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Moshe Stupel Victor Oxman Avi Sigler 《International Journal of Mathematical Education in Science & Technology》2017,48(1):149-161
We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribed circles tend to a limit in a monotonous manner.First, using geometrical software, we investigate four theorems that represent interesting geometrical properties, after which we present formal proofs that rest on a combination between different fields of mathematics: trigonometry, algebra and geometry, and the use of the concept of standard deviation that is taken from statistics. 相似文献
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Ghulam MUSTAFA 《数学年刊B辑(英文版)》2017,38(5):1077-1092
The objective of this article is to introduce a generalized algorithm to produce the m-point n-ary approximating subdivision schemes(for any integer m, n ≥ 2). The proposed algorithm has been derived from uniform B-spline blending functions. In particular, we study statistical and geometrical/traditional methods for the model selection and assessment for selecting a subdivision curve from the proposed family of schemes to model noisy and noisy free data. Moreover, we also discuss the deviation of subdivision curves generated by proposed family of schemes from convex polygonal curve. Furthermore, visual performances of the schemes have been presented to compare numerically the Gibbs oscillations with the existing family of schemes. 相似文献
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This paper deals with the stochastic response of structures loaded by non-Gaussian random fields. A finite element model is used to describe a cantilever beam assuming both linear and non-linear behavior. The cross-correlated stochastic field is generated by a numerical procedure based on the translation processes theory. The marginal distribution of the load is assumed to be lognormal and the correlation structure is based on the second-order Markov process. The statistical analysis of the results highlights the effects of the involved non-linearity and non-Gaussianity properties on the structures response. 相似文献
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基于Lagrange原理,建立了一套新的悬索大挠度动力特性和动力响应分析的有限体积法列式,推导了结点力向量、质量矩阵和单元刚度矩阵的显式表达式。该列式的一个显著特点是直接利用工程应变定义结构变形,其物理意义明确,列式简单,适用于各种垂度和荷载情况的悬索大挠度动力分析。实例动力特性和随机风振响应分析表明,该有限体积列式不仅计算效率高,而且具有良好的计算精度。 相似文献
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定量开采条件下径向渗流的液固耦合问题 总被引:2,自引:0,他引:2
考虑到多孔介质渗透率随孔隙度变化的特点,建立了力学模型,研究定量抽放问题;对于广义平面应力状态下的非线性渗流耦合问题,提出了解的构造方法和解耦方法;求出了耦合条件下的孔隙压力,多孔介质总应力、总应变和总位移的解析解;进行了实例计算,并与Biot理论进行了对比,结果表明两种理论的差别很大。因此在渗透系数有较明显变化的场舍下不能采用Biot理论进行分析。 相似文献
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Experimental study of non-linear energy pumping occurring at a single fast frequency 总被引:3,自引:0,他引:3
D. Michael McFarland 《International Journal of Non》2005,40(6):891-899
Experimental verification of passive non-linear energy pumping in a two-degree-of-freedom system comprising a damped linear oscillator coupled to an essentially non-linear attachment is carried out. In the experiments presented the non-linear attachment interacts with a single linear mode and, hence, energy pumping occurs at a single ‘fast’ frequency in the neighborhood of the eigenfrequency of the linear mode. Good agreement between simulated and experimental results was observed, in spite of the strongly (essentially) non-linear and transient nature of the dynamics of the system considered. The experiments bear out earlier predictions that a significant fraction of the energy introduced directly to a linear structure by an external impulsive (broadband) load can be transferred (pumped) to an essentially non-linear attachment, and dissipated there locally without spreading back to the system. In addition, the reported experimental results confirm that (a) non-linear energy pumping in systems of coupled oscillators can occur only above a certain threshold of the input energy, and (b) there is an optimal value of the energy input at which a maximum portion of the energy is absorbed and dissipated at the NES. 相似文献
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