyzed. The phase portrait, waveform and Poincaré map are used to analyze the periodic and
chaotic motions of the FGM rectangular plate. It is found that the FGM rectangular plate exhibits the chaotic motions under
certain circumstances. It is seen that the nonlinear dynamic responses of the FGM rectangular plate are more sensitive to
transverse excitation. The excitation force can be used as a controlling factor which can change the response of the FGM rectangular
plate from periodic motion to the chaotic motion. 相似文献
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Decay rates in a bimaterial circular cylinder under axisymmetric torsion loading are considered via an eigen-expansion near
the end of the cylinder. The decay rates depend on the shear modulus ratio of the materials and the radius ratio of inner
and outer cylinders. Following the derivation of the traditional Saint-Venant end effect of an isotropic bimaterial cylinder,
cases of anisotropic material (transversely isotropic material) and non-traditional Saint-Venant end effect (displacement
prescribed on the side surface) are considered. This study sheds some light on the decay studies for other geometric configurations
and the deformation modes of composite structures. 相似文献
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《International Journal of Solids and Structures》2003,40(13-14):3293-3310
In dynamics, Saint-Venant’s principle of exponential decay of stress resulting from a self-equilibrating load is not valid. For a beam type structure, a self-equilibrated load may penetrate well inside the beam. Although this effect has been known for a long time, at least since Lamb’s paper [Proc. Roy. Soc. Lon. Ser. A 93 (1916) 114], it was not clear how to characterize it quantitatively. In this paper we propose a “probabilistic approach” to evaluate the magnitude of the penetrating stress state. The key point is that, in engineering problems, the distribution of the self-equilibrated load is usually not known. By assigning to the self-equilibrated load some probabilistic measure one can find probabilistic characteristics of the penetrating stress state. We develop this reasoning for the simplest case: longitudinal vibrations of a two-dimensional semi-infinite, elastic isotropic homogeneous strip, excited by a periodic load at the end. We show the frequency range where Saint-Venant’s principle can be used with good accuracy, and thus, one-dimensional classical beam theory still can be applied. We characterize also the increase in this range which is achieved in the refined plate theory proposed by Berdichevsky and Le [J. Appl. Math. Mech. (PMM) 42 (1) (1978) 140]. 相似文献
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Summary This paper establishes a principle of Saint-Venant type associated with finite anti-plane shear of a cylinder whose cross-section is a semi-infinite strip. The long sides of the strip are traction-free, and the short side carries an arbitrarily distributed shear traction. At the infinity in the strip, the deformation is prescribed to be one of simple shear, and the associated shear stress is uniform. The analysis is based on the fully nonlinear theory of finite elastostatics and is carried out for a special class of homogenous, isotropic incompressible materials. It is shown that, along the parallel sides of the strip, the nonvanishing component of shear stress differs from its average value (taken across the strip) by an exponentially decaying function of the distance from the end. A lower bound is given for the rate of decay.Paper presented at the 15th International Congress of Theoretical and Applied Mechanics, Toronto, Canada, August 1980. 相似文献